# Linear and Quadratic Discriminant Analysis: Tutorial

arXiv: https://arxiv.org/abs/1906.02590 · HTML: https://mlsanity.com/paper/1906.02590/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 11 of 11)

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- [Interpretable Solutions for Breast Cancer Diagnosis with Grammatical Evolution and Data Augmentation](https://mlsanity.com/paper/2401.14255/) (2024)
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- [Spectral Priors vs. Attention: Investigating the Utility of Attention Mechanisms in EEG-Based Diagnosis](https://mlsanity.com/paper/2605.15433/) (2026)
- [Predicting Male Fertility Using Machine Learning: A Semen Parameters Based Analysis with the VISEM Dataset](https://mlsanity.com/paper/2607.08429/) (2026)

## Abstract (arXiv)

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.