MATLAB Implementation of Fisher Algorithm for Multi-Class Classification

This article presents a MATLAB implementation of the Fisher algorithm for multi-class classification scenarios. The Fisher algorithm is a classical linear discriminant analysis method that extracts the most discriminative features from limited sample data. In multi-class situations, the standard Fisher algorithm requires specific modifications to effectively distinguish between different categories during classification. The implementation involves several key technical aspects: first, calculating within-class and between-class scatter matrices to measure feature distribution patterns; second, solving the generalized eigenvalue problem to obtain optimal projection directions; third, implementing dimensionality reduction through linear transformation of feature vectors. The multiclassfisher main program handles these operations sequentially, including data preprocessing, matrix computation, and classification boundary determination. The provided multiclassfisher function serves as the core implementation, accepting input data matrices and class labels as parameters. It returns projection vectors and classification results, with internal processing that handles multiple classes by extending the binary Fisher criterion through one-versus-rest or other multi-class strategies. Through studying this implementation, readers will gain deeper understanding of Fisher algorithm applications in multi-class scenarios and be able to independently implement multi-category linear discriminant analysis using MATLAB programming techniques.