Linear Discriminant Analysis: MATLAB Implementation and Algorithm Explanation

This article provides a comprehensive overview of the Linear Discriminant Analysis (LDA) algorithm and its applications in pattern recognition and machine learning. LDA is a classical supervised learning algorithm designed to identify optimal linear directions (called "linear discriminants") that maximize separation between different classes of data points. Despite being a long-established technique, LDA remains widely used due to its strong capabilities in data visualization and feature extraction. Implementing LDA in MATLAB is straightforward - we demonstrate how to compute between-class and within-class scatter matrices using built-in functions like cov and mean, followed by eigenvalue decomposition to obtain projection vectors. The implementation typically involves calculating class statistics, constructing scatter matrices, and solving the generalized eigenvalue problem using MATLAB's eig function. We provide practical code examples showing how to transform data into lower-dimensional spaces while preserving class discriminatory information. Additionally, we explore LDA variants and extensions, including Regularized LDA for handling singular matrices and Quadratic Discriminant Analysis for nonlinear boundaries. The article concludes with guidance on selecting appropriate LDA models for real-world applications based on dataset characteristics and computational requirements.