Principal Component Analysis (PCA) Demystified

 

Dimensionality reduction using PCA is typically taught using a cooking recipe such as the following:

Have you ever wondered where this recipe originated from. Below is the underlying proof in detail:

Why is integral of normal distribution = 1 ? Where does the mysterious normalizing constant come from ?

 

The case of the Univariate Normal Distribution

 

The case of the Multivariate Normal Distribution

Gaussian or Euler-poisson Integral

Geometric Progression

Arithmetic Progression