Inner Source: The Key To Improving Software Asset Reusability

In this article, we discuss Inner Source as the key to improving software asset reusability, efficiency, and foster innovation for your engineering team.

Introduction

Can you afford to reinvent the wheel? I’m sure most of you will say a big NO. Similarly, in software development, it’s not very common to build a piece of software from scratch unless you are building something which was not done by anyone before you in the world. Typically, a development team gets help from a platform like  GitHub or gets help from other similar projects running within your organization. They copy the base code (let’s call it the initial codebase) from others and start developing on top of that. This is re-using the wheel.

This is one way of looking at reusability since they have reused someone else’s code. When we talk about improving the re-usability of software assets (code, libraries, etc.) within your organization then it inherits a few inefficiencies. Especially when you do not have a mechanism of giving back.

For example, what if a project team who is using your initial codebase improves it over a period of time to make it more efficient? What if they find a few bugs in the initial code and fix them? What if they address a few new security vulnerabilities? How do you now make sure that your initial codebase receives all these improvements? And this team can communicate back to the original creator of the base code? How do you make sure that if some new project team wants to reuse this asset, they get all the improvements as opposed to code their own improvements on top of the initial base code? How do you make sure you pass on these continuous improvements forward to your future software engineering teams?

Well, you need to build a culture within your software engineering practice to give back. It is giving back to the original codebase by continuously contributing to the improvements. It is like helping the community (your entire software engineering practice) with their contributions.

Inner Source is a way of software development that allows you to create this giving back culture within your organization. A transformative cultural shift towards gaining efficiency and improve software asset reusability. Let’s see how:

Understanding Opensource and Inner Source

To understand Inner Source, you need to understand how  Opensource software development works.

In opensource, the entire community of students, hobbyists, professional programmers contribute from across the globe abiding by  opensource licensing norms. The entire community participates in contributing in coding, bug fixes, providing feedback to build great software like Android, Kubernetes, Visual Studio Code, etc.

In Inner Source, it’s not open for the entire world. It is open to all of your software engineering teams within your organization. Be it co-located teams or remote teams. It’s like running open-source development within your organization’s firewall. Where your entire software engineering team contributes, collaborates, and innovates together.

In short — Opensource is open to all, Inner source is open to all your employees within your organization.

Inner Source is not a new kid in the block, this terminology is there for almost a decade now. It was originally coined by  Tim O’Reilly in 2000.

#devops #innovation #github #opensource

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Buddha Community

Custom Software vs Off-the-shelf Software: How to select a better one for your business?

Custom Software or Off-the-shelf software, the question in mind for many business personnel. Read this blog to get help to make the right decision that will benefit your business.
For a business that wants to upgrade and modernize itself with the help of software, a common dilemma it is whether to go for custom-made software or opt for off-the-shelf software. You can find many top software development companies worldwide, but before that all, you should first decide the type of software –an off-the-shelf software or a custom one.
This blog aims to overcome the dilemma and accord some clarity to a business looking to automate its business processes.

#custom software vs off-the-shelf software #custom software development companies #top software development companies #off-the-shelf software development #customized software solution #custom software development

Build an Android application with Kivy Python framework

If you’re a Python developer thinking about getting started with mobile development, then the Kivy framework is your best bet. With Kivy, you can develop platform-independent applications that compile for iOS, Android, Windows, macOS, and Linux. In this article, we’ll cover Android specifically because it is the most used.

We’ll build a simple random number generator app that you can install on your phone and test when you are done. To follow along with this article, you should be familiar with Python. Let’s get started!

Getting started with Kivy

First, you’ll need a new directory for your app. Make sure you have Python installed on your machine and open a new Python file. You’ll need to install the Kivy module from your terminal using either of the commands below. To avoid any package conflicts, be sure you’re installing Kivy in a virtual environment:

pip install kivy 
//
pip3 install kivy 

Once you have installed Kivy, you should see a success message from your terminal that looks like the screenshots below:

Kivy installation

Successful Kivy installation

 

Next, navigate into your project folder. In the main.py file, we’ll need to import the Kivy module and specify which version we want. You can use Kivy v2.0.0, but if you have a smartphone that is older than Android 8.0, I recommend using Kivy v1.9.0. You can mess around with the different versions during the build to see the differences in features and performance.

Add the version number right after the import kivy line as follows:

kivy.require('1.9.0')

Now, we’ll create a class that will basically define our app; I’ll name mine RandomNumber. This class will inherit the app class from Kivy. Therefore, you need to import the app by adding from kivy.app import App:

class RandomNumber(App): 

In the RandomNumber class, you’ll need to add a function called build, which takes a self parameter. To actually return the UI, we’ll use the build function. For now, I have it returned as a simple label. To do so, you’ll need to import Label using the line from kivy.uix.label import Label:

import kivy
from kivy.app import App
from kivy.uix.label import Label

class RandomNumber(App):
  def build(self):
    return Label(text="Random Number Generator")

Now, our app skeleton is complete! Before moving forward, you should create an instance of the RandomNumber class and run it in your terminal or IDE to see the interface:

import kivy from kivy.app import App from kivy.uix.label import Label class RandomNumber(App):  def build(self):    return Label(text="Random Number Generator") randomApp = RandomNumber() randomApp.run()

When you run the class instance with the text Random Number Generator, you should see a simple interface or window that looks like the screenshot below:

 

Simple interface after running the code

You won’t be able to run the text on Android until you’ve finished building the whole thing.

Outsourcing the interface

Next, we’ll need a way to outsource the interface. First, we’ll create a Kivy file in our directory that will house most of our design work. You’ll want to name this file the same name as your class using lowercase letters and a .kv extension. Kivy will automatically associate the class name and the file name, but it may not work on Android if they are exactly the same.

Inside that .kv file, you need to specify the layout for your app, including elements like the label, buttons, forms, etc. To keep this demonstration simple, I’ll add a label for the title Random Number, a label that will serve as a placeholder for the random number that is generated _, and a Generate button that calls the generate function.

My .kv file looks like the code below, but you can mess around with the different values to fit your requirements:

<boxLayout>:
    orientation: "vertical"
    Label:
        text: "Random Number"
        font_size: 30
        color: 0, 0.62, 0.96

    Label:
        text: "_"
        font_size: 30

    Button:
        text: "Generate"
        font_size: 15 

In the main.py file, you no longer need the Label import statement because the Kivy file takes care of your UI. However, you do need to import boxlayout, which you will use in the Kivy file.

In your main file, you need to add the import statement and edit your main.py file to read return BoxLayout() in the build method:

from kivy.uix.boxlayout import BoxLayout

If you run the command above, you should see a simple interface that has the random number title, the _ place holder, and the clickable generate button:

Random Number app rendered

Notice that you didn’t have to import anything for the Kivy file to work. Basically, when you run the app, it returns boxlayout by looking for a file inside the Kivy file with the same name as your class. Keep in mind, this is a simple interface, and you can make your app as robust as you want. Be sure to check out the Kv language documentation.

Generate the random number function

Now that our app is almost done, we’ll need a simple function to generate random numbers when a user clicks the generate button, then render that random number into the app interface. To do so, we’ll need to change a few things in our files.

First, we’ll import the module that we’ll use to generate a random number with import random. Then, we’ll create a function or method that calls the generated number. For this demonstration, I’ll use a range between 0 and 2000. Generating the random number is simple with the random.randint(0, 2000) command. We’ll add this into our code in a moment.

Next, we’ll create another class that will be our own version of the box layout. Our class will have to inherit the box layout class, which houses the method to generate random numbers and render them on the interface:

class MyRoot(BoxLayout):
    def __init__(self):
        super(MyRoot, self).__init__()

Within that class, we’ll create the generate method, which will not only generate random numbers but also manipulate the label that controls what is displayed as the random number in the Kivy file.

To accommodate this method, we’ll first need to make changes to the .kv file . Since the MyRoot class has inherited the box layout, you can make MyRoot the top level element in your .kv file:

<MyRoot>:
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15

Notice that you are still keeping all your UI specifications indented in the Box Layout. After this, you need to add an ID to the label that will hold the generated numbers, making it easy to manipulate when the generate function is called. You need to specify the relationship between the ID in this file and another in the main code at the top, just before the BoxLayout line:

<MyRoot>:
    random_label: random_label
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            id: random_label
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15

The random_label: random_label line basically means that the label with the ID random_label will be mapped to random_label in the main.py file, meaning that any action that manipulates random_label will be mapped on the label with the specified name.

We can now create the method to generate the random number in the main file:

def generate_number(self):
    self.random_label.text = str(random.randint(0, 2000))

# notice how the class method manipulates the text attributre of the random label by a# ssigning it a new random number generate by the 'random.randint(0, 2000)' funcion. S# ince this the random number generated is an integer, typecasting is required to make # it a string otherwise you will get a typeError in your terminal when you run it.

The MyRoot class should look like the code below:

class MyRoot(BoxLayout):
    def __init__(self):
        super(MyRoot, self).__init__()

    def generate_number(self):
        self.random_label.text = str(random.randint(0, 2000))

Congratulations! You’re now done with the main file of the app. The only thing left to do is make sure that you call this function when the generate button is clicked. You need only add the line on_press: root.generate_number() to the button selection part of your .kv file:

<MyRoot>:
    random_label: random_label
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            id: random_label
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15
            on_press: root.generate_number()

Now, you can run the app.

Compiling our app on Android

Before compiling our app on Android, I have some bad news for Windows users. You’ll need Linux or macOS to compile your Android application. However, you don’t need to have a separate Linux distribution, instead, you can use a virtual machine.

To compile and generate a full Android .apk application, we’ll use a tool called Buildozer. Let’s install Buildozer through our terminal using one of the commands below:

pip3 install buildozer
//
pip install buildozer

Now, we’ll install some of Buildozer’s required dependencies. I am on Linux Ergo, so I’ll use Linux-specific commands. You should execute these commands one by one:

sudo apt update
sudo apt install -y git zip unzip openjdk-13-jdk python3-pip autoconf libtool pkg-config zlib1g-dev libncurses5-dev libncursesw5-dev libtinfo5 cmake libffi-dev libssl-dev

pip3 install --upgrade Cython==0.29.19 virtualenv 

# add the following line at the end of your ~/.bashrc file
export PATH=$PATH:~/.local/bin/

After executing the specific commands, run buildozer init. You should see an output similar to the screenshot below:

Buildozer successful initialization

The command above creates a Buildozer .spec file, which you can use to make specifications to your app, including the name of the app, the icon, etc. The .spec file should look like the code block below:

[app]

# (str) Title of your application
title = My Application

# (str) Package name
package.name = myapp

# (str) Package domain (needed for android/ios packaging)
package.domain = org.test

# (str) Source code where the main.py live
source.dir = .

# (list) Source files to include (let empty to include all the files)
source.include_exts = py,png,jpg,kv,atlas

# (list) List of inclusions using pattern matching
#source.include_patterns = assets/*,images/*.png

# (list) Source files to exclude (let empty to not exclude anything)
#source.exclude_exts = spec

# (list) List of directory to exclude (let empty to not exclude anything)
#source.exclude_dirs = tests, bin

# (list) List of exclusions using pattern matching
#source.exclude_patterns = license,images/*/*.jpg

# (str) Application versioning (method 1)
version = 0.1

# (str) Application versioning (method 2)
# version.regex = __version__ = \['"\](.*)['"]
# version.filename = %(source.dir)s/main.py

# (list) Application requirements
# comma separated e.g. requirements = sqlite3,kivy
requirements = python3,kivy

# (str) Custom source folders for requirements
# Sets custom source for any requirements with recipes
# requirements.source.kivy = ../../kivy

# (list) Garden requirements
#garden_requirements =

# (str) Presplash of the application
#presplash.filename = %(source.dir)s/data/presplash.png

# (str) Icon of the application
#icon.filename = %(source.dir)s/data/icon.png

# (str) Supported orientation (one of landscape, sensorLandscape, portrait or all)
orientation = portrait

# (list) List of service to declare
#services = NAME:ENTRYPOINT_TO_PY,NAME2:ENTRYPOINT2_TO_PY

#
# OSX Specific
#

#
# author = © Copyright Info

# change the major version of python used by the app
osx.python_version = 3

# Kivy version to use
osx.kivy_version = 1.9.1

#
# Android specific
#

# (bool) Indicate if the application should be fullscreen or not
fullscreen = 0

# (string) Presplash background color (for new android toolchain)
# Supported formats are: #RRGGBB #AARRGGBB or one of the following names:
# red, blue, green, black, white, gray, cyan, magenta, yellow, lightgray,
# darkgray, grey, lightgrey, darkgrey, aqua, fuchsia, lime, maroon, navy,
# olive, purple, silver, teal.
#android.presplash_color = #FFFFFF

# (list) Permissions
#android.permissions = INTERNET

# (int) Target Android API, should be as high as possible.
#android.api = 27

# (int) Minimum API your APK will support.
#android.minapi = 21

# (int) Android SDK version to use
#android.sdk = 20

# (str) Android NDK version to use
#android.ndk = 19b

# (int) Android NDK API to use. This is the minimum API your app will support, it should usually match android.minapi.
#android.ndk_api = 21

# (bool) Use --private data storage (True) or --dir public storage (False)
#android.private_storage = True

# (str) Android NDK directory (if empty, it will be automatically downloaded.)
#android.ndk_path =

# (str) Android SDK directory (if empty, it will be automatically downloaded.)
#android.sdk_path =

# (str) ANT directory (if empty, it will be automatically downloaded.)
#android.ant_path =

# (bool) If True, then skip trying to update the Android sdk
# This can be useful to avoid excess Internet downloads or save time
# when an update is due and you just want to test/build your package
# android.skip_update = False

# (bool) If True, then automatically accept SDK license
# agreements. This is intended for automation only. If set to False,
# the default, you will be shown the license when first running
# buildozer.
# android.accept_sdk_license = False

# (str) Android entry point, default is ok for Kivy-based app
#android.entrypoint = org.renpy.android.PythonActivity

# (str) Android app theme, default is ok for Kivy-based app
# android.apptheme = "@android:style/Theme.NoTitleBar"

# (list) Pattern to whitelist for the whole project
#android.whitelist =

# (str) Path to a custom whitelist file
#android.whitelist_src =

# (str) Path to a custom blacklist file
#android.blacklist_src =

# (list) List of Java .jar files to add to the libs so that pyjnius can access
# their classes. Don't add jars that you do not need, since extra jars can slow
# down the build process. Allows wildcards matching, for example:
# OUYA-ODK/libs/*.jar
#android.add_jars = foo.jar,bar.jar,path/to/more/*.jar

# (list) List of Java files to add to the android project (can be java or a
# directory containing the files)
#android.add_src =

# (list) Android AAR archives to add (currently works only with sdl2_gradle
# bootstrap)
#android.add_aars =

# (list) Gradle dependencies to add (currently works only with sdl2_gradle
# bootstrap)
#android.gradle_dependencies =

# (list) add java compile options
# this can for example be necessary when importing certain java libraries using the 'android.gradle_dependencies' option
# see https://developer.android.com/studio/write/java8-support for further information
# android.add_compile_options = "sourceCompatibility = 1.8", "targetCompatibility = 1.8"

# (list) Gradle repositories to add {can be necessary for some android.gradle_dependencies}
# please enclose in double quotes 
# e.g. android.gradle_repositories = "maven { url 'https://kotlin.bintray.com/ktor' }"
#android.add_gradle_repositories =

# (list) packaging options to add 
# see https://google.github.io/android-gradle-dsl/current/com.android.build.gradle.internal.dsl.PackagingOptions.html
# can be necessary to solve conflicts in gradle_dependencies
# please enclose in double quotes 
# e.g. android.add_packaging_options = "exclude 'META-INF/common.kotlin_module'", "exclude 'META-INF/*.kotlin_module'"
#android.add_gradle_repositories =

# (list) Java classes to add as activities to the manifest.
#android.add_activities = com.example.ExampleActivity

# (str) OUYA Console category. Should be one of GAME or APP
# If you leave this blank, OUYA support will not be enabled
#android.ouya.category = GAME

# (str) Filename of OUYA Console icon. It must be a 732x412 png image.
#android.ouya.icon.filename = %(source.dir)s/data/ouya_icon.png

# (str) XML file to include as an intent filters in <activity> tag
#android.manifest.intent_filters =

# (str) launchMode to set for the main activity
#android.manifest.launch_mode = standard

# (list) Android additional libraries to copy into libs/armeabi
#android.add_libs_armeabi = libs/android/*.so
#android.add_libs_armeabi_v7a = libs/android-v7/*.so
#android.add_libs_arm64_v8a = libs/android-v8/*.so
#android.add_libs_x86 = libs/android-x86/*.so
#android.add_libs_mips = libs/android-mips/*.so

# (bool) Indicate whether the screen should stay on
# Don't forget to add the WAKE_LOCK permission if you set this to True
#android.wakelock = False

# (list) Android application meta-data to set (key=value format)
#android.meta_data =

# (list) Android library project to add (will be added in the
# project.properties automatically.)
#android.library_references =

# (list) Android shared libraries which will be added to AndroidManifest.xml using <uses-library> tag
#android.uses_library =

# (str) Android logcat filters to use
#android.logcat_filters = *:S python:D

# (bool) Copy library instead of making a libpymodules.so
#android.copy_libs = 1

# (str) The Android arch to build for, choices: armeabi-v7a, arm64-v8a, x86, x86_64
android.arch = armeabi-v7a

# (int) overrides automatic versionCode computation (used in build.gradle)
# this is not the same as app version and should only be edited if you know what you're doing
# android.numeric_version = 1

#
# Python for android (p4a) specific
#

# (str) python-for-android fork to use, defaults to upstream (kivy)
#p4a.fork = kivy

# (str) python-for-android branch to use, defaults to master
#p4a.branch = master

# (str) python-for-android git clone directory (if empty, it will be automatically cloned from github)
#p4a.source_dir =

# (str) The directory in which python-for-android should look for your own build recipes (if any)
#p4a.local_recipes =

# (str) Filename to the hook for p4a
#p4a.hook =

# (str) Bootstrap to use for android builds
# p4a.bootstrap = sdl2

# (int) port number to specify an explicit --port= p4a argument (eg for bootstrap flask)
#p4a.port =


#
# iOS specific
#

# (str) Path to a custom kivy-ios folder
#ios.kivy_ios_dir = ../kivy-ios
# Alternately, specify the URL and branch of a git checkout:
ios.kivy_ios_url = https://github.com/kivy/kivy-ios
ios.kivy_ios_branch = master

# Another platform dependency: ios-deploy
# Uncomment to use a custom checkout
#ios.ios_deploy_dir = ../ios_deploy
# Or specify URL and branch
ios.ios_deploy_url = https://github.com/phonegap/ios-deploy
ios.ios_deploy_branch = 1.7.0

# (str) Name of the certificate to use for signing the debug version
# Get a list of available identities: buildozer ios list_identities
#ios.codesign.debug = "iPhone Developer: <lastname> <firstname> (<hexstring>)"

# (str) Name of the certificate to use for signing the release version
#ios.codesign.release = %(ios.codesign.debug)s


[buildozer]

# (int) Log level (0 = error only, 1 = info, 2 = debug (with command output))
log_level = 2

# (int) Display warning if buildozer is run as root (0 = False, 1 = True)
warn_on_root = 1

# (str) Path to build artifact storage, absolute or relative to spec file
# build_dir = ./.buildozer

# (str) Path to build output (i.e. .apk, .ipa) storage
# bin_dir = ./bin

#    -----------------------------------------------------------------------------
#    List as sections
#
#    You can define all the "list" as [section:key].
#    Each line will be considered as a option to the list.
#    Let's take [app] / source.exclude_patterns.
#    Instead of doing:
#
#[app]
#source.exclude_patterns = license,data/audio/*.wav,data/images/original/*
#
#    This can be translated into:
#
#[app:source.exclude_patterns]
#license
#data/audio/*.wav
#data/images/original/*
#


#    -----------------------------------------------------------------------------
#    Profiles
#
#    You can extend section / key with a profile
#    For example, you want to deploy a demo version of your application without
#    HD content. You could first change the title to add "(demo)" in the name
#    and extend the excluded directories to remove the HD content.
#
#[app@demo]
#title = My Application (demo)
#
#[app:source.exclude_patterns@demo]
#images/hd/*
#
#    Then, invoke the command line with the "demo" profile:
#
#buildozer --profile demo android debug

If you want to specify things like the icon, requirements, loading screen, etc., you should edit this file. After making all the desired edits to your application, run buildozer -v android debug from your app directory to build and compile your application. This may take a while, especially if you have a slow machine.

After the process is done, your terminal should have some logs, one confirming that the build was successful:

Android successful build

You should also have an APK version of your app in your bin directory. This is the application executable that you will install and run on your phone:

Android .apk in the bin directory

Conclusion

Congratulations! If you have followed this tutorial step by step, you should have a simple random number generator app on your phone. Play around with it and tweak some values, then rebuild. Running the rebuild will not take as much time as the first build.

