Singular Value Decomposition (SVD) Part 1: Math Foundations

The most common way to represent data is through matrices. As a result, this makes the methods and algorithms designed to operate on matrices very convenient for data science. We will dive into the mysteries of one of them. This method has been proven successful in matrix manipulations such as low-rank approximation, but also in more practical applications like recommender systems. This method is known as Single Value Decomposition (SVD). This blog post is the first part of a series around SVD....

May 5, 2022 · 15 min

Singular Value Decomposition (SVD) Part 2: Math Foundations  [draft]

Introduction Humanity has always tackled challenges by breaking them down into smaller pieces. We have various tasks to achieve one unique goal, we have various steps to do one specific recipe, and I am sure you are familiar with the term divide and conquer. Look at this example. We know that $$18$$ can be decomposed into $$2$$ and $$3$$ such that $$18 = 2 \times 3 \times 3$$. Then, from that knowledge, we can infer that $$18$$ and all its multiples are divisible by $$2$$....

May 5, 2022 · 8 min