# Chapter 5 Principal component analysis

Principal Component Analysis (PCA) is a powerful multivariate technique designed to summarize the most important features and relations of $$k$$ numerical random variables $$X_1,\ldots,X_k$$. PCA does dimension reduction of the original dataset by computing a new set of variables, the principal components $$\text{PC}_1,\ldots \text{PC}_k$$, which explain the same information as $$X_1,\ldots,X_k$$ but in an ordered way: $$\text{PC}_1$$ explains the most of the information and $$\text{PC}_k$$ the least.

There is no response $$Y$$ or particular variable in PCA that deserves a particular attention – all variables are treated equally.