As you can see, building a mobile application with Python is fairly straightforward, as long as you are familiar with the framework or module you are working with. Regardless, the logic is executed the same way.

Get familiar with the Kivy module and it’s widgets. You can never know everything all at once. You only need to find a project and get your feet wet as early as possible. Happy coding.

Link: https://blog.logrocket.com/build-android-application-kivy-python-framework/

#python 

DeltaPy⁠⁠ — Tabular Data Augmentation & Feature Engineering

DeltaPy⁠⁠ — Tabular Data Augmentation & Feature Engineering

---

Finance Quant Machine Learning

• ML-Quant.com - Automated Research Repository

Introduction

Tabular augmentation is a new experimental space that makes use of novel and traditional data generation and synthesisation techniques to improve model prediction success. It is in essence a process of modular feature engineering and observation engineering while emphasising the order of augmentation to achieve the best predicted outcome from a given information set. DeltaPy was created with finance applications in mind, but it can be broadly applied to any data-rich environment.

To take full advantage of tabular augmentation for time-series you would perform the techniques in the following order: (1) transforming, (2) interacting, (3) mapping, (4) extracting, and (5) synthesising. What follows is a practical example of how the above methodology can be used. The purpose here is to establish a framework for table augmentation and to point and guide the user to existing packages.

For most the Colab Notebook format might be preferred. I have enabled comments if you want to ask question or address any issues you uncover. For anything pressing use the issues tab. Also have a look at the SSRN report for a more succinct insights.

Data augmentation can be defined as any method that could increase the size or improve the quality of a dataset by generating new features or instances without the collection of additional data-points. Data augmentation is of particular importance in image classification tasks where additional data can be created by cropping, padding, or flipping existing images.

Tabular cross-sectional and time-series prediction tasks can also benefit from augmentation. Here we divide tabular augmentation into columnular and row-wise methods. Row-wise methods are further divided into extraction and data synthesisation techniques, whereas columnular methods are divided into transformation, interaction, and mapping methods.

See the Skeleton Example, for a combination of multiple methods that lead to a halfing of the mean squared error.

Installation & Citation

---

pip install deltapy

@software{deltapy,
  title = {{DeltaPy}: Tabular Data Augmentation},
  author = {Snow, Derek},
  url = {https://github.com/firmai/deltapy/},
  version = {0.1.0},
  date = {2020-04-11},
}

 Snow, Derek, DeltaPy: A Framework for Tabular Data Augmentation in Python (April 22, 2020). Available at SSRN: https://ssrn.com/abstract=3582219

Function Glossary

---

Transformation

df_out = transform.robust_scaler(df.copy(), drop=["Close_1"]); df_out.head()
df_out = transform.standard_scaler(df.copy(), drop=["Close"]); df_out.head()           
df_out = transform.fast_fracdiff(df.copy(), ["Close","Open"],0.5); df_out.head()
df_out = transform.windsorization(df.copy(),"Close",para,strategy='both'); df_out.head()
df_out = transform.operations(df.copy(),["Close"]); df_out.head()
df_out = transform.triple_exponential_smoothing(df.copy(),["Close"], 12, .2,.2,.2,0); 
df_out = transform.naive_dec(df.copy(), ["Close","Open"]); df_out.head()
df_out = transform.bkb(df.copy(), ["Close"]); df_out.head()
df_out = transform.butter_lowpass_filter(df.copy(),["Close"],4); df_out.head()
df_out = transform.instantaneous_phases(df.copy(), ["Close"]); df_out.head()
df_out = transform.kalman_feat(df.copy(), ["Close"]); df_out.head()
df_out = transform.perd_feat(df.copy(),["Close"]); df_out.head()
df_out = transform.fft_feat(df.copy(), ["Close"]); df_out.head()
df_out = transform.harmonicradar_cw(df.copy(), ["Close"],0.3,0.2); df_out.head()
df_out = transform.saw(df.copy(),["Close","Open"]); df_out.head()
df_out = transform.modify(df.copy(),["Close"]); df_out.head()
df_out = transform.multiple_rolling(df, columns=["Close"]); df_out.head()
df_out = transform.multiple_lags(df, start=1, end=3, columns=["Close"]); df_out.head()
df_out  = transform.prophet_feat(df.copy().reset_index(),["Close","Open"],"Date", "D"); df_out.head()

Interaction

df_out = interact.lowess(df.copy(), ["Open","Volume"], df["Close"], f=0.25, iter=3); df_out.head()
df_out = interact.autoregression(df.copy()); df_out.head()
df_out = interact.muldiv(df.copy(), ["Close","Open"]); df_out.head()
df_out = interact.decision_tree_disc(df.copy(), ["Close"]); df_out.head()
df_out = interact.quantile_normalize(df.copy(), drop=["Close"]); df_out.head()
df_out = interact.tech(df.copy()); df_out.head()
df_out = interact.genetic_feat(df.copy()); df_out.head()

Mapping

df_out = mapper.pca_feature(df.copy(),variance_or_components=0.80,drop_cols=["Close_1"]); df_out.head()
df_out = mapper.cross_lag(df.copy()); df_out.head()
df_out = mapper.a_chi(df.copy()); df_out.head()
df_out = mapper.encoder_dataset(df.copy(), ["Close_1"], 15); df_out.head()
df_out = mapper.lle_feat(df.copy(),["Close_1"],4); df_out.head()
df_out = mapper.feature_agg(df.copy(),["Close_1"],4 ); df_out.head()
df_out = mapper.neigh_feat(df.copy(),["Close_1"],4 ); df_out.head()

Extraction

extract.abs_energy(df["Close"])
extract.cid_ce(df["Close"], True)
extract.mean_abs_change(df["Close"])
extract.mean_second_derivative_central(df["Close"])
extract.variance_larger_than_standard_deviation(df["Close"])
extract.var_index(df["Close"].values,var_index_param)
extract.symmetry_looking(df["Close"])
extract.has_duplicate_max(df["Close"])
extract.partial_autocorrelation(df["Close"])
extract.augmented_dickey_fuller(df["Close"])
extract.gskew(df["Close"])
extract.stetson_mean(df["Close"])
extract.length(df["Close"])
extract.count_above_mean(df["Close"])
extract.longest_strike_below_mean(df["Close"])
extract.wozniak(df["Close"])
extract.last_location_of_maximum(df["Close"])
extract.fft_coefficient(df["Close"])
extract.ar_coefficient(df["Close"])
extract.index_mass_quantile(df["Close"])
extract.number_cwt_peaks(df["Close"])
extract.spkt_welch_density(df["Close"])
extract.linear_trend_timewise(df["Close"])
extract.c3(df["Close"])
extract.binned_entropy(df["Close"])
extract.svd_entropy(df["Close"].values)
extract.hjorth_complexity(df["Close"])
extract.max_langevin_fixed_point(df["Close"])
extract.percent_amplitude(df["Close"])
extract.cad_prob(df["Close"])
extract.zero_crossing_derivative(df["Close"])
extract.detrended_fluctuation_analysis(df["Close"])
extract.fisher_information(df["Close"])
extract.higuchi_fractal_dimension(df["Close"])
extract.petrosian_fractal_dimension(df["Close"])
extract.hurst_exponent(df["Close"])
extract.largest_lyauponov_exponent(df["Close"])
extract.whelch_method(df["Close"])
extract.find_freq(df["Close"])
extract.flux_perc(df["Close"])
extract.range_cum_s(df["Close"])
extract.structure_func(df["Close"])
extract.kurtosis(df["Close"])
extract.stetson_k(df["Close"])

Test sets should ideally not be preprocessed with the training data, as in such a way one could be peaking ahead in the training data. The preprocessing parameters should be identified on the test set and then applied on the test set, i.e., the test set should not have an impact on the transformation applied. As an example, you would learn the parameters of PCA decomposition on the training set and then apply the parameters to both the train and the test set.

The benefit of pipelines become clear when one wants to apply multiple augmentation methods. It makes it easy to learn the parameters and then apply them widely. For the most part, this notebook does not concern itself with 'peaking ahead' or pipelines, for some functions, one might have to restructure to code and make use of open source packages to create your preferred solution.

Documentation by Example

Notebook Dependencies

pip install deltapy

pip install pykalman
pip install tsaug
pip install ta
pip install tsaug
pip install pandasvault
pip install gplearn
pip install ta
pip install seasonal
pip install pandasvault

Data and Package Load

import pandas as pd
import numpy as np
from deltapy import transform, interact, mapper, extract 
import warnings
warnings.filterwarnings('ignore')

def data_copy():
  df = pd.read_csv("https://github.com/firmai/random-assets-two/raw/master/numpy/tsla.csv")
  df["Close_1"] = df["Close"].shift(-1)
  df = df.dropna()
  df["Date"] = pd.to_datetime(df["Date"])
  df = df.set_index("Date")
  return df
df = data_copy(); df.head()

Some of these categories are fluid and some techniques could fit into multiple buckets. This is an attempt to find an exhaustive number of techniques, but not an exhaustive list of implementations of the techniques. For example, there are thousands of ways to smooth a time-series, but we have only includes 1-2 techniques of interest under each category.

(1) Transformation:

---

1. Scaling/Normalisation
2. Standardisation
3. Differencing
4. Capping
5. Operations
6. Smoothing
7. Decomposing
8. Filtering
9. Spectral Analysis
10. Waveforms
11. Modifications
12. Rolling
13. Lagging
14. Forecast Model

(2) Interaction:

---

1. Regressions
2. Operators
3. Discretising
4. Normalising
5. Distance
6. Speciality
7. Genetic

(3) Mapping:

---

1. Eigen Decomposition
2. Cross Decomposition
3. Kernel Approximation
4. Autoencoder
5. Manifold Learning
6. Clustering
7. Neighbouring

(4) Extraction:

---

1. Energy
2. Distance
3. Differencing
4. Derivative
5. Volatility
6. Shape
7. Occurrence
8. Autocorrelation
9. Stochasticity
10. Averages
11. Size
12. Count
13. Streaks
14. Location
15. Model Coefficients
16. Quantile
17. Peaks
18. Density
19. Linearity
20. Non-linearity
21. Entropy
22. Fixed Points
23. Amplitude
24. Probability
25. Crossings
26. Fluctuation
27. Information
28. Fractals
29. Exponent
30. Spectral Analysis
31. Percentile
32. Range
33. Structural
34. Distribution

 

(1) Transformation

Here transformation is any method that includes only one feature as an input to produce a new feature/s. Transformations can be applied to cross-section and time-series data. Some transformations are exclusive to time-series data (smoothing, filtering), but a handful of functions apply to both.

Where the time series methods has a centred mean, or are forward-looking, there is a need to recalculate the outputed time series on a running basis to ensure that information of the future does not leak into the model. The last value of this recalculated series or an extracted feature from this series can then be used as a running value that is only backward looking, satisfying the no 'peaking' ahead rule.

There are some packaged in Python that dynamically create time series and extracts their features, but none that incoropates the dynamic creation of a time series in combination with a wide application of prespecified list of extractions. Because this technique is expensive, we have a preference for models that only take historical data into account.

In this section we will include a list of all types of transformations, those that only use present information (operations), those that incorporate all values (interpolation methods), those that only include past values (smoothing functions), and those that incorporate a subset window of lagging and leading values (select filters). Only those that use historical values or are turned into prediction methods can be used out of the box. The entire time series can be used in the model development process for historical value methods, and only the forecasted values can be used for prediction models.

Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function is constructed that approximately fits the data. When using an interpolation method, you are taking future information into account e.g, cubic spline. You can use interpolation methods to forecast into the future (extrapolation), and then use those forecasts in a training set. Or you could recalculate the interpolation for each time step and then extract features out of that series (extraction method). Interpolation and other forward-looking methods can be used if they are turned into prediction problems, then the forecasted values can be trained and tested on, and the fitted data can be diregarded. In the list presented below the first five methods can be used for cross-section and time series data, after that the time-series only methods follow.

(1) Scaling/Normalisation

There are a multitude of scaling methods available. Scaling generally gets applied to the entire dataset and is especially necessary for certain algorithms. K-means make use of euclidean distance hence the need for scaling. For PCA because we are trying to identify the feature with maximus variance we also need scaling. Similarly, we need scaled features for gradient descent. Any algorithm that is not based on a distance measure is not affected by feature scaling. Some of the methods include range scalers like minimum-maximum scaler, maximum absolute scaler or even standardisation methods like the standard scaler can be used for scaling. The example used here is robust scaler. Normalisation is a good technique when you don't know the distribution of the data. Scaling looks into the future, so parameters have to be training on a training set and applied to a test set.

(i) Robust Scaler

Scaling according to the interquartile range, making it robust to outliers.

def robust_scaler(df, drop=None,quantile_range=(25, 75) ):
    if drop:
      keep = df[drop]
      df = df.drop(drop, axis=1)
    center = np.median(df, axis=0)
    quantiles = np.percentile(df, quantile_range, axis=0)
    scale = quantiles[1] - quantiles[0]
    df = (df - center) / scale
    if drop:
      df = pd.concat((keep,df),axis=1)
    return df

df_out = transform.robust_scaler(df.copy(), drop=["Close_1"]); df_out.head()

(2) Standardisation

When using a standardisation method, it is often more effective when the attribute itself if Gaussian. It is also useful to apply the technique when the model you want to use makes assumptions of Gaussian distributions like linear regression, logistic regression, and linear discriminant analysis. For most applications, standardisation is recommended.

(i) Standard Scaler

Standardize features by removing the mean and scaling to unit variance

def standard_scaler(df,drop ):
    if drop:
      keep = df[drop]
      df = df.drop(drop, axis=1)
    mean = np.mean(df, axis=0)
    scale = np.std(df, axis=0)
    df = (df - mean) / scale  
    if drop:
      df = pd.concat((keep,df),axis=1)
    return df


df_out = transform.standard_scaler(df.copy(), drop=["Close"]); df_out.head()           

(3) Differencing

Computing the differences between consecutive observation, normally used to obtain a stationary time series.

(i) Fractional Differencing

Fractional differencing, allows us to achieve stationarity while maintaining the maximum amount of memory compared to integer differencing.

import pylab as pl

def fast_fracdiff(x, cols, d):
    for col in cols:
      T = len(x[col])
      np2 = int(2 ** np.ceil(np.log2(2 * T - 1)))
      k = np.arange(1, T)
      b = (1,) + tuple(np.cumprod((k - d - 1) / k))
      z = (0,) * (np2 - T)
      z1 = b + z
      z2 = tuple(x[col]) + z
      dx = pl.ifft(pl.fft(z1) * pl.fft(z2))
      x[col+"_frac"] = np.real(dx[0:T])
    return x 
  
df_out = transform.fast_fracdiff(df.copy(), ["Close","Open"],0.5); df_out.head()

(4) Capping

Any method that provides sets a floor and a cap to a feature's value. Capping can affect the distribution of data, so it should not be exagerated. One can cap values by using the average, by using the max and min values, or by an arbitrary extreme value.

(i) Winzorisation

The transformation of features by limiting extreme values in the statistical data to reduce the effect of possibly spurious outliers by replacing it with a certain percentile value.

def outlier_detect(data,col,threshold=1,method="IQR"):
  
    if method == "IQR":
      IQR = data[col].quantile(0.75) - data[col].quantile(0.25)
      Lower_fence = data[col].quantile(0.25) - (IQR * threshold)
      Upper_fence = data[col].quantile(0.75) + (IQR * threshold)
    if method == "STD":
      Upper_fence = data[col].mean() + threshold * data[col].std()
      Lower_fence = data[col].mean() - threshold * data[col].std()   
    if method == "OWN":
      Upper_fence = data[col].mean() + threshold * data[col].std()
      Lower_fence = data[col].mean() - threshold * data[col].std() 
    if method =="MAD":
      median = data[col].median()
      median_absolute_deviation = np.median([np.abs(y - median) for y in data[col]])
      modified_z_scores = pd.Series([0.6745 * (y - median) / median_absolute_deviation for y in data[col]])
      outlier_index = np.abs(modified_z_scores) > threshold
      print('Num of outlier detected:',outlier_index.value_counts()[1])
      print('Proportion of outlier detected',outlier_index.value_counts()[1]/len(outlier_index))
      return outlier_index, (median_absolute_deviation, median_absolute_deviation)

    para = (Upper_fence, Lower_fence)
    tmp = pd.concat([data[col]>Upper_fence,data[col]<Lower_fence],axis=1)
    outlier_index = tmp.any(axis=1)
    print('Num of outlier detected:',outlier_index.value_counts()[1])
    print('Proportion of outlier detected',outlier_index.value_counts()[1]/len(outlier_index))
    
    return outlier_index, para

def windsorization(data,col,para,strategy='both'):
    """
    top-coding & bottom coding (capping the maximum of a distribution at an arbitrarily set value,vice versa)
    """

    data_copy = data.copy(deep=True)  
    if strategy == 'both':
        data_copy.loc[data_copy[col]>para[0],col] = para[0]
        data_copy.loc[data_copy[col]<para[1],col] = para[1]
    elif strategy == 'top':
        data_copy.loc[data_copy[col]>para[0],col] = para[0]
    elif strategy == 'bottom':
        data_copy.loc[data_copy[col]<para[1],col] = para[1]  
    return data_copy

_, para = transform.outlier_detect(df, "Close")
df_out = transform.windsorization(df.copy(),"Close",para,strategy='both'); df_out.head()

(5) Operations

Operations here are treated like traditional transformations. It is the replacement of a variable by a function of that variable. In a stronger sense, a transformation is a replacement that changes the shape of a distribution or relationship.

(i) Power, Log, Recipricol, Square Root

def operations(df,features):
  df_new = df[features]
  df_new = df_new - df_new.min()

  sqr_name = [str(fa)+"_POWER_2" for fa in df_new.columns]
  log_p_name = [str(fa)+"_LOG_p_one_abs" for fa in df_new.columns]
  rec_p_name = [str(fa)+"_RECIP_p_one" for fa in df_new.columns]
  sqrt_name = [str(fa)+"_SQRT_p_one" for fa in df_new.columns]

  df_sqr = pd.DataFrame(np.power(df_new.values, 2),columns=sqr_name, index=df.index)
  df_log = pd.DataFrame(np.log(df_new.add(1).abs().values),columns=log_p_name, index=df.index)
  df_rec = pd.DataFrame(np.reciprocal(df_new.add(1).values),columns=rec_p_name, index=df.index)
  df_sqrt = pd.DataFrame(np.sqrt(df_new.abs().add(1).values),columns=sqrt_name, index=df.index)

  dfs = [df, df_sqr, df_log, df_rec, df_sqrt]

  df=  pd.concat(dfs, axis=1)

  return df

df_out = transform.operations(df.copy(),["Close"]); df_out.head()

(6) Smoothing

Here we maintain that any method that has a component of historical averaging is a smoothing method such as a simple moving average and single, double and tripple exponential smoothing methods. These forms of non-causal filters are also popular in signal processing and are called filters, where exponential smoothing is called an IIR filter and a moving average a FIR filter with equal weighting factors.

(i) Tripple Exponential Smoothing (Holt-Winters Exponential Smoothing)

The Holt-Winters seasonal method comprises the forecast equation and three smoothing equations — one for the level $ℓt$, one for the trend &bt&, and one for the seasonal component $st$. This particular version is performed by looking at the last 12 periods. For that reason, the first 12 records should be disregarded because they can't make use of the required window size for a fair calculation. The calculation is such that values are still provided for those periods based on whatever data might be available.

def initial_trend(series, slen):
    sum = 0.0
    for i in range(slen):
        sum += float(series[i+slen] - series[i]) / slen
    return sum / slen

def initial_seasonal_components(series, slen):
    seasonals = {}
    season_averages = []
    n_seasons = int(len(series)/slen)
    # compute season averages
    for j in range(n_seasons):
        season_averages.append(sum(series[slen*j:slen*j+slen])/float(slen))
    # compute initial values
    for i in range(slen):
        sum_of_vals_over_avg = 0.0
        for j in range(n_seasons):
            sum_of_vals_over_avg += series[slen*j+i]-season_averages[j]
        seasonals[i] = sum_of_vals_over_avg/n_seasons
    return seasonals

def triple_exponential_smoothing(df,cols, slen, alpha, beta, gamma, n_preds):
    for col in cols:
      result = []
      seasonals = initial_seasonal_components(df[col], slen)
      for i in range(len(df[col])+n_preds):
          if i == 0: # initial values
              smooth = df[col][0]
              trend = initial_trend(df[col], slen)
              result.append(df[col][0])
              continue
          if i >= len(df[col]): # we are forecasting
              m = i - len(df[col]) + 1
              result.append((smooth + m*trend) + seasonals[i%slen])
          else:
              val = df[col][i]
              last_smooth, smooth = smooth, alpha*(val-seasonals[i%slen]) + (1-alpha)*(smooth+trend)
              trend = beta * (smooth-last_smooth) + (1-beta)*trend
              seasonals[i%slen] = gamma*(val-smooth) + (1-gamma)*seasonals[i%slen]
              result.append(smooth+trend+seasonals[i%slen])
      df[col+"_TES"] = result
    #print(seasonals)
    return df

df_out= transform.triple_exponential_smoothing(df.copy(),["Close"], 12, .2,.2,.2,0); df_out.head()

(7) Decomposing

Decomposition procedures are used in time series to describe the trend and seasonal factors in a time series. More extensive decompositions might also include long-run cycles, holiday effects, day of week effects and so on. Here, we’ll only consider trend and seasonal decompositions. A naive decomposition makes use of moving averages, other decomposition methods are available that make use of LOESS.

