Advanced Operations Using Numpy Arrays

In my previous post, I talk about Reduction Operations in Numpy Arrays. You may read through it before you move on to the more Advanced Operations below.

In my previous post, I talk about Reduction Operations in Numpy Arrays. You may read through it before you move on to the more Advanced Operations below.

The topics covered in this post are as follows:

• Introduction
• The Dot Product
• Singular Value Decomposition
• Inverse of a Matrix
• References

You can click on any of these above to jump to the respective section.

Introduction

Numpy consists of a subpackage called linalg which has functions particularly pertaining to linear algebra which is an integral part in the working of many DL and ML algorithms. We will discuss several concepts about these operations along with their numpy implementation which will inevitably become a part of your Data Science toolkit. We will be covering three of the most important operations that can be carried out with numpy arrays which are heavily used in DL and ML applications such as Natural Language Processing, Image Retrieval tasks and Customer Recommendation tasks. Without any further delay, let’s get started!

The Dot Product

In vector algebra, the dot product represnts a scalar quantity obtained by sum aggregating the product of vectors along the n-dimensional space respectively.

In linear algebra, dot product is typically used for finding out if two vectors are perpendicular to each other or to find out the magnitude of a single vector or to find out the projection of a vector along another vector.

In Data Science, the dot product is typically used to find out the similarity or distance between two or more vectors in some high dimensional space. When we perform nearest neighbour search this is what we typically use. The similarity found out using dot product is called cosine similarity because the dot product theoretically is given by the expression

The smaller the angle between the two vectors, more closely aligned the two vectors are since the cosine of an angle is high when the angle itself is small/low.

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