On Singular value decomposition and it's use in recommendation systems | Chirag Patil

Since the dawn of time, human beings have asked some fundamental questions: who are we? why are we here? is there life after death? Unable to answer any of these, in this post we will learn what Singular Value decomposition is and how it can be used in recommender systems. SVD (Singular Value Decomposition) is one of the most beautiful equation of mathematics and a highlight of linear algebra. You can think of it as a data reduction tool. It’s an algorithm that you need to learn if you want to make money using linear algebra. In this post I will only assume you can calculate eignevalues and eigenvectors :) You can skip to the second part of this discussion to avoid delving too deeply into the mathematical details and instead focus on understanding the more practical aspects related to recommendations - the applied side of the mathematics.

I will start by presenting to you the formula for singular value decomposition. Given an \(m\)-by-\(n\) matrix \(A\), the singular value decomposition (SVD) can be expressed as:

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