(i) Naive Decomposition

The base trend takes historical information into account and established moving averages; it does not have to be linear. To estimate the seasonal component for each season, simply average the detrended values for that season. If the seasonal variation looks constant, we should use the additive model. If the magnitude is increasing as a function of time, we will use multiplicative. Here because it is predictive in nature we are using a one sided moving average, as opposed to a two-sided centred average.

import statsmodels.api as sm

def naive_dec(df, columns, freq=2):
  for col in columns:
    decomposition = sm.tsa.seasonal_decompose(df[col], model='additive', freq = freq, two_sided=False)
    df[col+"_NDDT" ] = decomposition.trend
    df[col+"_NDDT"] = decomposition.seasonal
    df[col+"_NDDT"] = decomposition.resid
  return df

df_out = transform.naive_dec(df.copy(), ["Close","Open"]); df_out.head()

(8) Filtering

It is often useful to either low-pass filter (smooth) time series in order to reveal low-frequency features and trends, or to high-pass filter (detrend) time series in order to isolate high frequency transients (e.g. storms). Low pass filters use historical values, high-pass filters detrends with low-pass filters, so also indirectly uses historical values.

There are a few filters available, closely associated with decompositions and smoothing functions. The Hodrick-Prescott filter separates a time-series $yt$ into a trend $τt$ and a cyclical component $ζt$. The Christiano-Fitzgerald filter is a generalization of Baxter-King filter and can be seen as weighted moving average.

(i) Baxter-King Bandpass

The Baxter-King filter is intended to explicitly deal with the periodicity of the business cycle. By applying their band-pass filter to a series, they produce a new series that does not contain fluctuations at higher or lower than those of the business cycle. The parameters are arbitrarily chosen. This method uses a centred moving average that has to be changed to a lagged moving average before it can be used as an input feature. The maximum period of oscillation should be used as the point to truncate the dataset, as that part of the time series does not incorporate all the required datapoints.

import statsmodels.api as sm

def bkb(df, cols):
  for col in cols:
    df[col+"_BPF"] = sm.tsa.filters.bkfilter(df[[col]].values, 2, 10, len(df)-1)
  return df

df_out = transform.bkb(df.copy(), ["Close"]); df_out.head()

(ii) Butter Lowpass (IIR Filter Design)

The Butterworth filter is a type of signal processing filter designed to have a frequency response as flat as possible in the passban. Like other filtersm the first few values have to be disregarded for accurate downstream prediction. Instead of disregarding these values on a per case basis, they can be diregarded in one chunk once the database of transformed features have been developed.

from scipy import signal, integrate
def butter_lowpass(cutoff, fs=20, order=5):
    nyq = 0.5 * fs
    normal_cutoff = cutoff / nyq
    b, a = signal.butter(order, normal_cutoff, btype='low', analog=False)
    return b, a
    
def butter_lowpass_filter(df,cols, cutoff, fs=20, order=5):
    b, a = butter_lowpass(cutoff, fs, order=order)
    for col in cols:
      df[col+"_BUTTER"] = signal.lfilter(b, a, df[col])
    return df

df_out = transform.butter_lowpass_filter(df.copy(),["Close"],4); df_out.head()

(iii) Hilbert Transform Angle

The Hilbert transform is a time-domain to time-domain transformation which shifts the phase of a signal by 90 degrees. It is also a centred measure and would be difficult to use in a time series prediction setting, unless it is recalculated on a per step basis or transformed to be based on historical values only.

from scipy import signal
import numpy as np

def instantaneous_phases(df,cols):
    for col in cols:
      df[col+"_HILLB"] = np.unwrap(np.angle(signal.hilbert(df[col], axis=0)), axis=0)
    return df

df_out = transform.instantaneous_phases(df.copy(), ["Close"]); df_out.head()

(iiiv) Unscented Kalman Filter

The Kalman filter is better suited for estimating things that change over time. The most tangible example is tracking moving objects. A Kalman filter will be very close to the actual trajectory because it says the most recent measurement is more important than the older ones. The Unscented Kalman Filter (UKF) is a model based-techniques that recursively estimates the states (and with some modifications also parameters) of a nonlinear, dynamic, discrete-time system. The UKF is based on the typical prediction-correction style methods. The Kalman Smoother incorporates future values, the Filter doesn't and can be used for online prediction. The normal Kalman filter is a forward filter in the sense that it makes forecast of the current state using only current and past observations, whereas the smoother is based on computing a suitable linear combination of two filters, which are ran in forward and backward directions.

from pykalman import UnscentedKalmanFilter

def kalman_feat(df, cols):
  for col in cols:
    ukf = UnscentedKalmanFilter(lambda x, w: x + np.sin(w), lambda x, v: x + v, observation_covariance=0.1)
    (filtered_state_means, filtered_state_covariances) = ukf.filter(df[col])
    (smoothed_state_means, smoothed_state_covariances) = ukf.smooth(df[col])
    df[col+"_UKFSMOOTH"] = smoothed_state_means.flatten()
    df[col+"_UKFFILTER"] = filtered_state_means.flatten()
  return df 

df_out = transform.kalman_feat(df.copy(), ["Close"]); df_out.head()

(9) Spectral Analysis

There are a range of functions for spectral analysis. You can use periodograms and the welch method to estimate the power spectral density. You can also use the welch method to estimate the cross power spectral density. Other techniques include spectograms, Lomb-Scargle periodograms and, short time fourier transform.

(i) Periodogram

This returns an array of sample frequencies and the power spectrum of x, or the power spectral density of x.

from scipy import signal
def perd_feat(df, cols):
  for col in cols:
    sig = signal.periodogram(df[col],fs=1, return_onesided=False)
    df[col+"_FREQ"] = sig[0]
    df[col+"_POWER"] = sig[1]
  return df

df_out = transform.perd_feat(df.copy(),["Close"]); df_out.head()

(ii) Fast Fourier Transform

The FFT, or fast fourier transform is an algorithm that essentially uses convolution techniques to efficiently find the magnitude and location of the tones that make up the signal of interest. We can often play with the FFT spectrum, by adding and removing successive tones (which is akin to selectively filtering particular tones that make up the signal), in order to obtain a smoothed version of the underlying signal. This takes the entire signal into account, and as a result has to be recalculated on a running basis to avoid peaking into the future.

def fft_feat(df, cols):
  for col in cols:
    fft_df = np.fft.fft(np.asarray(df[col].tolist()))
    fft_df = pd.DataFrame({'fft':fft_df})
    df[col+'_FFTABS'] = fft_df['fft'].apply(lambda x: np.abs(x)).values
    df[col+'_FFTANGLE'] = fft_df['fft'].apply(lambda x: np.angle(x)).values
  return df 

df_out = transform.fft_feat(df.copy(), ["Close"]); df_out.head()

(10) Waveforms

The waveform of a signal is the shape of its graph as a function of time.

(i) Continuous Wave Radar

from scipy import signal
def harmonicradar_cw(df, cols, fs,fc):
    for col in cols:
      ttxt = f'CW: {fc} Hz'
      #%% input
      t = df[col]
      tx = np.sin(2*np.pi*fc*t)
      _,Pxx = signal.welch(tx,fs)
      #%% diode
      d = (signal.square(2*np.pi*fc*t))
      d[d<0] = 0.
      #%% output of diode
      rx = tx * d
      df[col+"_HARRAD"] = rx.values
    return df

df_out = transform.harmonicradar_cw(df.copy(), ["Close"],0.3,0.2); df_out.head()

(ii) Saw Tooth

Return a periodic sawtooth or triangle waveform.

def saw(df, cols):
  for col in cols:
    df[col+" SAW"] = signal.sawtooth(df[col])
  return df

df_out = transform.saw(df.copy(),["Close","Open"]); df_out.head()

(9) Modifications

A range of modification usually applied ot images, these values would have to be recalculate for each time-series.

(i) Various Techniques

from tsaug import *
def modify(df, cols):
  for col in cols:
    series = df[col].values
    df[col+"_magnify"], _ = magnify(series, series)
    df[col+"_affine"], _ = affine(series, series)
    df[col+"_crop"], _ = crop(series, series)
    df[col+"_cross_sum"], _ = cross_sum(series, series)
    df[col+"_resample"], _ = resample(series, series)
    df[col+"_trend"], _ = trend(series, series)

    df[col+"_random_affine"], _ = random_time_warp(series, series)
    df[col+"_random_crop"], _ = random_crop(series, series)
    df[col+"_random_cross_sum"], _ = random_cross_sum(series, series)
    df[col+"_random_sidetrack"], _ = random_sidetrack(series, series)
    df[col+"_random_time_warp"], _ = random_time_warp(series, series)
    df[col+"_random_magnify"], _ = random_magnify(series, series)
    df[col+"_random_jitter"], _ = random_jitter(series, series)
    df[col+"_random_trend"], _ = random_trend(series, series)
  return df

df_out = transform.modify(df.copy(),["Close"]); df_out.head()

(11) Rolling

Features that are calculated on a rolling basis over fixed window size.

(i) Mean, Standard Deviation

def multiple_rolling(df, windows = [1,2], functions=["mean","std"], columns=None):
  windows = [1+a for a in windows]
  if not columns:
    columns = df.columns.to_list()
  rolling_dfs = (df[columns].rolling(i)                                    # 1. Create window
                  .agg(functions)                                # 1. Aggregate
                  .rename({col: '{0}_{1:d}'.format(col, i)
                                for col in columns}, axis=1)  # 2. Rename columns
                for i in windows)                                # For each window
  df_out = pd.concat((df, *rolling_dfs), axis=1)
  da = df_out.iloc[:,len(df.columns):]
  da = [col[0] + "_" + col[1] for col in  da.columns.to_list()]
  df_out.columns = df.columns.to_list() + da 

  return  df_out                      # 3. Concatenate dataframes

df_out = transform.multiple_rolling(df, columns=["Close"]); df_out.head()

(12) Lagging

Lagged values from existing features.

(i) Single Steps

def multiple_lags(df, start=1, end=3,columns=None):
  if not columns:
    columns = df.columns.to_list()
  lags = range(start, end+1)  # Just two lags for demonstration.

  df = df.assign(**{
      '{}_t_{}'.format(col, t): df[col].shift(t)
      for t in lags
      for col in columns
  })
  return df

df_out = transform.multiple_lags(df, start=1, end=3, columns=["Close"]); df_out.head()

(13) Forecast Model

There are a range of time series model that can be implemented like AR, MA, ARMA, ARIMA, SARIMA, SARIMAX, VAR, VARMA, VARMAX, SES, and HWES. The models can be divided into autoregressive models and smoothing models. In an autoregression model, we forecast the variable of interest using a linear combination of past values of the variable. Each method might requre specific tuning and parameters to suit your prediction task. You need to drop a certain amount of historical data that you use during the fitting stage. Models that take seasonality into account need more training data.

(i) Prophet

Prophet is a procedure for forecasting time series data based on an additive model where non-linear trends are fit with yearly, weekly, and daily seasonality. You can apply additive models to your training data but also interactive models like deep learning models. The problem is that because these models have learned from future observations, there would this be a need to recalculate the time series on a running basis, or to only include the predicted as opposed to fitted values in future training and test sets. In this example, I train on 150 data points to illustrate how the remaining or so 100 datapoints can be used in a new prediction problem. You can plot with df["PROPHET"].plot() to see the effect.

You can apply additive models to your training data but also interactive models like deep learning models. The problem is that these models have learned from future observations, there would this be a need to recalculate the time series on a running basis, or to only include the predicted as opposed to fitted values in future training and test sets.

from fbprophet import Prophet

def prophet_feat(df, cols,date, freq,train_size=150):
  def prophet_dataframe(df): 
    df.columns = ['ds','y']
    return df

  def original_dataframe(df, freq, name):
    prophet_pred = pd.DataFrame({"Date" : df['ds'], name : df["yhat"]})
    prophet_pred = prophet_pred.set_index("Date")
    #prophet_pred.index.freq = pd.tseries.frequencies.to_offset(freq)
    return prophet_pred[name].values

  for col in cols:
    model = Prophet(daily_seasonality=True)
    fb = model.fit(prophet_dataframe(df[[date, col]].head(train_size)))
    forecast_len = len(df) - train_size
    future = model.make_future_dataframe(periods=forecast_len,freq=freq)
    future_pred = model.predict(future)
    df[col+"_PROPHET"] = list(original_dataframe(future_pred,freq,col))
  return df

df_out  = transform.prophet_feat(df.copy().reset_index(),["Close","Open"],"Date", "D"); df_out.head()

 

(2) Interaction

Interactions are defined as methods that require more than one feature to create an additional feature. Here we include normalising and discretising techniques that are non-feature specific. Almost all of these method can be applied to cross-section method. The only methods that are time specific is the technical features in the speciality section and the autoregression model.

(1) Regression

Regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome variable') and one or more independent variables.

(i) Lowess Smoother

The lowess smoother is a robust locally weighted regression. The function fits a nonparametric regression curve to a scatterplot.

from math import ceil
import numpy as np
from scipy import linalg
import math

def lowess(df, cols, y, f=2. / 3., iter=3):
    for col in cols:
      n = len(df[col])
      r = int(ceil(f * n))
      h = [np.sort(np.abs(df[col] - df[col][i]))[r] for i in range(n)]
      w = np.clip(np.abs((df[col][:, None] - df[col][None, :]) / h), 0.0, 1.0)
      w = (1 - w ** 3) ** 3
      yest = np.zeros(n)
      delta = np.ones(n)
      for iteration in range(iter):
          for i in range(n):
              weights = delta * w[:, i]
              b = np.array([np.sum(weights * y), np.sum(weights * y * df[col])])
              A = np.array([[np.sum(weights), np.sum(weights * df[col])],
                            [np.sum(weights * df[col]), np.sum(weights * df[col] * df[col])]])
              beta = linalg.solve(A, b)
              yest[i] = beta[0] + beta[1] * df[col][i]

          residuals = y - yest
          s = np.median(np.abs(residuals))
          delta = np.clip(residuals / (6.0 * s), -1, 1)
          delta = (1 - delta ** 2) ** 2
      df[col+"_LOWESS"] = yest

    return df

df_out = interact.lowess(df.copy(), ["Open","Volume"], df["Close"], f=0.25, iter=3); df_out.head()

Autoregression

Autoregression is a time series model that uses observations from previous time steps as input to a regression equation to predict the value at the next time step

from statsmodels.tsa.ar_model import AR
from timeit import default_timer as timer
def autoregression(df, drop=None, settings={"autoreg_lag":4}):

    autoreg_lag = settings["autoreg_lag"]
    if drop:
      keep = df[drop]
      df = df.drop([drop],axis=1).values

    n_channels = df.shape[0]
    t = timer()
    channels_regg = np.zeros((n_channels, autoreg_lag + 1))
    for i in range(0, n_channels):
        fitted_model = AR(df.values[i, :]).fit(autoreg_lag)
        # TODO: This is not the same as Matlab's for some reasons!
        # kk = ARMAResults(fitted_model)
        # autore_vals, dummy1, dummy2 = arburg(x[i, :], autoreg_lag) # This looks like Matlab's but slow
        channels_regg[i, 0: len(fitted_model.params)] = np.real(fitted_model.params)

    for i in range(channels_regg.shape[1]):
      df["LAG_"+str(i+1)] = channels_regg[:,i]
    
    if drop:
      df = pd.concat((keep,df),axis=1)

    t = timer() - t
    return df

df_out = interact.autoregression(df.copy()); df_out.head()

(2) Operator

Looking at interaction between different features. Here the methods employed are multiplication and division.

(i) Multiplication and Division

def muldiv(df, feature_list):
  for feat in feature_list:
    for feat_two in feature_list:
      if feat==feat_two:
        continue
      else:
       df[feat+"/"+feat_two] = df[feat]/(df[feat_two]-df[feat_two].min()) #zero division guard
       df[feat+"_X_"+feat_two] = df[feat]*(df[feat_two])

  return df

df_out = interact.muldiv(df.copy(), ["Close","Open"]); df_out.head()

(3) Discretising

In statistics and machine learning, discretization refers to the process of converting or partitioning continuous attributes, features or variables to discretized or nominal attributes

(i) Decision Tree Discretiser

The first method that will be applies here is a supersived discretiser. Discretisation with Decision Trees consists of using a decision tree to identify the optimal splitting points that would determine the bins or contiguous intervals.

from sklearn.tree import DecisionTreeRegressor

def decision_tree_disc(df, cols, depth=4 ):
  for col in cols:
    df[col +"_m1"] = df[col].shift(1)
    df = df.iloc[1:,:]
    tree_model = DecisionTreeRegressor(max_depth=depth,random_state=0)
    tree_model.fit(df[col +"_m1"].to_frame(), df[col])
    df[col+"_Disc"] = tree_model.predict(df[col +"_m1"].to_frame())
  return df

df_out = interact.decision_tree_disc(df.copy(), ["Close"]); df_out.head()

(4) Normalising

Normalising normally pertains to the scaling of data. There are many method available, interacting normalising methods makes use of all the feature's attributes to do the scaling.

(i) Quantile Normalisation

In statistics, quantile normalization is a technique for making two distributions identical in statistical properties.

import numpy as np
import pandas as pd

def quantile_normalize(df, drop):

    if drop:
      keep = df[drop]
      df = df.drop(drop,axis=1)

    #compute rank
    dic = {}
    for col in df:
      dic.update({col : sorted(df[col])})
    sorted_df = pd.DataFrame(dic)
    rank = sorted_df.mean(axis = 1).tolist()
    #sort
    for col in df:
        t = np.searchsorted(np.sort(df[col]), df[col])
        df[col] = [rank[i] for i in t]
    
    if drop:
      df = pd.concat((keep,df),axis=1)
    return df

df_out = interact.quantile_normalize(df.copy(), drop=["Close"]); df_out.head()

(5) Distance

There are multiple types of distance functions like Euclidean, Mahalanobis, and Minkowski distance. Here we are using a contrived example in a location based haversine distance.

(i) Haversine Distance

The Haversine (or great circle) distance is the angular distance between two points on the surface of a sphere.

from math import sin, cos, sqrt, atan2, radians
def haversine_distance(row, lon="Open", lat="Close"):
    c_lat,c_long = radians(52.5200), radians(13.4050)
    R = 6373.0
    long = radians(row['Open'])
    lat = radians(row['Close'])
    
    dlon = long - c_long
    dlat = lat - c_lat
    a = sin(dlat / 2)**2 + cos(lat) * cos(c_lat) * sin(dlon / 2)**2
    c = 2 * atan2(sqrt(a), sqrt(1 - a))
    
    return R * c

df_out['distance_central'] = df.apply(interact.haversine_distance,axis=1); df_out.head()

(6) Speciality

(i) Technical Features

Technical indicators are heuristic or mathematical calculations based on the price, volume, or open interest of a security or contract used by traders who follow technical analysis. By analyzing historical data, technical analysts use indicators to predict future price movements.

import ta

def tech(df):
  return ta.add_all_ta_features(df, open="Open", high="High", low="Low", close="Close", volume="Volume")
  
df_out = interact.tech(df.copy()); df_out.head()

(7) Genetic

Genetic programming has shown promise in constructing feature by osing original features to form high-level ones that can help algorithms achieve better performance.

(i) Symbolic Transformer

A symbolic transformer is a supervised transformer that begins by building a population of naive random formulas to represent a relationship.

df.head()

from gplearn.genetic import SymbolicTransformer

def genetic_feat(df, num_gen=20, num_comp=10):
  function_set = ['add', 'sub', 'mul', 'div',
                  'sqrt', 'log', 'abs', 'neg', 'inv','tan']

  gp = SymbolicTransformer(generations=num_gen, population_size=200,
                          hall_of_fame=100, n_components=num_comp,
                          function_set=function_set,
                          parsimony_coefficient=0.0005,
                          max_samples=0.9, verbose=1,
                          random_state=0, n_jobs=6)

  gen_feats = gp.fit_transform(df.drop("Close_1", axis=1), df["Close_1"]); df.iloc[:,:8]
  gen_feats = pd.DataFrame(gen_feats, columns=["gen_"+str(a) for a in range(gen_feats.shape[1])])
  gen_feats.index = df.index
  return pd.concat((df,gen_feats),axis=1)

df_out = interact.genetic_feat(df.copy()); df_out.head()

 

(3) Mapping

Methods that help with the summarisation of features by remapping them to achieve some aim like the maximisation of variability or class separability. These methods tend to be unsupervised, but can also take an supervised form.

