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.