Linear and Quadratic Discriminant Analysis: Tutorial

TL;DR

This tutorial provides a comprehensive overview of Linear and Quadratic Discriminant Analysis, covering their derivation, parameter estimation, and connections to other statistical methods, supported by simulations.

Contribution

It offers a detailed, unified explanation of LDA and QDA, including their theoretical foundations, derivations, and relationships to other classification techniques.

Findings

LDA and QDA are derived for multiple classes.

LDA and Fisher discriminant analysis are proven equivalent.

Simulations illustrate theoretical concepts.

Abstract

This tutorial explains Linear Discriminant Analysis (LDA) and Quadratic Discriminant Analysis (QDA) as two fundamental classification methods in statistical and probabilistic learning. We start with the optimization of decision boundary on which the posteriors are equal. Then, LDA and QDA are derived for binary and multiple classes. The estimation of parameters in LDA and QDA are also covered. Then, we explain how LDA and QDA are related to metric learning, kernel principal component analysis, Mahalanobis distance, logistic regression, Bayes optimal classifier, Gaussian naive Bayes, and likelihood ratio test. We also prove that LDA and Fisher discriminant analysis are equivalent. We finally clarify some of the theoretical concepts with simulations we provide.