(1) Eigen Decomposition

Eigendecomposition or sometimes spectral decomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors. Some examples are LDA and PCA.

(i) Principal Component Analysis

Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components.

def pca_feature(df, memory_issues=False,mem_iss_component=False,variance_or_components=0.80,n_components=5 ,drop_cols=None, non_linear=True):
    
  if non_linear:
    pca = KernelPCA(n_components = n_components, kernel='rbf', fit_inverse_transform=True, random_state = 33, remove_zero_eig= True)
  else:
    if memory_issues:
      if not mem_iss_component:
        raise ValueError("If you have memory issues, you have to preselect mem_iss_component")
      pca = IncrementalPCA(mem_iss_component)
    else:
      if variance_or_components>1:
        pca = PCA(n_components=variance_or_components) 
      else: # automated selection based on variance
        pca = PCA(n_components=variance_or_components,svd_solver="full") 
  if drop_cols:
    X_pca = pca.fit_transform(df.drop(drop_cols,axis=1))
    return pd.concat((df[drop_cols],pd.DataFrame(X_pca, columns=["PCA_"+str(i+1) for i in range(X_pca.shape[1])],index=df.index)),axis=1)

  else:
    X_pca = pca.fit_transform(df)
    return pd.DataFrame(X_pca, columns=["PCA_"+str(i+1) for i in range(X_pca.shape[1])],index=df.index)


  return df

df_out = mapper.pca_feature(df.copy(), variance_or_components=0.9, n_components=8,non_linear=False)

(2) Cross Decomposition

These families of algorithms are useful to find linear relations between two multivariate datasets.

(1) Canonical Correlation Analysis

Canonical-correlation analysis (CCA) is a way of inferring information from cross-covariance matrices.

from sklearn.cross_decomposition import CCA

def cross_lag(df, drop=None, lags=1, components=4 ):

  if drop:
    keep = df[drop]
    df = df.drop([drop],axis=1)

  df_2 = df.shift(lags)
  df = df.iloc[lags:,:]
  df_2 = df_2.dropna().reset_index(drop=True)

  cca = CCA(n_components=components)
  cca.fit(df_2, df)

  X_c, df_2 = cca.transform(df_2, df)
  df_2 = pd.DataFrame(df_2, index=df.index)
  df_2 = df.add_prefix('crd_')

  if drop:
    df = pd.concat([keep,df,df_2],axis=1)
  else:
    df = pd.concat([df,df_2],axis=1)
  return df

df_out = mapper.cross_lag(df.copy()); df_out.head()

(3) Kernel Approximation

Functions that approximate the feature mappings that correspond to certain kernels, as they are used for example in support vector machines.

(i) Additive Chi2 Kernel

Computes the additive chi-squared kernel between observations in X and Y The chi-squared kernel is computed between each pair of rows in X and Y. X and Y have to be non-negative.

from sklearn.kernel_approximation import AdditiveChi2Sampler

def a_chi(df, drop=None, lags=1, sample_steps=2 ):

  if drop:
    keep = df[drop]
    df = df.drop([drop],axis=1)

  df_2 = df.shift(lags)
  df = df.iloc[lags:,:]
  df_2 = df_2.dropna().reset_index(drop=True)

  chi2sampler = AdditiveChi2Sampler(sample_steps=sample_steps)

  df_2 = chi2sampler.fit_transform(df_2, df["Close"])

  df_2 = pd.DataFrame(df_2, index=df.index)
  df_2 = df.add_prefix('achi_')

  if drop:
    df = pd.concat([keep,df,df_2],axis=1)
  else:
    df = pd.concat([df,df_2],axis=1)
  return df

df_out = mapper.a_chi(df.copy()); df_out.head()

(4) Autoencoder

An autoencoder is a type of artificial neural network used to learn efficient data codings in an unsupervised manner. The aim of an autoencoder is to learn a representation (encoding) for a set of data, typically for dimensionality reduction, by training the network to ignore noise.

(i) Feed Forward

The simplest form of an autoencoder is a feedforward, non-recurrent neural network similar to single layer perceptrons that participate in multilayer perceptrons

from sklearn.preprocessing import minmax_scale
import tensorflow as tf
import numpy as np

def encoder_dataset(df, drop=None, dimesions=20):

  if drop:
    train_scaled = minmax_scale(df.drop(drop,axis=1).values, axis = 0)
  else:
    train_scaled = minmax_scale(df.values, axis = 0)

  # define the number of encoding dimensions
  encoding_dim = dimesions
  # define the number of features
  ncol = train_scaled.shape[1]
  input_dim = tf.keras.Input(shape = (ncol, ))

  # Encoder Layers
  encoded1 = tf.keras.layers.Dense(3000, activation = 'relu')(input_dim)
  encoded2 = tf.keras.layers.Dense(2750, activation = 'relu')(encoded1)
  encoded3 = tf.keras.layers.Dense(2500, activation = 'relu')(encoded2)
  encoded4 = tf.keras.layers.Dense(750, activation = 'relu')(encoded3)
  encoded5 = tf.keras.layers.Dense(500, activation = 'relu')(encoded4)
  encoded6 = tf.keras.layers.Dense(250, activation = 'relu')(encoded5)
  encoded7 = tf.keras.layers.Dense(encoding_dim, activation = 'relu')(encoded6)

  encoder = tf.keras.Model(inputs = input_dim, outputs = encoded7)
  encoded_input = tf.keras.Input(shape = (encoding_dim, ))

  encoded_train = pd.DataFrame(encoder.predict(train_scaled),index=df.index)
  encoded_train = encoded_train.add_prefix('encoded_')
  if drop:
    encoded_train = pd.concat((df[drop],encoded_train),axis=1)

  return encoded_train

df_out = mapper.encoder_dataset(df.copy(), ["Close_1"], 15); df_out.head()

df_out.head()

(5) Manifold Learning

Manifold Learning can be thought of as an attempt to generalize linear frameworks like PCA to be sensitive to non-linear structure in data.

(i) Local Linear Embedding

Locally Linear Embedding is a method of non-linear dimensionality reduction. It tries to reduce these n-Dimensions while trying to preserve the geometric features of the original non-linear feature structure.

from sklearn.manifold import LocallyLinearEmbedding

def lle_feat(df, drop=None, components=4):

  if drop:
    keep = df[drop]
    df = df.drop(drop, axis=1)

  embedding = LocallyLinearEmbedding(n_components=components)
  em = embedding.fit_transform(df)
  df = pd.DataFrame(em,index=df.index)
  df = df.add_prefix('lle_')
  if drop:
    df = pd.concat((keep,df),axis=1)
  return df

df_out = mapper.lle_feat(df.copy(),["Close_1"],4); df_out.head()

(6) Clustering

Most clustering techniques start with a bottom up approach: each observation starts in its own cluster, and clusters are successively merged together with some measure. Although these clustering techniques are typically used for observations, it can also be used for feature dimensionality reduction; especially hierarchical clustering techniques.

(i) Feature Agglomeration

Feature agglomerative uses clustering to group together features that look very similar, thus decreasing the number of features.

import numpy as np
from sklearn import datasets, cluster

def feature_agg(df, drop=None, components=4):

  if drop:
    keep = df[drop]
    df = df.drop(drop, axis=1)

  components = min(df.shape[1]-1,components)
  agglo = cluster.FeatureAgglomeration(n_clusters=components)
  agglo.fit(df)
  df = pd.DataFrame(agglo.transform(df),index=df.index)
  df = df.add_prefix('feagg_')

  if drop:
    return pd.concat((keep,df),axis=1)
  else:
    return df


df_out = mapper.feature_agg(df.copy(),["Close_1"],4 ); df_out.head()

(7) Neigbouring

Neighbouring points can be calculated using distance metrics like Hamming, Manhattan, Minkowski distance. The principle behind nearest neighbor methods is to find a predefined number of training samples closest in distance to the new point, and predict the label from these.

(i) Nearest Neighbours

Unsupervised learner for implementing neighbor searches.

from sklearn.neighbors import NearestNeighbors

def neigh_feat(df, drop, neighbors=6):
  
  if drop:
    keep = df[drop]
    df = df.drop(drop, axis=1)

  components = min(df.shape[0]-1,neighbors)
  neigh = NearestNeighbors(n_neighbors=neighbors)
  neigh.fit(df)
  neigh = neigh.kneighbors()[0]
  df = pd.DataFrame(neigh, index=df.index)
  df = df.add_prefix('neigh_')

  if drop:
    return pd.concat((keep,df),axis=1)
  else:
    return df

  return df

df_out = mapper.neigh_feat(df.copy(),["Close_1"],4 ); df_out.head()

 

(4) Extraction

When working with extraction, you have decide the size of the time series history to take into account when calculating a collection of walk-forward feature values. To facilitate our extraction, we use an excellent package called TSfresh, and also some of their default features. For completeness, we also include 12 or so custom features to be added to the extraction pipeline.

The time series methods in the transformation section and the interaction section are similar to the methods we will uncover in the extraction section, however, for transformation and interaction methods the output is an entire new time series, whereas extraction methods takes as input multiple constructed time series and extracts a singular value from each time series to reconstruct an entirely new time series.

Some methods naturally fit better in one format over another, e.g., lags are too expensive for extraction; time series decomposition only has to be performed once, because it has a low level of 'leakage' so is better suited to transformation; and forecast methods attempt to predict multiple future training samples, so won't work with extraction that only delivers one value per time series. Furthermore all non time-series (cross-sectional) transformation and extraction techniques can not make use of extraction as it is solely a time-series method.

Lastly, when we want to double apply specific functions we can apply it as a transformation/interaction then all the extraction methods can be applied to this feature as well. For example, if we calculate a smoothing function (transformation) then all other extraction functions (median, entropy, linearity etc.) can now be applied to that smoothing function, including the application of the smoothing function itself, e.g., a double smooth, double lag, double filter etc. So separating these methods out give us great flexibility.

Decorator

def set_property(key, value):
    """
    This method returns a decorator that sets the property key of the function to value
    """
    def decorate_func(func):
        setattr(func, key, value)
        if func.__doc__ and key == "fctype":
            func.__doc__ = func.__doc__ + "\n\n    *This function is of type: " + value + "*\n"
        return func
    return decorate_func

(1) Energy

You can calculate the linear, non-linear and absolute energy of a time series. In signal processing, the energy $E_S$ of a continuous-time signal $x(t)$ is defined as the area under the squared magnitude of the considered signal. Mathematically, $E_{s}=\langle x(t), x(t)\rangle=\int_{-\infty}^{\infty}|x(t)|^{2} d t$

(i) Absolute Energy

Returns the absolute energy of the time series which is the sum over the squared values

#-> In Package
def abs_energy(x):

    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    return np.dot(x, x)

extract.abs_energy(df["Close"])

(2) Distance

Here we widely define distance measures as those that take a difference between attributes or series of datapoints.

(i) Complexity-Invariant Distance

This function calculator is an estimate for a time series complexity.

#-> In Package
def cid_ce(x, normalize):

    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    if normalize:
        s = np.std(x)
        if s!=0:
            x = (x - np.mean(x))/s
        else:
            return 0.0

    x = np.diff(x)
    return np.sqrt(np.dot(x, x))

extract.cid_ce(df["Close"], True)

(3) Differencing

Many alternatives to differencing exists, one can for example take the difference of every other value, take the squared difference, take the fractional difference, or like our example, take the mean absolute difference.

(i) Mean Absolute Change

Returns the mean over the absolute differences between subsequent time series values.

#-> In Package
def mean_abs_change(x):
    return np.mean(np.abs(np.diff(x)))

extract.mean_abs_change(df["Close"])

(4) Derivative

Features where the emphasis is on the rate of change.

(i) Mean Central Second Derivative

Returns the mean value of a central approximation of the second derivative

#-> In Package
def _roll(a, shift):
    if not isinstance(a, np.ndarray):
        a = np.asarray(a)
    idx = shift % len(a)
    return np.concatenate([a[-idx:], a[:-idx]])

def mean_second_derivative_central(x):

    diff = (_roll(x, 1) - 2 * np.array(x) + _roll(x, -1)) / 2.0
    return np.mean(diff[1:-1])

extract.mean_second_derivative_central(df["Close"])

(5) Volatility

Volatility is a statistical measure of the dispersion of a time-series.

(i) Variance Larger than Standard Deviation

#-> In Package
def variance_larger_than_standard_deviation(x):

    y = np.var(x)
    return y > np.sqrt(y)

extract.variance_larger_than_standard_deviation(df["Close"])

(ii) Variability Index

Variability Index is a way to measure how smooth or 'variable' a time series is.

var_index_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

@set_property("fctype", "combiner")
@set_property("custom", True)
def var_index(time,param=var_index_param):
    final = []
    keys = []
    for key, magnitude in param.items():
      w = 1.0 / np.power(np.subtract(time[1:], time[:-1]), 2)
      w_mean = np.mean(w)

      N = len(time)
      sigma2 = np.var(magnitude)

      S1 = sum(w * (magnitude[1:] - magnitude[:-1]) ** 2)
      S2 = sum(w)

      eta_e = (w_mean * np.power(time[N - 1] -
                time[0], 2) * S1 / (sigma2 * S2 * N ** 2))
      final.append(eta_e)
      keys.append(key)
    return {"Interact__{}".format(k): eta_e for eta_e, k in zip(final,keys) }

extract.var_index(df["Close"].values,var_index_param)

(6) Shape

Features that emphasises a particular shape not ordinarily considered as a distribution statistic. Extends to derivations of the original time series too For example a feature looking at the sinusoidal shape of an autocorrelation plot.

(i) Symmetrical

Boolean variable denoting if the distribution of x looks symmetric.

#-> In Package
def symmetry_looking(x, param=[{"r": 0.2}]):

    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    mean_median_difference = np.abs(np.mean(x) - np.median(x))
    max_min_difference = np.max(x) - np.min(x)
    return [("r_{}".format(r["r"]), mean_median_difference < (r["r"] * max_min_difference))
            for r in param]
            
extract.symmetry_looking(df["Close"])

(7) Occurrence

Looking at the occurrence, and reoccurence of defined values.

(i) Has Duplicate Max

#-> In Package
def has_duplicate_max(x):
    """
    Checks if the maximum value of x is observed more than once

    :param x: the time series to calculate the feature of
    :type x: numpy.ndarray
    :return: the value of this feature
    :return type: bool
    """
    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    return np.sum(x == np.max(x)) >= 2

extract.has_duplicate_max(df["Close"])

(8) Autocorrelation

Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.

(i) Partial Autocorrelation

Partial autocorrelation is a summary of the relationship between an observation in a time series with observations at prior time steps with the relationships of intervening observations removed.

#-> In Package
from statsmodels.tsa.stattools import acf, adfuller, pacf

def partial_autocorrelation(x, param=[{"lag": 1}]):

    # Check the difference between demanded lags by param and possible lags to calculate (depends on len(x))
    max_demanded_lag = max([lag["lag"] for lag in param])
    n = len(x)

    # Check if list is too short to make calculations
    if n <= 1:
        pacf_coeffs = [np.nan] * (max_demanded_lag + 1)
    else:
        if (n <= max_demanded_lag):
            max_lag = n - 1
        else:
            max_lag = max_demanded_lag
        pacf_coeffs = list(pacf(x, method="ld", nlags=max_lag))
        pacf_coeffs = pacf_coeffs + [np.nan] * max(0, (max_demanded_lag - max_lag))

    return [("lag_{}".format(lag["lag"]), pacf_coeffs[lag["lag"]]) for lag in param]

extract.partial_autocorrelation(df["Close"])

(9) Stochasticity

Stochastic refers to a randomly determined process. Any features trying to capture stochasticity by degree or type are included under this branch.

(i) Augmented Dickey Fuller

The Augmented Dickey-Fuller test is a hypothesis test which checks whether a unit root is present in a time series sample.

#-> In Package
def augmented_dickey_fuller(x, param=[{"attr": "teststat"}]):

    res = None
    try:
        res = adfuller(x)
    except LinAlgError:
        res = np.NaN, np.NaN, np.NaN
    except ValueError: # occurs if sample size is too small
        res = np.NaN, np.NaN, np.NaN
    except MissingDataError: # is thrown for e.g. inf or nan in the data
        res = np.NaN, np.NaN, np.NaN

    return [('attr_"{}"'.format(config["attr"]),
                  res[0] if config["attr"] == "teststat"
             else res[1] if config["attr"] == "pvalue"
             else res[2] if config["attr"] == "usedlag" else np.NaN)
            for config in param]

extract.augmented_dickey_fuller(df["Close"])

(10) Averages

(i) Median of Magnitudes Skew

@set_property("fctype", "simple")
@set_property("custom", True)
def gskew(x):
    interpolation="nearest"
    median_mag = np.median(x)
    F_3_value = np.percentile(x, 3, interpolation=interpolation)
    F_97_value = np.percentile(x, 97, interpolation=interpolation)

    skew = (np.median(x[x <= F_3_value]) +
            np.median(x[x >= F_97_value]) - 2 * median_mag)

    return skew

extract.gskew(df["Close"])

(ii) Stetson Mean

An iteratively weighted mean used in the Stetson variability index

stestson_param = {"weight":100., "alpha":2., "beta":2., "tol":1.e-6, "nmax":20}

@set_property("fctype", "combiner")
@set_property("custom", True)
def stetson_mean(x, param=stestson_param):
    
    weight= stestson_param["weight"]
    alpha= stestson_param["alpha"]
    beta = stestson_param["beta"]
    tol= stestson_param["tol"]
    nmax= stestson_param["nmax"]
    
    
    mu = np.median(x)
    for i in range(nmax):
        resid = x - mu
        resid_err = np.abs(resid) * np.sqrt(weight)
        weight1 = weight / (1. + (resid_err / alpha)**beta)
        weight1 /= weight1.mean()
        diff = np.mean(x * weight1) - mu
        mu += diff
        if (np.abs(diff) < tol*np.abs(mu) or np.abs(diff) < tol):
            break

    return mu

extract.stetson_mean(df["Close"])

(11) Size

(i) Lenght

#-> In Package
def length(x):
    return len(x)
    
extract.length(df["Close"])

(12) Count

(i) Count Above Mean

Returns the number of values in x that are higher than the mean of x

#-> In Package
def count_above_mean(x):
    m = np.mean(x)
    return np.where(x > m)[0].size

extract.count_above_mean(df["Close"])

(13) Streaks

(i) Longest Strike Below Mean

Returns the length of the longest consecutive subsequence in x that is smaller than the mean of x

#-> In Package
import itertools
def get_length_sequences_where(x):

    if len(x) == 0:
        return [0]
    else:
        res = [len(list(group)) for value, group in itertools.groupby(x) if value == 1]
        return res if len(res) > 0 else [0]

def longest_strike_below_mean(x):

    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    return np.max(get_length_sequences_where(x <= np.mean(x))) if x.size > 0 else 0

extract.longest_strike_below_mean(df["Close"])

(ii) Wozniak

This is an astronomical feature, we count the number of three consecutive data points that are brighter or fainter than $2σ$ and normalize the number by $N−2$

woz_param = [{"consecutiveStar": n} for n in [2, 4]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def wozniak(magnitude, param=woz_param):

    iters = []
    for consecutiveStar in [stars["consecutiveStar"] for stars in param]:
      N = len(magnitude)
      if N < consecutiveStar:
          return 0
      sigma = np.std(magnitude)
      m = np.mean(magnitude)
      count = 0

      for i in range(N - consecutiveStar + 1):
          flag = 0
          for j in range(consecutiveStar):
              if(magnitude[i + j] > m + 2 * sigma or
                  magnitude[i + j] < m - 2 * sigma):
                  flag = 1
              else:
                  flag = 0
                  break
          if flag:
              count = count + 1
      iters.append(count * 1.0 / (N - consecutiveStar + 1))

    return [("consecutiveStar_{}".format(config["consecutiveStar"]), iters[en] )  for en, config in enumerate(param)]

extract.wozniak(df["Close"])

(14) Location

(i) Last location of Maximum

Returns the relative last location of the maximum value of x. last_location_of_minimum(x),

#-> In Package
def last_location_of_maximum(x):

    x = np.asarray(x)
    return 1.0 - np.argmax(x[::-1]) / len(x) if len(x) > 0 else np.NaN

extract.last_location_of_maximum(df["Close"])

(15) Model Coefficients

Any coefficient that are obtained from a model that might help in the prediction problem. For example here we might include coefficients of polynomial $h(x)$, which has been fitted to the deterministic dynamics of Langevin model.

