In this Neural Networks Tutorial, we are going to talk about Convolutional Neural Networks. We will cover what convolutional neural networks are and how they work. We will also cover the different elements of CNNs and talk about some of the parameters. We will see some applications of how CNNs are used in self-driving cars and how Tesla and Waymo use them.
The code example is available on my GitHub: https://github.com/niconielsen32
CNN’s are a special type of ANN which accepts images as inputs. Below is the representation of a basic neuron of an ANN which takes as input X vector. The values in the X vector is then multiplied by corresponding weights to form a linear combination. To thus, a non-linearity function or an activation function is imposed so as to get the final output.
Neuron representation, Image by author
Talking about grayscale images, they have pixel ranges from 0 to 255 i.e. 8-bit pixel values. If the size of the image is NxM, then the size of the input vector will be NM. For RGB images, it would be NM*3. Consider an RGB image with size 30x30. This would require 2700 neurons. An RGB image of size 256x256 would require over 100000 neurons. ANN takes a vector of inputs and gives a product as a vector from another hidden layer that is fully connected to the input. The number of weights, parameters for 224x224x3 is very high. A single neuron in the output layer will have 224x224x3 weights coming into it. This would require more computation, memory, and data. CNN exploits the structure of images leading to a sparse connection between input and output neurons. Each layer performs convolution on CNN. CNN takes input as an image volume for the RGB image. Basically, an image is taken as an input and we apply kernel/filter on the image to get the output. CNN also enables parameter sharing between the output neurons which means that a feature detector (for example horizontal edge detector) that’s useful in one part of the image is probably useful in another part of the image.
Every output neuron is connected to a small neighborhood in the input through a weight matrix also referred to as a kernel or a weight matrix. We can define multiple kernels for every convolution layer each giving rise to an output. Each filter is moved around the input image giving rise to a 2nd output. The outputs corresponding to each filter are stacked giving rise to an output volume.
Convolution operation, Image by indoml
Here the matrix values are multiplied with corresponding values of kernel filter and then summation operation is performed to get the final output. The kernel filter slides over the input matrix in order to get the output vector. If the input matrix has dimensions of Nx and Ny, and the kernel matrix has dimensions of Fx and Fy, then the final output will have a dimension of Nx-Fx+1 and Ny-Fy+1. In CNN’s, weights represent a kernel filter. K kernel maps will provide k kernel features.
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Image classification is the process of segmenting images into different categories based on their features. A feature could be the edges in an image, the pixel intensity, the change in pixel values, and many more. We will try and understand these components later on. For the time being let’s look into the images below (refer to Figure 1). The three images belong to the same individual however varies when compared across features like the color of the image, position of the face, the background color, color of the shirt, and many more. The biggest challenge when working with images is the uncertainty of these features. To the human eye, it looks all the same, however, when converted to data you may not find a specific pattern across these images easily.
Figure 1. Illustrates the portrait of the Author taken in 2014 and 2019 respectively.
An image consists of the smallest indivisible segments called pixels and every pixel has a strength often known as the pixel intensity. Whenever we study a digital image, it usually comes with three color channels, i.e. the Red-Green-Blue channels, popularly known as the “RGB” values. Why RGB? Because it has been seen that a combination of these three can produce all possible color pallets. Whenever we work with a color image, the image is made up of multiple pixels with every pixel consisting of three different values for the RGB channels. Let’s code and understand what we are talking about.
import cv2 import seaborn as sns import matplotlib.pyplot as plt %matplotlib inline sns.set(color_codes=True) ## Read the image image = cv2.imread('Portrait-Image.png') #--imread() helps in loading an image into jupyter including its pixel values plt.imshow(cv2.cvtColor(image, cv2.COLOR_BGR2RGB)) ## as opencv loads in BGR format by default, we want to show it in RGB. plt.show() image.shape
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This post provides the details of the architecture of _Convolutional Neural Network _(CNN), functions and training of each layer, ending with a summary of the training of CNN.
3. First Convolutional Layer:
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TL;DR This is the first in a [series of posts] where I will discuss the evolution and future trends in the field of deep learning on graphs.
