Multivariate Statistical Analysis: Discriminant Analysis, PCA, and Factor Analysis

This English version was machine-translated from the Chinese original. Technical terms may require verification.

Multivariate statistical analysis extends univariate statistical inference to settings where several measurements are observed together. These notes introduce the main ideas behind discriminant analysis, principal component analysis (PCA), factor analysis, clustering, correspondence analysis, and contingency-table analysis.

The opening discussion connects the subject with sampling distributions and inference for multivariate normal models. The later sections focus on dimensionality reduction and classification: PCA and factor analysis summarize correlated variables, while discriminant analysis and clustering assign observations to meaningful groups. The original derivations and formulas remain available in the Chinese source notes.

Readers who want the prerequisite probability and inference background can start with the introductory multivariate statistics notes and then review the mathematical statistics notes before working through the examples here.