(i) FFT Coefficient

Calculates the fourier coefficients of the one-dimensional discrete Fourier Transform for real input.

#-> In Package
def fft_coefficient(x, param = [{"coeff": 10, "attr": "real"}]):

    assert min([config["coeff"] for config in param]) >= 0, "Coefficients must be positive or zero."
    assert set([config["attr"] for config in param]) <= set(["imag", "real", "abs", "angle"]), \
        'Attribute must be "real", "imag", "angle" or "abs"'

    fft = np.fft.rfft(x)

    def complex_agg(x, agg):
        if agg == "real":
            return x.real
        elif agg == "imag":
            return x.imag
        elif agg == "abs":
            return np.abs(x)
        elif agg == "angle":
            return np.angle(x, deg=True)

    res = [complex_agg(fft[config["coeff"]], config["attr"]) if config["coeff"] < len(fft)
           else np.NaN for config in param]
    index = [('coeff_{}__attr_"{}"'.format(config["coeff"], config["attr"]),res[0]) for config in param]
    return index

extract.fft_coefficient(df["Close"])

(ii) AR Coefficient

This feature calculator fits the unconditional maximum likelihood of an autoregressive AR(k) process.

#-> In Package
from statsmodels.tsa.ar_model import AR

def ar_coefficient(x, param=[{"coeff": 5, "k": 5}]):

    calculated_ar_params = {}

    x_as_list = list(x)
    calculated_AR = AR(x_as_list)

    res = {}

    for parameter_combination in param:
        k = parameter_combination["k"]
        p = parameter_combination["coeff"]

        column_name = "k_{}__coeff_{}".format(k, p)

        if k not in calculated_ar_params:
            try:
                calculated_ar_params[k] = calculated_AR.fit(maxlag=k, solver="mle").params
            except (LinAlgError, ValueError):
                calculated_ar_params[k] = [np.NaN]*k

        mod = calculated_ar_params[k]

        if p <= k:
            try:
                res[column_name] = mod[p]
            except IndexError:
                res[column_name] = 0
        else:
            res[column_name] = np.NaN

    return [(key, value) for key, value in res.items()]

extract.ar_coefficient(df["Close"])

(16) Quantiles

This includes finding normal quantile values in the series, but also quantile derived measures like change quantiles and index max quantiles.

(i) Index Mass Quantile

The relative index $i$ where $q%$ of the mass of the time series $x$ lie left of $i$ .

#-> In Package
def index_mass_quantile(x, param=[{"q": 0.3}]):

    x = np.asarray(x)
    abs_x = np.abs(x)
    s = sum(abs_x)

    if s == 0:
        # all values in x are zero or it has length 0
        return [("q_{}".format(config["q"]), np.NaN) for config in param]
    else:
        # at least one value is not zero
        mass_centralized = np.cumsum(abs_x) / s
        return [("q_{}".format(config["q"]), (np.argmax(mass_centralized >= config["q"])+1)/len(x)) for config in param]

extract.index_mass_quantile(df["Close"])

(17) Peaks

(i) Number of CWT Peaks

This feature calculator searches for different peaks in x.

from scipy.signal import cwt, find_peaks_cwt, ricker, welch

cwt_param = [ka for ka in [2,6,9]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def number_cwt_peaks(x, param=cwt_param):

    return [("CWTPeak_{}".format(n), len(find_peaks_cwt(vector=x, widths=np.array(list(range(1, n + 1))), wavelet=ricker))) for n in param]

extract.number_cwt_peaks(df["Close"])

(18) Density

The density, and more specifically the power spectral density of the signal describes the power present in the signal as a function of frequency, per unit frequency.

(i) Cross Power Spectral Density

This feature calculator estimates the cross power spectral density of the time series $x$ at different frequencies.

#-> In Package
def spkt_welch_density(x, param=[{"coeff": 5}]):
    freq, pxx = welch(x, nperseg=min(len(x), 256))
    coeff = [config["coeff"] for config in param]
    indices = ["coeff_{}".format(i) for i in coeff]

    if len(pxx) <= np.max(coeff):  # There are fewer data points in the time series than requested coefficients

        # filter coefficients that are not contained in pxx
        reduced_coeff = [coefficient for coefficient in coeff if len(pxx) > coefficient]
        not_calculated_coefficients = [coefficient for coefficient in coeff
                                       if coefficient not in reduced_coeff]

        # Fill up the rest of the requested coefficients with np.NaNs
        return zip(indices, list(pxx[reduced_coeff]) + [np.NaN] * len(not_calculated_coefficients))
    else:
        return pxx[coeff].ravel()[0]

extract.spkt_welch_density(df["Close"])

(19) Linearity

Any measure of linearity that might make use of something like the linear least-squares regression for the values of the time series. This can be against the time series minus one and many other alternatives.

(i) Linear Trend Time Wise

Calculate a linear least-squares regression for the values of the time series versus the sequence from 0 to length of the time series minus one.

from scipy.stats import linregress

#-> In Package
def linear_trend_timewise(x, param= [{"attr": "pvalue"}]):

    ix = x.index

    # Get differences between each timestamp and the first timestamp in seconds.
    # Then convert to hours and reshape for linear regression
    times_seconds = (ix - ix[0]).total_seconds()
    times_hours = np.asarray(times_seconds / float(3600))

    linReg = linregress(times_hours, x.values)

    return [("attr_\"{}\"".format(config["attr"]), getattr(linReg, config["attr"]))
            for config in param]

extract.linear_trend_timewise(df["Close"])

(20) Non-Linearity

(i) Schreiber Non-Linearity

#-> In Package
def c3(x, lag=3):
    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    n = x.size
    if 2 * lag >= n:
        return 0
    else:
        return np.mean((_roll(x, 2 * -lag) * _roll(x, -lag) * x)[0:(n - 2 * lag)])

extract.c3(df["Close"])

(21) Entropy

Any feature looking at the complexity of a time series. This is typically used in medical signal disciplines (EEG, EMG). There are multiple types of measures like spectral entropy, permutation entropy, sample entropy, approximate entropy, Lempel-Ziv complexity and other. This includes entropy measures and there derivations.

(i) Binned Entropy

Bins the values of x into max_bins equidistant bins.

#-> In Package
def binned_entropy(x, max_bins=10):
    if not isinstance(x, (np.ndarray, pd.Series)):
        x = np.asarray(x)
    hist, bin_edges = np.histogram(x, bins=max_bins)
    probs = hist / x.size
    return - np.sum(p * np.math.log(p) for p in probs if p != 0)

extract.binned_entropy(df["Close"])

(ii) SVD Entropy

SVD entropy is an indicator of the number of eigenvectors that are needed for an adequate explanation of the data set.

svd_param = [{"Tau": ta, "DE": de}
                      for ta in [4] 
                      for de in [3,6]]
                      
def _embed_seq(X,Tau,D):
  N =len(X)
  if D * Tau > N:
      print("Cannot build such a matrix, because D * Tau > N")
      exit()
  if Tau<1:
      print("Tau has to be at least 1")
      exit()
  Y= np.zeros((N - (D - 1) * Tau, D))

  for i in range(0, N - (D - 1) * Tau):
      for j in range(0, D):
          Y[i][j] = X[i + j * Tau]
  return Y                     

@set_property("fctype", "combiner")
@set_property("custom", True)
def svd_entropy(epochs, param=svd_param):
    axis=0
    
    final = []
    for par in param:

      def svd_entropy_1d(X, Tau, DE):
          Y = _embed_seq(X, Tau, DE)
          W = np.linalg.svd(Y, compute_uv=0)
          W /= sum(W)  # normalize singular values
          return -1 * np.sum(W * np.log(W))

      Tau = par["Tau"]
      DE = par["DE"]

      final.append(np.apply_along_axis(svd_entropy_1d, axis, epochs, Tau, DE).ravel()[0])


    return [("Tau_\"{}\"__De_{}\"".format(par["Tau"], par["DE"]), final[en]) for en, par in enumerate(param)]

extract.svd_entropy(df["Close"].values)

(iii) Hjort

The Complexity parameter represents the change in frequency. The parameter compares the signal's similarity to a pure sine wave, where the value converges to 1 if the signal is more similar.

def _hjorth_mobility(epochs):
    diff = np.diff(epochs, axis=0)
    sigma0 = np.std(epochs, axis=0)
    sigma1 = np.std(diff, axis=0)
    return np.divide(sigma1, sigma0)

@set_property("fctype", "simple")
@set_property("custom", True)
def hjorth_complexity(epochs):
    diff1 = np.diff(epochs, axis=0)
    diff2 = np.diff(diff1, axis=0)
    sigma1 = np.std(diff1, axis=0)
    sigma2 = np.std(diff2, axis=0)
    return np.divide(np.divide(sigma2, sigma1), _hjorth_mobility(epochs))

extract.hjorth_complexity(df["Close"])

(22) Fixed Points

Fixed points and equilibria as identified from fitted models.

(i) Langevin Fixed Points

Largest fixed point of dynamics $max\ {h(x)=0}$ estimated from polynomial $h(x)$ which has been fitted to the deterministic dynamics of Langevin model

#-> In Package
def _estimate_friedrich_coefficients(x, m, r):
    assert m > 0, "Order of polynomial need to be positive integer, found {}".format(m)
    df = pd.DataFrame({'signal': x[:-1], 'delta': np.diff(x)})
    try:
        df['quantiles'] = pd.qcut(df.signal, r)
    except ValueError:
        return [np.NaN] * (m + 1)

    quantiles = df.groupby('quantiles')

    result = pd.DataFrame({'x_mean': quantiles.signal.mean(), 'y_mean': quantiles.delta.mean()})
    result.dropna(inplace=True)

    try:
        return np.polyfit(result.x_mean, result.y_mean, deg=m)
    except (np.linalg.LinAlgError, ValueError):
        return [np.NaN] * (m + 1)


def max_langevin_fixed_point(x, r=3, m=30):
    coeff = _estimate_friedrich_coefficients(x, m, r)

    try:
        max_fixed_point = np.max(np.real(np.roots(coeff)))
    except (np.linalg.LinAlgError, ValueError):
        return np.nan

    return max_fixed_point

extract.max_langevin_fixed_point(df["Close"])

(23) Amplitude

Features derived from peaked values in either the positive or negative direction.

(i) Willison Amplitude

This feature is defined as the amount of times that the change in the signal amplitude exceeds a threshold.

will_param = [ka for ka in [0.2,3]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def willison_amplitude(X, param=will_param):
  return [("Thresh_{}".format(n),np.sum(np.abs(np.diff(X)) >= n)) for n in param]

extract.willison_amplitude(df["Close"])

(ii) Percent Amplitude

Returns the largest distance from the median value, measured as a percentage of the median

perc_param = [{"base":ba, "exponent":exp} for ba in [3,5] for exp in [-0.1,-0.2]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def percent_amplitude(x, param =perc_param):
    final = []
    for par in param:
      linear_scale_data = par["base"] ** (par["exponent"] * x)
      y_max = np.max(linear_scale_data)
      y_min = np.min(linear_scale_data)
      y_med = np.median(linear_scale_data)
      final.append(max(abs((y_max - y_med) / y_med), abs((y_med - y_min) / y_med)))

    return [("Base_{}__Exp{}".format(pa["base"],pa["exponent"]),fin) for fin, pa in zip(final,param)]

extract.percent_amplitude(df["Close"])

(24) Probability

(i) Cadence Probability

Given the observed distribution of time lags cads, compute the probability that the next observation occurs within time minutes of an arbitrary epoch.

#-> fixes required
import scipy.stats as stats

cad_param = [0.1,1000, -234]

@set_property("fctype", "combiner")
@set_property("custom", True)
def cad_prob(cads, param=cad_param):
    return [("time_{}".format(time), stats.percentileofscore(cads, float(time) / (24.0 * 60.0)) / 100.0) for time in param]
    
extract.cad_prob(df["Close"])

(25) Crossings

Calculates the crossing of the series with other defined values or series.

(i) Zero Crossing Derivative

The positioning of the edge point is located at the zero crossing of the first derivative of the filter.

zero_param = [0.01, 8]

@set_property("fctype", "combiner")
@set_property("custom", True)
def zero_crossing_derivative(epochs, param=zero_param):
    diff = np.diff(epochs)
    norm = diff-diff.mean()
    return [("e_{}".format(e), np.apply_along_axis(lambda epoch: np.sum(((epoch[:-5] <= e) & (epoch[5:] > e))), 0, norm).ravel()[0]) for e in param]

extract.zero_crossing_derivative(df["Close"])

(26) Fluctuations

These features are again from medical signal sciences, but under this category we would include values such as fluctuation based entropy measures, fluctuation of correlation dynamics, and co-fluctuations.

(i) Detrended Fluctuation Analysis (DFA)

DFA Calculate the Hurst exponent using DFA analysis.

from scipy.stats import kurtosis as _kurt
from scipy.stats import skew as _skew
import numpy as np

@set_property("fctype", "simple")
@set_property("custom", True)
def detrended_fluctuation_analysis(epochs):
    def dfa_1d(X, Ave=None, L=None):
        X = np.array(X)

        if Ave is None:
            Ave = np.mean(X)

        Y = np.cumsum(X)
        Y -= Ave

        if L is None:
            L = np.floor(len(X) * 1 / (
                    2 ** np.array(list(range(1, int(np.log2(len(X))) - 4))))
                            )
            
        F = np.zeros(len(L))  # F(n) of different given box length n

        for i in range(0, len(L)):
            n = int(L[i])  # for each box length L[i]
            if n == 0:
                print("time series is too short while the box length is too big")
                print("abort")
                exit()
            for j in range(0, len(X), n):  # for each box
                if j + n < len(X):
                    c = list(range(j, j + n))
                    # coordinates of time in the box
                    c = np.vstack([c, np.ones(n)]).T
                    # the value of data in the box
                    y = Y[j:j + n]
                    # add residue in this box
                    F[i] += np.linalg.lstsq(c, y, rcond=None)[1]
            F[i] /= ((len(X) / n) * n)
        F = np.sqrt(F)

        stacked = np.vstack([np.log(L), np.ones(len(L))])
        stacked_t = stacked.T
        Alpha = np.linalg.lstsq(stacked_t, np.log(F), rcond=None)

        return Alpha[0][0]

    return np.apply_along_axis(dfa_1d, 0, epochs).ravel()[0]

extract.detrended_fluctuation_analysis(df["Close"])

(27) Information

Closely related to entropy and complexity measures. Any measure that attempts to measure the amount of information from an observable variable is included here.

(i) Fisher Information

Fisher information is a statistical information concept distinct from, and earlier than, Shannon information in communication theory.

def _embed_seq(X, Tau, D):

    shape = (X.size - Tau * (D - 1), D)
    strides = (X.itemsize, Tau * X.itemsize)
    return np.lib.stride_tricks.as_strided(X, shape=shape, strides=strides)

fisher_param = [{"Tau":ta, "DE":de} for ta in [3,15] for de in [10,5]]

@set_property("fctype", "combiner")
@set_property("custom", True)
def fisher_information(epochs, param=fisher_param):
    def fisher_info_1d(a, tau, de):
        # taken from pyeeg improvements

        mat = _embed_seq(a, tau, de)
        W = np.linalg.svd(mat, compute_uv=False)
        W /= sum(W)  # normalize singular values
        FI_v = (W[1:] - W[:-1]) ** 2 / W[:-1]
        return np.sum(FI_v)

    return [("Tau_{}__DE_{}".format(par["Tau"], par["DE"]),np.apply_along_axis(fisher_info_1d, 0, epochs, par["Tau"], par["DE"]).ravel()[0]) for par in param]

extract.fisher_information(df["Close"])

(28) Fractals

In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is measured.

(i) Highuchi Fractal

Compute a Higuchi Fractal Dimension of a time series

hig_para = [{"Kmax": 3},{"Kmax": 5}]

@set_property("fctype", "combiner")
@set_property("custom", True)
def higuchi_fractal_dimension(epochs, param=hig_para):
    def hfd_1d(X, Kmax):
        
        L = []
        x = []
        N = len(X)
        for k in range(1, Kmax):
            Lk = []
            for m in range(0, k):
                Lmk = 0
                for i in range(1, int(np.floor((N - m) / k))):
                    Lmk += abs(X[m + i * k] - X[m + i * k - k])
                Lmk = Lmk * (N - 1) / np.floor((N - m) / float(k)) / k
                Lk.append(Lmk)
            L.append(np.log(np.mean(Lk)))
            x.append([np.log(float(1) / k), 1])

        (p, r1, r2, s) = np.linalg.lstsq(x, L, rcond=None)
        return p[0]
    
    return [("Kmax_{}".format(config["Kmax"]), np.apply_along_axis(hfd_1d, 0, epochs, config["Kmax"]).ravel()[0] ) for  config in param]
    
extract.higuchi_fractal_dimension(df["Close"])

(ii) Petrosian Fractal

Compute a Petrosian Fractal Dimension of a time series.

@set_property("fctype", "simple")
@set_property("custom", True)
def petrosian_fractal_dimension(epochs):
    def pfd_1d(X, D=None):
        # taken from pyeeg
        """Compute Petrosian Fractal Dimension of a time series from either two
        cases below:
            1. X, the time series of type list (default)
            2. D, the first order differential sequence of X (if D is provided,
               recommended to speed up)
        In case 1, D is computed using Numpy's difference function.
        To speed up, it is recommended to compute D before calling this function
        because D may also be used by other functions whereas computing it here
        again will slow down.
        """
        if D is None:
            D = np.diff(X)
            D = D.tolist()
        N_delta = 0  # number of sign changes in derivative of the signal
        for i in range(1, len(D)):
            if D[i] * D[i - 1] < 0:
                N_delta += 1
        n = len(X)
        return np.log10(n) / (np.log10(n) + np.log10(n / n + 0.4 * N_delta))
    return np.apply_along_axis(pfd_1d, 0, epochs).ravel()[0]

extract.petrosian_fractal_dimension(df["Close"])

(29) Exponent

(i) Hurst Exponent

The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series, and the rate at which these decrease as the lag between pairs of values increases.

@set_property("fctype", "simple")
@set_property("custom", True)
def hurst_exponent(epochs):
    def hurst_1d(X):

        X = np.array(X)
        N = X.size
        T = np.arange(1, N + 1)
        Y = np.cumsum(X)
        Ave_T = Y / T

        S_T = np.zeros(N)
        R_T = np.zeros(N)
        for i in range(N):
            S_T[i] = np.std(X[:i + 1])
            X_T = Y - T * Ave_T[i]
            R_T[i] = np.ptp(X_T[:i + 1])

        for i in range(1, len(S_T)):
            if np.diff(S_T)[i - 1] != 0:
                break
        for j in range(1, len(R_T)):
            if np.diff(R_T)[j - 1] != 0:
                break
        k = max(i, j)
        assert k < 10, "rethink it!"

        R_S = R_T[k:] / S_T[k:]
        R_S = np.log(R_S)

        n = np.log(T)[k:]
        A = np.column_stack((n, np.ones(n.size)))
        [m, c] = np.linalg.lstsq(A, R_S, rcond=None)[0]
        H = m
        return H
    return np.apply_along_axis(hurst_1d, 0, epochs).ravel()[0]

extract.hurst_exponent(df["Close"])

(ii) Largest Lyauponov Exponent

In mathematics the Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a quantity that characterizes the rate of separation of infinitesimally close trajectories.

def _embed_seq(X, Tau, D):
    shape = (X.size - Tau * (D - 1), D)
    strides = (X.itemsize, Tau * X.itemsize)
    return np.lib.stride_tricks.as_strided(X, shape=shape, strides=strides)

lyaup_param = [{"Tau":4, "n":3, "T":10, "fs":9},{"Tau":8, "n":7, "T":15, "fs":6}]

@set_property("fctype", "combiner")
@set_property("custom", True)
def largest_lyauponov_exponent(epochs, param=lyaup_param):
    def LLE_1d(x, tau, n, T, fs):

        Em = _embed_seq(x, tau, n)
        M = len(Em)
        A = np.tile(Em, (len(Em), 1, 1))
        B = np.transpose(A, [1, 0, 2])
        square_dists = (A - B) ** 2  # square_dists[i,j,k] = (Em[i][k]-Em[j][k])^2
        D = np.sqrt(square_dists[:, :, :].sum(axis=2))  # D[i,j] = ||Em[i]-Em[j]||_2

        # Exclude elements within T of the diagonal
        band = np.tri(D.shape[0], k=T) - np.tri(D.shape[0], k=-T - 1)
        band[band == 1] = np.inf
        neighbors = (D + band).argmin(axis=0)  # nearest neighbors more than T steps away

        # in_bounds[i,j] = (i+j <= M-1 and i+neighbors[j] <= M-1)
        inc = np.tile(np.arange(M), (M, 1))
        row_inds = (np.tile(np.arange(M), (M, 1)).T + inc)
        col_inds = (np.tile(neighbors, (M, 1)) + inc.T)
        in_bounds = np.logical_and(row_inds <= M - 1, col_inds <= M - 1)
        # Uncomment for old (miscounted) version
        # in_bounds = numpy.logical_and(row_inds < M - 1, col_inds < M - 1)
        row_inds[~in_bounds] = 0
        col_inds[~in_bounds] = 0

        # neighbor_dists[i,j] = ||Em[i+j]-Em[i+neighbors[j]]||_2
        neighbor_dists = np.ma.MaskedArray(D[row_inds, col_inds], ~in_bounds)
        J = (~neighbor_dists.mask).sum(axis=1)  # number of in-bounds indices by row
        # Set invalid (zero) values to 1; log(1) = 0 so sum is unchanged

        neighbor_dists[neighbor_dists == 0] = 1

        # !!! this fixes the divide by zero in log error !!!
        neighbor_dists.data[neighbor_dists.data == 0] = 1

        d_ij = np.sum(np.log(neighbor_dists.data), axis=1)
        mean_d = d_ij[J > 0] / J[J > 0]

        x = np.arange(len(mean_d))
        X = np.vstack((x, np.ones(len(mean_d)))).T
        [m, c] = np.linalg.lstsq(X, mean_d, rcond=None)[0]
        Lexp = fs * m
        return Lexp

    return [("Tau_{}__n_{}__T_{}__fs_{}".format(par["Tau"], par["n"], par["T"], par["fs"]), np.apply_along_axis(LLE_1d, 0, epochs, par["Tau"], par["n"], par["T"], par["fs"]).ravel()[0]) for par in param]
  
extract.largest_lyauponov_exponent(df["Close"])

(30) Spectral Analysis

Spectral analysis is analysis in terms of a spectrum of frequencies or related quantities such as energies, eigenvalues, etc.

