Principal Component Analysis (PCA) from scratch

Principal Component Analysis (PCA) is a popular dimensionality reduction algorithm with applications ranging from data visualization to algorithmic trading and I'm really excited to share this algorithm with you. In this video, we'll derive the PCA algorithm using basic linear algebra and calculus and then implement it from scratch in python.

PCA is a dimensionality reduction algorithm which takes high dimensional data and projects to a low dimensional space in a way that maximizes the variance of the projected data.

We will show that the optimal projection matrix W is equal to L eigenvectors corresponding to the largest eigenvalues of the empirical covariance matrix Sigma. See the python notebook below for software implementation of PCA from scratch.

Link to notebook:
https://github.com/vsmolyakov/youtube...

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00:00 Introduction
00:51 Overview
01:21 Formulation
02:42 Derivation
05:39 Python Notebook