Classic LDA Feature Selection Algorithm

The classic Linear Discriminant Analysis (LDA) is a supervised dimensionality reduction and feature selection method widely used in pattern recognition and machine learning. The core concept of LDA is to maximize the ratio between between-class scatter and within-class scatter, thereby finding the optimal projection direction for effective data classification.

Implementing LDA feature selection in MATLAB typically involves the following key steps:

Data Preprocessing: Begin by loading the dataset and performing standardization to ensure comparable scales across different feature dimensions. This can be implemented using MATLAB's zscore function or manual normalization.

Within-Class Scatter Matrix Calculation: Compute mean vectors for each class and calculate the within-class covariance matrix to measure the dispersion of samples within the same category. This involves using mean and cov functions with appropriate class grouping.

Between-Class Scatter Matrix Calculation: Based on global mean and class-specific means, construct the between-class covariance matrix to quantify differences between distinct categories. This requires careful matrix operations to maintain mathematical accuracy.

Eigenvector Solution: Solve the generalized eigenvalue problem to obtain optimal projection directions. The corresponding eigenvectors form the feature subspace selected by LDA, typically implemented through MATLAB's eig function applied to the matrix ratio.

Dimensionality Reduction and Classification: Project original data using selected feature vectors for dimension reduction, after which classifiers like SVM or KNN can be applied for task optimization using functions such as fitcsvm or fitcknn.

LDA is particularly suitable for classification problems, though its linear assumption limits effectiveness for non-linearly separable data. MATLAB provides built-in functions like fitcdiscr for convenient LDA implementation, but manual coding helps deepen understanding of the underlying mathematical principles and matrix operations.