(i) Whelch Method

The Whelch Method is an approach for spectral density estimation. It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies.

from scipy import signal, integrate

whelch_param = [100,200]

@set_property("fctype", "combiner")
@set_property("custom", True)
def whelch_method(data, param=whelch_param):

  final = []
  for Fs in param:
    f, pxx = signal.welch(data, fs=Fs, nperseg=1024)
    d = {'psd': pxx, 'freqs': f}
    df = pd.DataFrame(data=d)
    dfs = df.sort_values(['psd'], ascending=False)
    rows = dfs.iloc[:10]
    final.append(rows['freqs'].mean())
  
  return [("Fs_{}".format(pa),fin) for pa, fin in zip(param,final)]

extract.whelch_method(df["Close"])

#-> Basically same as above
freq_param = [{"fs":50, "sel":15},{"fs":200, "sel":20}]

@set_property("fctype", "combiner")
@set_property("custom", True)
def find_freq(serie, param=freq_param):

    final = []
    for par in param:
      fft0 = np.fft.rfft(serie*np.hanning(len(serie)))
      freqs = np.fft.rfftfreq(len(serie), d=1.0/par["fs"])
      fftmod = np.array([np.sqrt(fft0[i].real**2 + fft0[i].imag**2) for i in range(0, len(fft0))])
      d = {'fft': fftmod, 'freq': freqs}
      df = pd.DataFrame(d)
      hop = df.sort_values(['fft'], ascending=False)
      rows = hop.iloc[:par["sel"]]
      final.append(rows['freq'].mean())

    return [("Fs_{}__sel{}".format(pa["fs"],pa["sel"]),fin) for pa, fin in zip(param,final)]

extract.find_freq(df["Close"])

(31) Percentile

(i) Flux Percentile

Flux (or radiant flux) is the total amount of energy that crosses a unit area per unit time. Flux is an astronomical value, measured in joules per square metre per second (joules/m2/s), or watts per square metre. Here we provide the ratio of flux percentiles.

#-> In Package

import math
def flux_perc(magnitude):
    sorted_data = np.sort(magnitude)
    lc_length = len(sorted_data)

    F_60_index = int(math.ceil(0.60 * lc_length))
    F_40_index = int(math.ceil(0.40 * lc_length))
    F_5_index = int(math.ceil(0.05 * lc_length))
    F_95_index = int(math.ceil(0.95 * lc_length))

    F_40_60 = sorted_data[F_60_index] - sorted_data[F_40_index]
    F_5_95 = sorted_data[F_95_index] - sorted_data[F_5_index]
    F_mid20 = F_40_60 / F_5_95

    return {"FluxPercentileRatioMid20": F_mid20}

extract.flux_perc(df["Close"])

(32) Range

(i) Range of Cummulative Sum

@set_property("fctype", "simple")
@set_property("custom", True)
def range_cum_s(magnitude):
    sigma = np.std(magnitude)
    N = len(magnitude)
    m = np.mean(magnitude)
    s = np.cumsum(magnitude - m) * 1.0 / (N * sigma)
    R = np.max(s) - np.min(s)
    return {"Rcs": R}

extract.range_cum_s(df["Close"])

(33) Structural

Structural features, potential placeholders for future research.

(i) Structure Function

The structure function of rotation measures (RMs) contains information on electron density and magnetic field fluctuations when used i astronomy. It becomes a custom feature when used with your own unique time series data.

from scipy.interpolate import interp1d

struct_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

@set_property("fctype", "combiner")
@set_property("custom", True)
def structure_func(time, param=struct_param):

      dict_final = {}
      for key, magnitude in param.items():
        dict_final[key] = []
        Nsf, Np = 100, 100
        sf1, sf2, sf3 = np.zeros(Nsf), np.zeros(Nsf), np.zeros(Nsf)
        f = interp1d(time, magnitude)

        time_int = np.linspace(np.min(time), np.max(time), Np)
        mag_int = f(time_int)

        for tau in np.arange(1, Nsf):
            sf1[tau - 1] = np.mean(
                np.power(np.abs(mag_int[0:Np - tau] - mag_int[tau:Np]), 1.0))
            sf2[tau - 1] = np.mean(
                np.abs(np.power(
                    np.abs(mag_int[0:Np - tau] - mag_int[tau:Np]), 2.0)))
            sf3[tau - 1] = np.mean(
                np.abs(np.power(
                    np.abs(mag_int[0:Np - tau] - mag_int[tau:Np]), 3.0)))
        sf1_log = np.log10(np.trim_zeros(sf1))
        sf2_log = np.log10(np.trim_zeros(sf2))
        sf3_log = np.log10(np.trim_zeros(sf3))

        if len(sf1_log) and len(sf2_log):
            m_21, b_21 = np.polyfit(sf1_log, sf2_log, 1)
        else:

            m_21 = np.nan

        if len(sf1_log) and len(sf3_log):
            m_31, b_31 = np.polyfit(sf1_log, sf3_log, 1)
        else:

            m_31 = np.nan

        if len(sf2_log) and len(sf3_log):
            m_32, b_32 = np.polyfit(sf2_log, sf3_log, 1)
        else:

            m_32 = np.nan
        dict_final[key].append(m_21)
        dict_final[key].append(m_31)
        dict_final[key].append(m_32)

      return [("StructureFunction_{}__m_{}".format(key, name), li)  for key, lis in dict_final.items() for name, li in zip([21,31,32], lis)]

struct_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

extract.structure_func(df["Close"],struct_param)

(34) Distribution

(i) Kurtosis

#-> In Package
def kurtosis(x):

    if not isinstance(x, pd.Series):
        x = pd.Series(x)
    return pd.Series.kurtosis(x)

extract.kurtosis(df["Close"])

(ii) Stetson Kurtosis

@set_property("fctype", "simple")
@set_property("custom", True)
def stetson_k(x):
    """A robust kurtosis statistic."""
    n = len(x)
    x0 = stetson_mean(x, 1./20**2)
    delta_x = np.sqrt(n / (n - 1.)) * (x - x0) / 20
    ta = 1. / 0.798 * np.mean(np.abs(delta_x)) / np.sqrt(np.mean(delta_x**2))
    return ta
  
extract.stetson_k(df["Close"])

(5) Synthesise

Time-Series synthesisation (TSS) happens before the feature extraction step and Cross Sectional Synthesisation (CSS) happens after the feature extraction step. Currently I will only include a CSS package, in the future, I would further work on developing out this section. This area still has a lot of performance and stability issues. In the future it might be a more viable candidate to improve prediction.

from lightgbm import LGBMRegressor
from sklearn.metrics import mean_squared_error

def model(df_final):
  model = LGBMRegressor()
  test =  df_final.head(int(len(df_final)*0.4))
  train = df_final[~df_final.isin(test)].dropna()
  model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
  preds = model.predict(test.drop(["Close_1"],axis=1))
  test =  df_final.head(int(len(df_final)*0.4))
  train = df_final[~df_final.isin(test)].dropna()
  model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
  val = mean_squared_error(test["Close_1"],preds); 
  return val

pip install ctgan

from ctgan import CTGANSynthesizer

#discrete_columns = [""]
ctgan = CTGANSynthesizer()
ctgan.fit(df,epochs=10) #15

Random Benchmark

np.random.seed(1)
df_in = df.copy()
df_in["Close_1"] = np.random.permutation(df_in["Close_1"].values)
model(df_in)

Generated Performance

df_gen = ctgan.sample(len(df_in)*100)
model(df_gen)

As expected a cross-sectional technique, does not work well on time-series data, in the future, other methods will be investigated.

 

(6) Skeleton Example

Here I will perform tabular agumenting methods on a small dataset single digit features and around 250 instances. This is not necessarily the best sized dataset to highlight the performance of tabular augmentation as some method like extraction would be overkill as it would lead to dimensionality problems. It is also good to know that there are close to infinite number of ways to perform these augmentation methods. In the future, automated augmentation methods can guide the experiment process.

The approach taken in this skeleton is to develop running models that are tested after each augmentation to highlight what methods might work well on this particular dataset. The metric we will use is mean squared error. In this implementation we do not have special hold-out sets.

The above framework of implementation will be consulted, but one still have to be strategic as to when you apply what function, and you have to make sure that you are processing your data with appropriate techniques (drop null values, fill null values) at the appropriate time.

Validation

Develop Model and Define Metric

from lightgbm import LGBMRegressor
from sklearn.metrics import mean_squared_error

def model(df_final):
  model = LGBMRegressor()
  test =  df_final.head(int(len(df_final)*0.4))
  train = df_final[~df_final.isin(test)].dropna()
  model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
  preds = model.predict(test.drop(["Close_1"],axis=1))
  test =  df_final.head(int(len(df_final)*0.4))
  train = df_final[~df_final.isin(test)].dropna()
  model = model.fit(train.drop(["Close_1"],axis=1),train["Close_1"])
  val = mean_squared_error(test["Close_1"],preds); 
  return val

Reload Data

df = data_copy()

model(df)

302.61676570345287

(1) (7) (i) Transformation - Decomposition - Naive

## If Inferred Seasonality is Too Large Default to Five
seasons = transform.infer_seasonality(df["Close"],index=0) 
df_out = transform.naive_dec(df.copy(), ["Close","Open"], freq=5)
model(df_out) #improvement

274.34477082783525

(1) (8) (i) Transformation - Filter - Baxter-King-Bandpass

df_out = transform.bkb(df_out, ["Close","Low"])
df_best = df_out.copy()
model(df_out) #improvement

267.1826850968307

(1) (3) (i) Transformation - Differentiation - Fractional

df_out = transform.fast_fracdiff(df_out, ["Close_BPF"],0.5)
model(df_out) #null

267.7083192402742

(1) (1) (i) Transformation - Scaling - Robust Scaler

df_out = df_out.dropna()
df_out = transform.robust_scaler(df_out, drop=["Close_1"])
model(df_out) #noisy

270.96980399571214

(2) (2) (i) Interactions - Operator - Multiplication/Division

df_out.head()

	Close_1	High	Low	Open	Close	Volume	Adj Close	Close_NDDT	Close_NDDS	Close_NDDR	Open_NDDT	Open_NDDS	Open_NDDR	Close_BPF	Low_BPF	Close_BPF_frac
Date
2019-01-08	338.529999	1.018413	0.964048	1.096600	1.001175	-0.162616	1.001175	0.832297	0.834964	1.335433	0.758743	0.691596	2.259884	-2.534142	-2.249135	-3.593612
2019-01-09	344.970001	1.012068	1.023302	1.011466	1.042689	-0.501798	1.042689	0.908963	-0.165036	1.111346	0.835786	0.333361	1.129783	-3.081959	-2.776302	-2.523465
2019-01-10	347.260010	1.035581	1.027563	0.996969	1.126762	-0.367576	1.126762	1.029347	2.120026	0.853697	0.907588	0.000000	0.533777	-2.052768	-2.543449	-0.747382
2019-01-11	334.399994	1.073153	1.120506	1.098313	1.156658	-0.586571	1.156658	1.109144	-5.156051	0.591990	1.002162	-0.666639	0.608516	-0.694642	-0.831670	0.414063
2019-01-14	344.429993	0.999627	1.056991	1.102135	0.988773	-0.541752	0.988773	1.107633	0.000000	-0.660350	1.056302	-0.915491	0.263025	-0.645590	-0.116166	-0.118012

df_out = interact.muldiv(df_out, ["Close","Open_NDDS","Low_BPF"]) 
model(df_out) #noisy

285.6420643864313

df_r = df_out.copy()

(2) (6) (i) Interactions - Speciality - Technical

import ta
df = interact.tech(df)
df_out = pd.merge(df_out,  df.iloc[:,7:], left_index=True, right_index=True, how="left")

Clean Dataframe and Metric

"""Droping column where missing values are above a threshold"""
df_out = df_out.dropna(thresh = len(df_out)*0.95, axis = "columns") 
df_out = df_out.dropna()
df_out = df_out.replace([np.inf, -np.inf], np.nan).ffill().fillna(0)
close = df_out["Close"].copy()
df_d = df_out.copy()
model(df_out) #improve

592.52971755184

(3) (1) (i) Mapping - Eigen Decomposition - PCA

from sklearn.decomposition import PCA, IncrementalPCA, KernelPCA

df_out = transform.robust_scaler(df_out, drop=["Close_1"])

df_out = df_out.replace([np.inf, -np.inf], np.nan).ffill().fillna(0)
df_out = mapper.pca_feature(df_out, drop_cols=["Close_1"], variance_or_components=0.9, n_components=8,non_linear=False)

model(df_out) #noisy but not too bad given the 10 fold dimensionality reduction

687.158330455884

(4) Extracting

Here at first, I show the functions that have been added to the DeltaPy fork of tsfresh. You have to add your own personal adjustments based on the features you would like to construct. I am using self-developed features, but you can also use TSFresh's community functions.

The following files have been appropriately ammended (Get in contact for advice)

1. https://github.com/firmai/tsfresh/blob/master/tsfresh/feature_extraction/settings.py
2. https://github.com/firmai/tsfresh/blob/master/tsfresh/feature_extraction/feature_calculators.py
3. https://github.com/firmai/tsfresh/blob/master/tsfresh/feature_extraction/extraction.py

(4) (10) (i) Extracting - Averages - GSkew

extract.gskew(df_out["PCA_1"])

-0.7903067336449059

(4) (21) (ii) Extracting - Entropy - SVD Entropy

svd_param = [{"Tau": ta, "DE": de}
                      for ta in [4] 
                      for de in [3,6]]

extract.svd_entropy(df_out["PCA_1"],svd_param)

[('Tau_"4"__De_3"', 0.7234823323374294),
 ('Tau_"4"__De_6"', 1.3014347840145244)]

(4) (13) (ii) Extracting - Streaks - Wozniak

woz_param = [{"consecutiveStar": n} for n in [2, 4]]

extract.wozniak(df_out["PCA_1"],woz_param)

[('consecutiveStar_2', 0.012658227848101266), ('consecutiveStar_4', 0.0)]

(4) (28) (i) Extracting - Fractal - Higuchi

hig_param = [{"Kmax": 3},{"Kmax": 5}]

extract.higuchi_fractal_dimension(df_out["PCA_1"],hig_param)

[('Kmax_3', 0.577913816027104), ('Kmax_5', 0.8176960510304725)]

(4) (5) (ii) Extracting - Volatility - Variability Index

var_index_param = {"Volume":df["Volume"].values, "Open": df["Open"].values}

extract.var_index(df["Close"].values,var_index_param)

{'Interact__Open': 0.00396022538846289,
 'Interact__Volume': 0.20550155114176533}

Time Series Extraction

pip install git+git://github.com/firmai/tsfresh.git

#Construct the preferred input dataframe.
from tsfresh.utilities.dataframe_functions import roll_time_series
df_out["ID"] = 0
periods = 30
df_out = df_out.reset_index()
df_ts = roll_time_series(df_out,"ID","Date",None,1,periods)
counts = df_ts['ID'].value_counts()
df_ts = df_ts[df_ts['ID'].isin(counts[counts > periods].index)]

#Perform extraction
from tsfresh.feature_extraction import extract_features, CustomFCParameters
settings_dict = CustomFCParameters()
settings_dict["var_index"] = {"PCA_1":None, "PCA_2": None}
df_feat = extract_features(df_ts.drop(["Close_1"],axis=1),default_fc_parameters=settings_dict,column_id="ID",column_sort="Date")

Feature Extraction: 100%|██████████| 5/5 [00:10<00:00,  2.14s/it]

# Cleaning operations
import pandasvault as pv
df_feat2 = df_feat.copy()
df_feat = df_feat.dropna(thresh = len(df_feat)*0.50, axis = "columns")
df_feat_cons = pv.constant_feature_detect(data=df_feat,threshold=0.9)
df_feat = df_feat.drop(df_feat_cons, axis=1)
df_feat = df_feat.ffill()
df_feat = pd.merge(df_feat,df[["Close_1"]],left_index=True,right_index=True,how="left")
print(df_feat.shape)
model(df_feat) #noisy

7  variables are found to be almost constant
(208, 48)
2064.7813982935995

from tsfresh import select_features
from tsfresh.utilities.dataframe_functions import impute

impute(df_feat)
df_feat_2 = select_features(df_feat.drop(["Close_1"],axis=1),df_feat["Close_1"],fdr_level=0.05)
df_feat_2["Close_1"] = df_feat["Close_1"]
model(df_feat_2) #improvement (b/ not an augmentation method)

1577.5273071299482

(3) (6) (i) Feature Agglomoration;   (1)(2)(i) Standard Scaler.

Like in this step, after (1), (2), (3), (4) and (5), you can often circle back to the initial steps to normalise the data and dimensionally reduce the data for the final model.

import numpy as np
from sklearn import datasets, cluster

def feature_agg(df, drop, components):
  components = min(df.shape[1]-1,components)
  agglo = cluster.FeatureAgglomeration(n_clusters=components,)
  df = df.drop(drop,axis=1)
  agglo.fit(df)
  df = pd.DataFrame(agglo.transform(df))
  df = df.add_prefix('fe_agg_')

  return df

df_final = transform.standard_scaler(df_feat_2, drop=["Close_1"])
df_final = mapper.feature_agg(df_final,["Close_1"],4)
df_final.index = df_feat.index
df_final["Close_1"] = df_feat["Close_1"]
model(df_final) #noisy

1949.89085894338

Final Model After Applying 13 Arbitrary Augmentation Techniques

model(df_final) #improvement

1949.89085894338

Original Model Before Augmentation

df_org = df.iloc[:,:7][df.index.isin(df_final.index)]
model(df_org)

389.783990984133

Best Model After Developing 8 Augmenting Features

df_best = df_best.replace([np.inf, -np.inf], np.nan).ffill().fillna(0)
model(df_best)

267.1826850968307

Commentary

There are countless ways in which the current model can be improved, this can take on an automated process where all techniques are tested against a hold out set, for example, we can perform the operation below, and even though it improves the score here, there is a need for more robust tests. The skeleton example above is not meant to highlight the performance of the package. It simply serves as an example of how one can go about applying augmentation methods.

Quite naturally this example suffers from dimensionality issues with array shapes reaching (208, 48), furthermore you would need a sample that is at least 50-100 times larger before machine learning methods start to make sense.

Nonetheless, in this example, Transformation, Interactions and Mappings (applied to extraction output) performed fairly well. Extraction augmentation was overkill, but created a reasonable model when dimensionally reduced. A better selection of one of the 50+ augmentation methods and the order of augmentation could further help improve the outcome if robustly tested against development sets.

[1] DeltaPy Development

Author: firmai
Source Code: https://github.com/firmai/deltapy

#engineering 

Cree Una Aplicación De Android Con El Marco Kivy Python

Si es un desarrollador de Python que está pensando en comenzar con el desarrollo móvil, entonces el marco Kivy es su mejor opción. Con Kivy, puede desarrollar aplicaciones independientes de la plataforma que compilan para iOS, Android, Windows, macOS y Linux. En este artículo, cubriremos Android específicamente porque es el más utilizado.

