This tutorial covers mathematics underlying principal component analysis, including definition of PCs, how to find PCs, and derivation of PCs.

### 1 Introduction to Principal Component Analysis

#### 1.1 Main idea of Principal Component Analysis

The central idea of principal component analysis (PCA) is to reduce the dimensionality of a data set consisting of a large number of interrelated variables, while retaining as much as possible of the variation present in the data set.

This is achieved by transforming the original set of variables to a new set of variables, the principal components (PCs), which are uncorrelated, and which are ordered so that the first *a few* retain most of the variation present in all the original variables. Read more Mathematics Underlying Principal Component Analysis