Plurrrr

Sun 31 May 2020

Principal Component Analysis

Principal components analysis (PCA) is one of a family of techniques for taking high-dimensional data, and using the dependencies between the variables to represent it in a more tractable, lower-dimensional form, without losing too much information. It has been widely used for data compression and de-noising. However, its entire mathematical process is sometimes ambiguous to the user.

In this article, I would like to discuss the entire process of PCA mathematically, including PCA projection and reconstruction, with most of the derivations and proofs provided. At the end of the article, I implemented PCA projection and reconstruction from scratch. After reading this article, there should be more black box in PCA anymore.

Source: Principal Component Analysis, an article by Lei Mao.