Construiremos una aplicación generadora de números aleatorios simple que puede instalar en su teléfono y probar cuando haya terminado. Para continuar con este artículo, debe estar familiarizado con Python. ¡Empecemos!

Primeros pasos con Kivy

Primero, necesitará un nuevo directorio para su aplicación. Asegúrese de tener Python instalado en su máquina y abra un nuevo archivo de Python. Deberá instalar el módulo Kivy desde su terminal usando cualquiera de los comandos a continuación. Para evitar conflictos de paquetes, asegúrese de instalar Kivy en un entorno virtual:

pip install kivy 
//
pip3 install kivy 

Una vez que haya instalado Kivy, debería ver un mensaje de éxito de su terminal que se parece a las capturas de pantalla a continuación:

Instalación decepcionada

Instalación exitosa de Kivy

 

A continuación, navegue a la carpeta de su proyecto. En el main.pyarchivo, necesitaremos importar el módulo Kivy y especificar qué versión queremos. Puede usar Kivy v2.0.0, pero si tiene un teléfono inteligente anterior a Android 8.0, le recomiendo usar Kivy v1.9.0. Puede jugar con las diferentes versiones durante la compilación para ver las diferencias en las características y el rendimiento.

Agregue el número de versión justo después de la import kivylínea de la siguiente manera:

kivy.require('1.9.0')

Ahora, crearemos una clase que básicamente definirá nuestra aplicación; Voy a nombrar el mío RandomNumber. Esta clase heredará la appclase de Kivy. Por lo tanto, debe importar appagregando from kivy.app import App:

class RandomNumber(App): 

En la RandomNumberclase, deberá agregar una función llamada build, que toma un selfparámetro. Para devolver la interfaz de usuario, usaremos la buildfunción. Por ahora, lo tengo devuelto como una simple etiqueta. Para hacerlo, deberá importar Labelusando la línea from kivy.uix.label import Label:

import kivy
from kivy.app import App
from kivy.uix.label import Label

class RandomNumber(App):
  def build(self):
    return Label(text="Random Number Generator")

¡Ahora, el esqueleto de nuestra aplicación está completo! Antes de continuar, debe crear una instancia de la RandomNumberclase y ejecutarla en su terminal o IDE para ver la interfaz:

importar kivy de kivy.app importar aplicación de kivy.uix.label clase de etiqueta de importación RandomNumber(App): def build(self): return Label(text="Generador de números aleatorios") randomApp = RandomNumber() randomApp.run()

Cuando ejecuta la instancia de clase con el texto Random Number Generator, debería ver una interfaz o ventana simple que se parece a la siguiente captura de pantalla:

 

Interfaz simple después de ejecutar el código.

No podrá ejecutar el texto en Android hasta que haya terminado de construir todo.

Externalización de la interfaz

A continuación, necesitaremos una forma de subcontratar la interfaz. Primero, crearemos un archivo Kivy en nuestro directorio que albergará la mayor parte de nuestro trabajo de diseño. Querrá nombrar este archivo con el mismo nombre que su clase usando letras minúsculas y una .kvextensión. Kivy asociará automáticamente el nombre de la clase y el nombre del archivo, pero es posible que no funcione en Android si son exactamente iguales.

Dentro de ese .kvarchivo, debe especificar el diseño de su aplicación, incluidos elementos como la etiqueta, los botones, los formularios, etc. Para simplificar esta demostración, agregaré una etiqueta para el título Random Number, una etiqueta que servirá como marcador de posición. para el número aleatorio que se genera _, y un Generatebotón que llama a la generatefunción.

Mi .kvarchivo se parece al siguiente código, pero puede jugar con los diferentes valores para que se ajusten a sus requisitos:

<boxLayout>:
    orientation: "vertical"
    Label:
        text: "Random Number"
        font_size: 30
        color: 0, 0.62, 0.96

    Label:
        text: "_"
        font_size: 30

    Button:
        text: "Generate"
        font_size: 15 

En el main.pyarchivo, ya no necesita la Labeldeclaración de importación porque el archivo Kivy se encarga de su interfaz de usuario. Sin embargo, necesita importar boxlayout, que utilizará en el archivo Kivy.

En su archivo principal, debe agregar la declaración de importación y editar su main.pyarchivo para leer return BoxLayout()el buildmétodo:

from kivy.uix.boxlayout import BoxLayout

Si ejecuta el comando anterior, debería ver una interfaz simple que tiene el título del número aleatorio, el _marcador de posición y el generatebotón en el que se puede hacer clic:

Aplicación de números aleatorios renderizada

Tenga en cuenta que no tuvo que importar nada para que funcione el archivo Kivy. Básicamente, cuando ejecuta la aplicación, regresa boxlayoutbuscando un archivo dentro del archivo Kivy con el mismo nombre que su clase. Tenga en cuenta que esta es una interfaz simple y puede hacer que su aplicación sea tan robusta como desee. Asegúrese de consultar la documentación del idioma Kv .

Generar la función de números aleatorios

Ahora que nuestra aplicación está casi terminada, necesitaremos una función simple para generar números aleatorios cuando un usuario haga clic en el generatebotón y luego mostrar ese número aleatorio en la interfaz de la aplicación. Para hacerlo, necesitaremos cambiar algunas cosas en nuestros archivos.

Primero, importaremos el módulo que usaremos para generar un número aleatorio con import random. Luego, crearemos una función o método que llame al número generado. Para esta demostración, usaré un rango entre 0y 2000. Generar el número aleatorio es simple con el random.randint(0, 2000)comando. Agregaremos esto a nuestro código en un momento.

A continuación, crearemos otra clase que será nuestra propia versión del box layout. Nuestra clase tendrá que heredar la box layoutclase, que alberga el método para generar números aleatorios y representarlos en la interfaz:

class MyRoot(BoxLayout):
    def __init__(self):
        super(MyRoot, self).__init__()

Dentro de esa clase, crearemos el generatemétodo, que no solo generará números aleatorios, sino que también manipulará la etiqueta que controla lo que se muestra como número aleatorio en el archivo Kivy.

Para acomodar este método, primero necesitaremos hacer cambios en el .kvarchivo. Dado que la MyRootclase ha heredado el box layout, puede crear MyRootel elemento de nivel superior en su .kvarchivo:

<MyRoot>:
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15

Tenga en cuenta que todavía mantiene todas las especificaciones de la interfaz de usuario con sangría en el archivo Box Layout. Después de esto, debe agregar una identificación a la etiqueta que contendrá los números generados, lo que facilita la manipulación cuando generatese llama a la función. Debe especificar la relación entre la ID en este archivo y otra en el código principal en la parte superior, justo antes de la BoxLayoutlínea:

<MyRoot>:
    random_label: random_label
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            id: random_label
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15

La random_label: random_labellínea básicamente significa que la etiqueta con el ID random_labelse asignará a random_labelen el main.pyarchivo, lo que significa que cualquier acción que manipula random_labelserán mapeados en la etiqueta con el nombre especificado.

Ahora podemos crear el método para generar el número aleatorio en el archivo principal:

def generate_number(self):
    self.random_label.text = str(random.randint(0, 2000))

# notice how the class method manipulates the text attributre of the random label by a# ssigning it a new random number generate by the 'random.randint(0, 2000)' funcion. S# ince this the random number generated is an integer, typecasting is required to make # it a string otherwise you will get a typeError in your terminal when you run it.

La MyRootclase debería parecerse al siguiente código:

class MyRoot(BoxLayout):
    def __init__(self):
        super(MyRoot, self).__init__()

    def generate_number(self):
        self.random_label.text = str(random.randint(0, 2000))

¡Felicidades! Ya ha terminado con el archivo principal de la aplicación. Lo único que queda por hacer es asegurarse de llamar a esta función cuando se haga generateclic en el botón. Solo necesita agregar la línea on_press: root.generate_number()a la parte de selección de botones de su .kvarchivo:

<MyRoot>:
    random_label: random_label
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            id: random_label
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15
            on_press: root.generate_number()

Ahora, puede ejecutar la aplicación.

Compilando nuestra aplicación en Android

Antes de compilar nuestra aplicación en Android, tengo malas noticias para los usuarios de Windows. Necesitará Linux o macOS para compilar su aplicación de Android. Sin embargo, no necesita tener una distribución de Linux separada, en su lugar, puede usar una máquina virtual.

Para compilar y generar una .apkaplicación Android completa , usaremos una herramienta llamada Buildozer . Instalemos Buildozer a través de nuestra terminal usando uno de los siguientes comandos:

pip3 install buildozer
//
pip install buildozer

Ahora, instalaremos algunas de las dependencias requeridas de Buildozer. Estoy en Linux Ergo, así que usaré comandos específicos de Linux. Debe ejecutar estos comandos uno por uno:

sudo apt update
sudo apt install -y git zip unzip openjdk-13-jdk python3-pip autoconf libtool pkg-config zlib1g-dev libncurses5-dev libncursesw5-dev libtinfo5 cmake libffi-dev libssl-dev

pip3 install --upgrade Cython==0.29.19 virtualenv 

# add the following line at the end of your ~/.bashrc file
export PATH=$PATH:~/.local/bin/

Después de ejecutar los comandos específicos, ejecute buildozer init. Debería ver un resultado similar a la captura de pantalla a continuación:

Inicialización exitosa de Buildozer

El comando anterior crea un .specarchivo Buildozer , que puede usar para hacer especificaciones para su aplicación, incluido el nombre de la aplicación, el ícono, etc. El .specarchivo debe verse como el bloque de código a continuación:

[app]

# (str) Title of your application
title = My Application

# (str) Package name
package.name = myapp

# (str) Package domain (needed for android/ios packaging)
package.domain = org.test

# (str) Source code where the main.py live
source.dir = .

# (list) Source files to include (let empty to include all the files)
source.include_exts = py,png,jpg,kv,atlas

# (list) List of inclusions using pattern matching
#source.include_patterns = assets/*,images/*.png

# (list) Source files to exclude (let empty to not exclude anything)
#source.exclude_exts = spec

# (list) List of directory to exclude (let empty to not exclude anything)
#source.exclude_dirs = tests, bin

# (list) List of exclusions using pattern matching
#source.exclude_patterns = license,images/*/*.jpg

# (str) Application versioning (method 1)
version = 0.1

# (str) Application versioning (method 2)
# version.regex = __version__ = \['"\](.*)['"]
# version.filename = %(source.dir)s/main.py

# (list) Application requirements
# comma separated e.g. requirements = sqlite3,kivy
requirements = python3,kivy

# (str) Custom source folders for requirements
# Sets custom source for any requirements with recipes
# requirements.source.kivy = ../../kivy

# (list) Garden requirements
#garden_requirements =

# (str) Presplash of the application
#presplash.filename = %(source.dir)s/data/presplash.png

# (str) Icon of the application
#icon.filename = %(source.dir)s/data/icon.png

# (str) Supported orientation (one of landscape, sensorLandscape, portrait or all)
orientation = portrait

# (list) List of service to declare
#services = NAME:ENTRYPOINT_TO_PY,NAME2:ENTRYPOINT2_TO_PY

#
# OSX Specific
#

#
# author = © Copyright Info

# change the major version of python used by the app
osx.python_version = 3

# Kivy version to use
osx.kivy_version = 1.9.1

#
# Android specific
#

# (bool) Indicate if the application should be fullscreen or not
fullscreen = 0

# (string) Presplash background color (for new android toolchain)
# Supported formats are: #RRGGBB #AARRGGBB or one of the following names:
# red, blue, green, black, white, gray, cyan, magenta, yellow, lightgray,
# darkgray, grey, lightgrey, darkgrey, aqua, fuchsia, lime, maroon, navy,
# olive, purple, silver, teal.
#android.presplash_color = #FFFFFF

# (list) Permissions
#android.permissions = INTERNET

# (int) Target Android API, should be as high as possible.
#android.api = 27

# (int) Minimum API your APK will support.
#android.minapi = 21

# (int) Android SDK version to use
#android.sdk = 20

# (str) Android NDK version to use
#android.ndk = 19b

# (int) Android NDK API to use. This is the minimum API your app will support, it should usually match android.minapi.
#android.ndk_api = 21

# (bool) Use --private data storage (True) or --dir public storage (False)
#android.private_storage = True

# (str) Android NDK directory (if empty, it will be automatically downloaded.)
#android.ndk_path =

# (str) Android SDK directory (if empty, it will be automatically downloaded.)
#android.sdk_path =

# (str) ANT directory (if empty, it will be automatically downloaded.)
#android.ant_path =

# (bool) If True, then skip trying to update the Android sdk
# This can be useful to avoid excess Internet downloads or save time
# when an update is due and you just want to test/build your package
# android.skip_update = False

# (bool) If True, then automatically accept SDK license
# agreements. This is intended for automation only. If set to False,
# the default, you will be shown the license when first running
# buildozer.
# android.accept_sdk_license = False

# (str) Android entry point, default is ok for Kivy-based app
#android.entrypoint = org.renpy.android.PythonActivity

# (str) Android app theme, default is ok for Kivy-based app
# android.apptheme = "@android:style/Theme.NoTitleBar"

# (list) Pattern to whitelist for the whole project
#android.whitelist =

# (str) Path to a custom whitelist file
#android.whitelist_src =

# (str) Path to a custom blacklist file
#android.blacklist_src =

# (list) List of Java .jar files to add to the libs so that pyjnius can access
# their classes. Don't add jars that you do not need, since extra jars can slow
# down the build process. Allows wildcards matching, for example:
# OUYA-ODK/libs/*.jar
#android.add_jars = foo.jar,bar.jar,path/to/more/*.jar

# (list) List of Java files to add to the android project (can be java or a
# directory containing the files)
#android.add_src =

# (list) Android AAR archives to add (currently works only with sdl2_gradle
# bootstrap)
#android.add_aars =

# (list) Gradle dependencies to add (currently works only with sdl2_gradle
# bootstrap)
#android.gradle_dependencies =

# (list) add java compile options
# this can for example be necessary when importing certain java libraries using the 'android.gradle_dependencies' option
# see https://developer.android.com/studio/write/java8-support for further information
# android.add_compile_options = "sourceCompatibility = 1.8", "targetCompatibility = 1.8"

# (list) Gradle repositories to add {can be necessary for some android.gradle_dependencies}
# please enclose in double quotes 
# e.g. android.gradle_repositories = "maven { url 'https://kotlin.bintray.com/ktor' }"
#android.add_gradle_repositories =

# (list) packaging options to add 
# see https://google.github.io/android-gradle-dsl/current/com.android.build.gradle.internal.dsl.PackagingOptions.html
# can be necessary to solve conflicts in gradle_dependencies
# please enclose in double quotes 
# e.g. android.add_packaging_options = "exclude 'META-INF/common.kotlin_module'", "exclude 'META-INF/*.kotlin_module'"
#android.add_gradle_repositories =

# (list) Java classes to add as activities to the manifest.
#android.add_activities = com.example.ExampleActivity

# (str) OUYA Console category. Should be one of GAME or APP
# If you leave this blank, OUYA support will not be enabled
#android.ouya.category = GAME

# (str) Filename of OUYA Console icon. It must be a 732x412 png image.
#android.ouya.icon.filename = %(source.dir)s/data/ouya_icon.png

# (str) XML file to include as an intent filters in <activity> tag
#android.manifest.intent_filters =

# (str) launchMode to set for the main activity
#android.manifest.launch_mode = standard

# (list) Android additional libraries to copy into libs/armeabi
#android.add_libs_armeabi = libs/android/*.so
#android.add_libs_armeabi_v7a = libs/android-v7/*.so
#android.add_libs_arm64_v8a = libs/android-v8/*.so
#android.add_libs_x86 = libs/android-x86/*.so
#android.add_libs_mips = libs/android-mips/*.so

# (bool) Indicate whether the screen should stay on
# Don't forget to add the WAKE_LOCK permission if you set this to True
#android.wakelock = False

# (list) Android application meta-data to set (key=value format)
#android.meta_data =

# (list) Android library project to add (will be added in the
# project.properties automatically.)
#android.library_references =

# (list) Android shared libraries which will be added to AndroidManifest.xml using <uses-library> tag
#android.uses_library =

# (str) Android logcat filters to use
#android.logcat_filters = *:S python:D

# (bool) Copy library instead of making a libpymodules.so
#android.copy_libs = 1

# (str) The Android arch to build for, choices: armeabi-v7a, arm64-v8a, x86, x86_64
android.arch = armeabi-v7a

# (int) overrides automatic versionCode computation (used in build.gradle)
# this is not the same as app version and should only be edited if you know what you're doing
# android.numeric_version = 1

#
# Python for android (p4a) specific
#

# (str) python-for-android fork to use, defaults to upstream (kivy)
#p4a.fork = kivy

# (str) python-for-android branch to use, defaults to master
#p4a.branch = master

# (str) python-for-android git clone directory (if empty, it will be automatically cloned from github)
#p4a.source_dir =

# (str) The directory in which python-for-android should look for your own build recipes (if any)
#p4a.local_recipes =

# (str) Filename to the hook for p4a
#p4a.hook =

# (str) Bootstrap to use for android builds
# p4a.bootstrap = sdl2

# (int) port number to specify an explicit --port= p4a argument (eg for bootstrap flask)
#p4a.port =


#
# iOS specific
#

# (str) Path to a custom kivy-ios folder
#ios.kivy_ios_dir = ../kivy-ios
# Alternately, specify the URL and branch of a git checkout:
ios.kivy_ios_url = https://github.com/kivy/kivy-ios
ios.kivy_ios_branch = master

# Another platform dependency: ios-deploy
# Uncomment to use a custom checkout
#ios.ios_deploy_dir = ../ios_deploy
# Or specify URL and branch
ios.ios_deploy_url = https://github.com/phonegap/ios-deploy
ios.ios_deploy_branch = 1.7.0

# (str) Name of the certificate to use for signing the debug version
# Get a list of available identities: buildozer ios list_identities
#ios.codesign.debug = "iPhone Developer: <lastname> <firstname> (<hexstring>)"

# (str) Name of the certificate to use for signing the release version
#ios.codesign.release = %(ios.codesign.debug)s


[buildozer]

# (int) Log level (0 = error only, 1 = info, 2 = debug (with command output))
log_level = 2

# (int) Display warning if buildozer is run as root (0 = False, 1 = True)
warn_on_root = 1

# (str) Path to build artifact storage, absolute or relative to spec file
# build_dir = ./.buildozer

# (str) Path to build output (i.e. .apk, .ipa) storage
# bin_dir = ./bin

#    -----------------------------------------------------------------------------
#    List as sections
#
#    You can define all the "list" as [section:key].
#    Each line will be considered as a option to the list.
#    Let's take [app] / source.exclude_patterns.
#    Instead of doing:
#
#[app]
#source.exclude_patterns = license,data/audio/*.wav,data/images/original/*
#
#    This can be translated into:
#
#[app:source.exclude_patterns]
#license
#data/audio/*.wav
#data/images/original/*
#


#    -----------------------------------------------------------------------------
#    Profiles
#
#    You can extend section / key with a profile
#    For example, you want to deploy a demo version of your application without
#    HD content. You could first change the title to add "(demo)" in the name
#    and extend the excluded directories to remove the HD content.
#
#[app@demo]
#title = My Application (demo)
#
#[app:source.exclude_patterns@demo]
#images/hd/*
#
#    Then, invoke the command line with the "demo" profile:
#
#buildozer --profile demo android debug

Si desea especificar cosas como el ícono, los requisitos, la pantalla de carga, etc., debe editar este archivo. Después de realizar todas las ediciones deseadas en su aplicación, ejecute buildozer -v android debugdesde el directorio de su aplicación para construir y compilar su aplicación. Esto puede llevar un tiempo, especialmente si tiene una máquina lenta.

Una vez finalizado el proceso, su terminal debería tener algunos registros, uno que confirme que la compilación fue exitosa:

Construcción exitosa de Android

También debe tener una versión APK de su aplicación en su directorio bin. Este es el ejecutable de la aplicación que instalará y ejecutará en su teléfono:

Android .apk en el directorio bin

Conclusión

¡Felicidades! Si ha seguido este tutorial paso a paso, debería tener una aplicación simple de generador de números aleatorios en su teléfono. Juega con él y ajusta algunos valores, luego reconstruye. Ejecutar la reconstrucción no llevará tanto tiempo como la primera compilación.

Como puede ver, crear una aplicación móvil con Python es bastante sencillo , siempre que esté familiarizado con el marco o módulo con el que está trabajando. Independientemente, la lógica se ejecuta de la misma manera.

Familiarícese con el módulo Kivy y sus widgets. Nunca se puede saber todo a la vez. Solo necesita encontrar un proyecto y mojarse los pies lo antes posible. Codificación feliz.