Deep learning on graphs, also known as Geometric deep learning (GDL) , Graph representation learning (GRL), or relational inductive biases , has recently become one of the hottest topics in machine learning. While early works on graph learning go back at least a decade  if not two , it is undoubtedly the past few years’ progress that has taken these methods from a niche into the spotlight of the ML community and even to the popular science press (with Quanta Magazine running a series of excellent articles on geometric deep learning for the study of manifolds, drug discovery, and protein science).
Graphs are powerful mathematical abstractions that can describe complex systems of relations and interactions in fields ranging from biology and high-energy physics to social science and economics. Since the amount of graph-structured data produced in some of these fields nowadays is enormous (prominent examples being social networks like Twitter and Facebook), it is very tempting to try to apply deep learning techniques that have been remarkably successful in other data-rich settings.
There are multiple flavours to graph learning problems that are largely application-dependent. One dichotomy is between node-wise and graph-wise problems, where in the former one tries to predict properties of individual nodes in the graph (e.g. identify malicious users in a social network), while in the latter one tries to make a prediction about the entire graph (e.g. predict solubility of a molecule). Furthermore, like in traditional ML problems, we can distinguish between supervised and unsupervised (or self-supervised) settings, as well as transductive and inductive problems.
Similarly to convolutional neural networks used in image analysis and computer vision, the key to efficient learning on graphs is designing local operations with shared weights that do message passing  between every node and its neighbours. A major difference compared to classical deep neural networks dealing with grid-structured data is that on graphs such operations are permutation-invariant, i.e. independent of the order of neighbour nodes, as there is usually no canonical way of ordering them.
Despite their promise and a series of success stories of graph representation learning (among which I can selfishly list the [acquisition by Twitter] of the graph-based fake news detection startup Fabula AI I have founded together with my students), we have not witnessed so far anything close to the smashing success convolutional networks have had in computer vision. In the following, I will try to outline my views on the possible reasons and how the field could progress in the next few years.
**Standardised benchmarks **like ImageNet were surely one of the key success factors of deep learning in computer vision, with some  even arguing that data was more important than algorithms for the deep learning revolution. We have nothing similar to ImageNet in scale and complexity in the graph learning community yet. The [Open Graph Benchmark] launched in 2019 is perhaps the first attempt toward this goal trying to introduce challenging graph learning tasks on interesting real-world graph-structured datasets. One of the hurdles is that tech companies producing diverse and rich graphs from their users’ activity are reluctant to share these data due to concerns over privacy laws such as GDPR. A notable exception is Twitter that made a dataset of 160 million tweets with corresponding user engagement graphs available to the research community under certain privacy-preserving restrictions as part of the [RecSys Challenge]. I hope that many companies will follow suit in the future.
**Software libraries **available in the public domain played a paramount role in “democratising” deep learning and making it a popular tool. If until recently, graph learning implementations were primarily a collection of poorly written and scarcely tested code, nowadays there are libraries such as [PyTorch Geometric] or [Deep Graph Library (DGL)] that are professionally written and maintained with the help of industry sponsorship. It is not uncommon to see an implementation of a new graph deep learning architecture weeks after it appears on arxiv.
Scalability is one of the key factors limiting industrial applications that often need to deal with very large graphs (think of Twitter social network with hundreds of millions of nodes and billions of edges) and low latency constraints. The academic research community has until recently almost ignored this aspect, with many models described in the literature completely inadequate for large-scale settings. Furthermore, graphics hardware (GPU), whose happy marriage with classical deep learning architectures was one of the primary forces driving their mutual success, is not necessarily the best fit for graph-structured data. In the long run, we might need specialised hardware for graphs .
**Dynamic graphs **are another aspect that is scarcely addressed in the literature. While graphs are a common way of modelling complex systems, such an abstraction is often too simplistic as real-world systems are dynamic and evolve in time. Sometimes it is the temporal behaviour that provides crucial insights about the system. Despite some recent progress, designing graph neural network models capable of efficiently dealing with continuous-time graphs represented as a stream of node- or edge-wise events is still an open research question.
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