Fisher Criterion Linear Classifier Design

The purpose of using Fisher criterion linear classifier design is to further deepen the understanding of classifier design concepts. Through customized implementations, we can better comprehend linear classifiers and understand the principle of Fisher's method for determining optimal linear decision boundaries. The Fisher criterion maximizes class separability by optimizing the ratio between inter-class scatter and intra-class scatter matrices. In code implementation, this typically involves calculating mean vectors for each class, computing within-class and between-class scatter matrices, and solving for the optimal projection direction through eigenvalue decomposition. Therefore, for learning and applying linear classifiers, Fisher criterion-based design is crucial as it provides a fundamental approach for pattern recognition problems with clear mathematical foundations and straightforward implementation using matrix operations in programming languages like Python or MATLAB.