Enlace: https://blog.logrocket.com/build-android-application-kivy-python-framework/

#python 

KivyPythonフレームワークを使用してAndroidアプリケーションを構築する

あなたがモバイル開発を始めることを考えているPython開発者なら、Kivyフレームワークが最善の策です。Kivyを使用すると、iOS、Android、Windows、macOS、およびLinux用にコンパイルされるプラットフォームに依存しないアプリケーションを開発できます。この記事では、Androidが最も使用されているため、特にAndroidについて説明します。

簡単な乱数ジェネレーターアプリを作成します。このアプリを携帯電話にインストールして、完了したらテストできます。この記事を続けるには、Pythonに精通している必要があります。始めましょう！

Kivyを使い始める

まず、アプリ用の新しいディレクトリが必要になります。マシンにPythonがインストールされていることを確認し、新しいPythonファイルを開きます。以下のコマンドのいずれかを使用して、ターミナルからKivyモジュールをインストールする必要があります。パッケージの競合を避けるために、Kivyを仮想環境にインストールしていることを確認してください。

pip install kivy 
//
pip3 install kivy 

Kivyをインストールすると、以下のスクリーンショットのような成功メッセージがターミナルから表示されます。

がっかりしたインストール

Kivyのインストールに成功

 

次に、プロジェクトフォルダに移動します。このmain.pyファイルで、Kivyモジュールをインポートし、必要なバージョンを指定する必要があります。Kivy v2.0.0を使用できますが、Android 8.0より古いスマートフォンを使用している場合は、Kivyv1.9.0を使用することをお勧めします。ビルド中にさまざまなバージョンをいじって、機能とパフォーマンスの違いを確認できます。

import kivy次のように、行の直後にバージョン番号を追加します。

kivy.require('1.9.0')

次に、基本的にアプリを定義するクラスを作成します。私の名前を付けますRandomNumber。このクラスはappKivyからクラスを継承します。したがって、次appを追加してインポートする必要がありますfrom kivy.app import App。

class RandomNumber(App): 

ではRandomNumberクラスは、呼び出された関数を追加する必要がありますbuildとり、selfパラメータを。実際にUIを返すには、このbuild関数を使用します。今のところ、単純なラベルとして返送しています。そのためには、次Labelの行を使用してインポートする必要がありますfrom kivy.uix.label import Label。

import kivy
from kivy.app import App
from kivy.uix.label import Label

class RandomNumber(App):
  def build(self):
    return Label(text="Random Number Generator")

これで、アプリのスケルトンが完成しました。先に進む前に、RandomNumberクラスのインスタンスを作成し、ターミナルまたはIDEで実行して、インターフェイスを確認する必要があります。

import kivy from kivy.app import App from kivy.uix.label import Label class RandomNumber（App）：def build（self）：return Label（text = "Random Number Generator"）randomApp = RandomNumber（）randomApp.run（）

テキストを使用してクラスインスタンスを実行すると、Random Number Generator次のスクリーンショットのような単純なインターフェイスまたはウィンドウが表示されます。

 

コードを実行した後のシンプルなインターフェイス

すべての構築が完了するまで、Androidでテキストを実行することはできません。

インターフェースのアウトソーシング

次に、インターフェースをアウトソーシングする方法が必要になります。まず、ディレクトリにKivyファイルを作成します。このファイルには、ほとんどの設計作業が含まれています。このファイルには、小文字と.kv拡張子を使用して、クラスと同じ名前を付けることができます。Kivyはクラス名とファイル名を自動的に関連付けますが、それらがまったく同じである場合、Androidでは機能しない可能性があります。

その.kvファイル内で、ラベル、ボタン、フォームなどの要素を含むアプリのレイアウトを指定する必要があります。このデモを簡単にするために、タイトルRandom Numberのラベル、プレースホルダーとして機能するラベルを追加します。生成される乱数_、および関数Generateを呼び出すボタンgenerate。

私の.kvファイルは以下のコードのように見えますが、要件に合わせてさまざまな値をいじることができます。

<boxLayout>:
    orientation: "vertical"
    Label:
        text: "Random Number"
        font_size: 30
        color: 0, 0.62, 0.96

    Label:
        text: "_"
        font_size: 30

    Button:
        text: "Generate"
        font_size: 15 

このmain.pyファイルではLabel、KivyファイルがUIを処理するため、importステートメントは不要になりました。ただし、boxlayoutKivyファイルで使用するをインポートする必要があります。

メインファイルで、importステートメントを追加し、main.pyファイルを編集return BoxLayout()してbuildメソッドで読み取る必要があります。

from kivy.uix.boxlayout import BoxLayout

上記のコマンドを実行すると、乱数のタイトル、_プレースホルダー、およびクリック可能なgenerateボタンを備えたシンプルなインターフェイスが表示されます。

レンダリングされた乱数アプリ

Kivyファイルを機能させるために何もインポートする必要がなかったことに注意してください。基本的に、アプリを実行するboxlayoutと、クラスと同じ名前のKivyファイル内のファイルを検索して戻ります。これはシンプルなインターフェースであり、アプリを必要に応じて堅牢にすることができます。Kv言語のドキュメントを必ず確認してください。

乱数関数を生成する

アプリがほぼ完成したので、ユーザーがgenerateボタンをクリックしたときに乱数を生成し、その乱数をアプリのインターフェイスにレンダリングする簡単な関数が必要になります。そのためには、ファイル内のいくつかの変更を行う必要があります。

まず、で乱数を生成するために使用するモジュールをインポートしますimport random。次に、生成された番号を呼び出す関数またはメソッドを作成します。このデモでは、私は間の範囲を使用します0と2000。このrandom.randint(0, 2000)コマンドを使用すると、乱数を簡単に生成できます。これをすぐにコードに追加します。

次に、独自のバージョンとなる別のクラスを作成しますbox layout。このbox layoutクラスは、乱数を生成してインターフェイス上でレンダリングするメソッドを含むクラスを継承する必要があります。

class MyRoot(BoxLayout):
    def __init__(self):
        super(MyRoot, self).__init__()

そのクラス内で、generate乱数を生成するだけでなく、Kivyファイルに乱数として表示されるものを制御するラベルを操作するメソッドを作成します。

この方法に対応するには、最初に.kvファイルに変更を加える必要があります。以来MyRootクラスが継承しているbox layout、あなたが作ることができるMyRootあなたのトップレベルの要素.kvファイルを：

<MyRoot>:
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15

でインデントされたすべてのUI仕様を保持していることに注意してくださいBox Layout。この後、生成された番号を保持するIDをラベルに追加して、generate関数が呼び出されたときに簡単に操作できるようにする必要があります。このファイルのIDと、上部のメインコードの別のIDとの関係を、次のBoxLayout行の直前に指定する必要があります。

<MyRoot>:
    random_label: random_label
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            id: random_label
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15

このrandom_label: random_label行は基本的に、IDrandom_labelを持つラベルがファイルrandom_label内にマップされることをmain.py意味します。つまり、操作random_labelするアクションはすべて、指定された名前のラベルにマップされます。

これで、メインファイルに乱数を生成するメソッドを作成できます。

def generate_number(self):
    self.random_label.text = str(random.randint(0, 2000))

# notice how the class method manipulates the text attributre of the random label by a# ssigning it a new random number generate by the 'random.randint(0, 2000)' funcion. S# ince this the random number generated is an integer, typecasting is required to make # it a string otherwise you will get a typeError in your terminal when you run it.

MyRootこのクラスは、以下のコードのようになります。

class MyRoot(BoxLayout):
    def __init__(self):
        super(MyRoot, self).__init__()

    def generate_number(self):
        self.random_label.text = str(random.randint(0, 2000))

おめでとう！これで、アプリのメインファイルが完成しました。あとは、generateボタンがクリックされたときに必ずこの関数を呼び出すようにしてください。ファイルのon_press: root.generate_number()ボタン選択部分に行を追加するだけで済み.kvます。

<MyRoot>:
    random_label: random_label
    BoxLayout:
        orientation: "vertical"
        Label:
            text: "Random Number"
            font_size: 30
            color: 0, 0.62, 0.96

        Label:
            id: random_label
            text: "_"
            font_size: 30

        Button:
            text: "Generate"
            font_size: 15
            on_press: root.generate_number()

これで、アプリを実行できます。

Androidでアプリをコンパイルする

Androidでアプリをコンパイルする前に、Windowsユーザーにとって悪いニュースがあります。Androidアプリケーションをコンパイルするには、LinuxまたはmacOSが必要です。ただし、個別のLinuxディストリビューションを用意する必要はなく、代わりに仮想マシンを使用できます。

完全なAndroid.apkアプリケーションをコンパイルして生成するには、Buildozerというツールを使用します。以下のコマンドのいずれかを使用して、ターミナルからBuildozerをインストールしましょう。

pip3 install buildozer
//
pip install buildozer

次に、Buildozerに必要な依存関係のいくつかをインストールします。私はLinuxErgoを使用しているので、Linux固有のコマンドを使用します。これらのコマンドを1つずつ実行する必要があります。

sudo apt update
sudo apt install -y git zip unzip openjdk-13-jdk python3-pip autoconf libtool pkg-config zlib1g-dev libncurses5-dev libncursesw5-dev libtinfo5 cmake libffi-dev libssl-dev

pip3 install --upgrade Cython==0.29.19 virtualenv 

# add the following line at the end of your ~/.bashrc file
export PATH=$PATH:~/.local/bin/

特定のコマンドを実行した後、を実行しbuildozer initます。以下のスクリーンショットのような出力が表示されます。

Buildozerの初期化が成功しました

上記のコマンドはBuildozer.specファイルを作成します。このファイルを使用して、アプリの名前やアイコンなどをアプリに指定.specできます。ファイルは次のコードブロックのようになります。

[app]

# (str) Title of your application
title = My Application

# (str) Package name
package.name = myapp

# (str) Package domain (needed for android/ios packaging)
package.domain = org.test

# (str) Source code where the main.py live
source.dir = .

# (list) Source files to include (let empty to include all the files)
source.include_exts = py,png,jpg,kv,atlas

# (list) List of inclusions using pattern matching
#source.include_patterns = assets/*,images/*.png

# (list) Source files to exclude (let empty to not exclude anything)
#source.exclude_exts = spec

# (list) List of directory to exclude (let empty to not exclude anything)
#source.exclude_dirs = tests, bin

# (list) List of exclusions using pattern matching
#source.exclude_patterns = license,images/*/*.jpg

# (str) Application versioning (method 1)
version = 0.1

# (str) Application versioning (method 2)
# version.regex = __version__ = \['"\](.*)['"]
# version.filename = %(source.dir)s/main.py

# (list) Application requirements
# comma separated e.g. requirements = sqlite3,kivy
requirements = python3,kivy

# (str) Custom source folders for requirements
# Sets custom source for any requirements with recipes
# requirements.source.kivy = ../../kivy

# (list) Garden requirements
#garden_requirements =

# (str) Presplash of the application
#presplash.filename = %(source.dir)s/data/presplash.png

# (str) Icon of the application
#icon.filename = %(source.dir)s/data/icon.png

# (str) Supported orientation (one of landscape, sensorLandscape, portrait or all)
orientation = portrait

# (list) List of service to declare
#services = NAME:ENTRYPOINT_TO_PY,NAME2:ENTRYPOINT2_TO_PY

#
# OSX Specific
#

#
# author = © Copyright Info

# change the major version of python used by the app
osx.python_version = 3

# Kivy version to use
osx.kivy_version = 1.9.1

#
# Android specific
#

# (bool) Indicate if the application should be fullscreen or not
fullscreen = 0

# (string) Presplash background color (for new android toolchain)
# Supported formats are: #RRGGBB #AARRGGBB or one of the following names:
# red, blue, green, black, white, gray, cyan, magenta, yellow, lightgray,
# darkgray, grey, lightgrey, darkgrey, aqua, fuchsia, lime, maroon, navy,
# olive, purple, silver, teal.
#android.presplash_color = #FFFFFF

# (list) Permissions
#android.permissions = INTERNET

# (int) Target Android API, should be as high as possible.
#android.api = 27

# (int) Minimum API your APK will support.
#android.minapi = 21

# (int) Android SDK version to use
#android.sdk = 20

# (str) Android NDK version to use
#android.ndk = 19b

# (int) Android NDK API to use. This is the minimum API your app will support, it should usually match android.minapi.
#android.ndk_api = 21

# (bool) Use --private data storage (True) or --dir public storage (False)
#android.private_storage = True

# (str) Android NDK directory (if empty, it will be automatically downloaded.)
#android.ndk_path =

# (str) Android SDK directory (if empty, it will be automatically downloaded.)
#android.sdk_path =

# (str) ANT directory (if empty, it will be automatically downloaded.)
#android.ant_path =

# (bool) If True, then skip trying to update the Android sdk
# This can be useful to avoid excess Internet downloads or save time
# when an update is due and you just want to test/build your package
# android.skip_update = False

# (bool) If True, then automatically accept SDK license
# agreements. This is intended for automation only. If set to False,
# the default, you will be shown the license when first running
# buildozer.
# android.accept_sdk_license = False

# (str) Android entry point, default is ok for Kivy-based app
#android.entrypoint = org.renpy.android.PythonActivity

# (str) Android app theme, default is ok for Kivy-based app
# android.apptheme = "@android:style/Theme.NoTitleBar"

# (list) Pattern to whitelist for the whole project
#android.whitelist =

# (str) Path to a custom whitelist file
#android.whitelist_src =

# (str) Path to a custom blacklist file
#android.blacklist_src =

# (list) List of Java .jar files to add to the libs so that pyjnius can access
# their classes. Don't add jars that you do not need, since extra jars can slow
# down the build process. Allows wildcards matching, for example:
# OUYA-ODK/libs/*.jar
#android.add_jars = foo.jar,bar.jar,path/to/more/*.jar

# (list) List of Java files to add to the android project (can be java or a
# directory containing the files)
#android.add_src =

# (list) Android AAR archives to add (currently works only with sdl2_gradle
# bootstrap)
#android.add_aars =

# (list) Gradle dependencies to add (currently works only with sdl2_gradle
# bootstrap)
#android.gradle_dependencies =

# (list) add java compile options
# this can for example be necessary when importing certain java libraries using the 'android.gradle_dependencies' option
# see https://developer.android.com/studio/write/java8-support for further information
# android.add_compile_options = "sourceCompatibility = 1.8", "targetCompatibility = 1.8"

# (list) Gradle repositories to add {can be necessary for some android.gradle_dependencies}
# please enclose in double quotes 
# e.g. android.gradle_repositories = "maven { url 'https://kotlin.bintray.com/ktor' }"
#android.add_gradle_repositories =

# (list) packaging options to add 
# see https://google.github.io/android-gradle-dsl/current/com.android.build.gradle.internal.dsl.PackagingOptions.html
# can be necessary to solve conflicts in gradle_dependencies
# please enclose in double quotes 
# e.g. android.add_packaging_options = "exclude 'META-INF/common.kotlin_module'", "exclude 'META-INF/*.kotlin_module'"
#android.add_gradle_repositories =

# (list) Java classes to add as activities to the manifest.
#android.add_activities = com.example.ExampleActivity

# (str) OUYA Console category. Should be one of GAME or APP
# If you leave this blank, OUYA support will not be enabled
#android.ouya.category = GAME

# (str) Filename of OUYA Console icon. It must be a 732x412 png image.
#android.ouya.icon.filename = %(source.dir)s/data/ouya_icon.png

# (str) XML file to include as an intent filters in <activity> tag
#android.manifest.intent_filters =

# (str) launchMode to set for the main activity
#android.manifest.launch_mode = standard

# (list) Android additional libraries to copy into libs/armeabi
#android.add_libs_armeabi = libs/android/*.so
#android.add_libs_armeabi_v7a = libs/android-v7/*.so
#android.add_libs_arm64_v8a = libs/android-v8/*.so
#android.add_libs_x86 = libs/android-x86/*.so
#android.add_libs_mips = libs/android-mips/*.so

# (bool) Indicate whether the screen should stay on
# Don't forget to add the WAKE_LOCK permission if you set this to True
#android.wakelock = False

# (list) Android application meta-data to set (key=value format)
#android.meta_data =

# (list) Android library project to add (will be added in the
# project.properties automatically.)
#android.library_references =

# (list) Android shared libraries which will be added to AndroidManifest.xml using <uses-library> tag
#android.uses_library =

# (str) Android logcat filters to use
#android.logcat_filters = *:S python:D

# (bool) Copy library instead of making a libpymodules.so
#android.copy_libs = 1

# (str) The Android arch to build for, choices: armeabi-v7a, arm64-v8a, x86, x86_64
android.arch = armeabi-v7a

# (int) overrides automatic versionCode computation (used in build.gradle)
# this is not the same as app version and should only be edited if you know what you're doing
# android.numeric_version = 1

#
# Python for android (p4a) specific
#

# (str) python-for-android fork to use, defaults to upstream (kivy)
#p4a.fork = kivy

# (str) python-for-android branch to use, defaults to master
#p4a.branch = master

# (str) python-for-android git clone directory (if empty, it will be automatically cloned from github)
#p4a.source_dir =

# (str) The directory in which python-for-android should look for your own build recipes (if any)
#p4a.local_recipes =

# (str) Filename to the hook for p4a
#p4a.hook =

# (str) Bootstrap to use for android builds
# p4a.bootstrap = sdl2

# (int) port number to specify an explicit --port= p4a argument (eg for bootstrap flask)
#p4a.port =


#
# iOS specific
#

# (str) Path to a custom kivy-ios folder
#ios.kivy_ios_dir = ../kivy-ios
# Alternately, specify the URL and branch of a git checkout:
ios.kivy_ios_url = https://github.com/kivy/kivy-ios
ios.kivy_ios_branch = master

# Another platform dependency: ios-deploy
# Uncomment to use a custom checkout
#ios.ios_deploy_dir = ../ios_deploy
# Or specify URL and branch
ios.ios_deploy_url = https://github.com/phonegap/ios-deploy
ios.ios_deploy_branch = 1.7.0

# (str) Name of the certificate to use for signing the debug version
# Get a list of available identities: buildozer ios list_identities
#ios.codesign.debug = "iPhone Developer: <lastname> <firstname> (<hexstring>)"

# (str) Name of the certificate to use for signing the release version
#ios.codesign.release = %(ios.codesign.debug)s


[buildozer]

# (int) Log level (0 = error only, 1 = info, 2 = debug (with command output))
log_level = 2

# (int) Display warning if buildozer is run as root (0 = False, 1 = True)
warn_on_root = 1

# (str) Path to build artifact storage, absolute or relative to spec file
# build_dir = ./.buildozer

# (str) Path to build output (i.e. .apk, .ipa) storage
# bin_dir = ./bin

#    -----------------------------------------------------------------------------
#    List as sections
#
#    You can define all the "list" as [section:key].
#    Each line will be considered as a option to the list.
#    Let's take [app] / source.exclude_patterns.
#    Instead of doing:
#
#[app]
#source.exclude_patterns = license,data/audio/*.wav,data/images/original/*
#
#    This can be translated into:
#
#[app:source.exclude_patterns]
#license
#data/audio/*.wav
#data/images/original/*
#


#    -----------------------------------------------------------------------------
#    Profiles
#
#    You can extend section / key with a profile
#    For example, you want to deploy a demo version of your application without
#    HD content. You could first change the title to add "(demo)" in the name
#    and extend the excluded directories to remove the HD content.
#
#[app@demo]
#title = My Application (demo)
#
#[app:source.exclude_patterns@demo]
#images/hd/*
#
#    Then, invoke the command line with the "demo" profile:
#
#buildozer --profile demo android debug

アイコン、要件、ロード画面などを指定する場合は、このファイルを編集する必要があります。アプリケーションに必要なすべての編集を行った後buildozer -v android debug、アプリディレクトリから実行して、アプリケーションをビルドおよびコンパイルします。特に低速のマシンを使用している場合は、これに時間がかかることがあります。

プロセスが完了すると、端末にいくつかのログが表示され、ビルドが成功したことを確認できます。

Androidの成功したビルド

また、binディレクトリにアプリのAPKバージョンが必要です。これは、携帯電話にインストールして実行するアプリケーションの実行可能ファイルです。

binディレクトリのAndroid.apk

結論

おめでとう！このチュートリアルをステップバイステップで実行した場合は、電話に単純な乱数ジェネレーターアプリがインストールされているはずです。それをいじって、いくつかの値を微調整してから、再構築してください。再構築の実行は、最初のビルドほど時間はかかりません。

ご覧のとおり、Pythonを使用したモバイルアプリケーションの構築は、使用しているフレームワークまたはモジュールに精通している限り、かなり簡単です。とにかく、ロジックは同じ方法で実行されます。

Kivyモジュールとそのウィジェットに慣れてください。すべてを一度に知ることはできません。プロジェクトを見つけて、できるだけ早く足を濡らすだけです。ハッピーコーディング。

リンク：https：//blog.logrocket.com/build-android-application-kivy-python-framework/

#python