Fisher Linear Discriminant: A Core Linear Classification Algorithm

In machine learning, Fisher Linear Discriminant stands as one of the foundational linear classification algorithms. The core principle involves projecting d-dimensional samples onto an optimally selected projection line that maximizes inter-class separation while minimizing intra-class variance. This implementation in MATLAB will demonstrate the algorithmic workflow including key functions like mean calculation and scatter matrix computation, along with four threshold selection techniques (such as midpoint threshold and Bayesian optimal threshold) to enhance classification performance. The article further elaborates on the theoretical foundations of Fisher Linear Discriminant, detailing the mathematical derivation of projection vectors and separation criteria. Practical implementation aspects will cover data preprocessing steps, eigenvalue decomposition for optimal direction calculation, and common challenges like small sample size scenarios with corresponding solutions. Through this technical walkthrough, readers will gain comprehensive understanding of the algorithm's mechanics and acquire practical skills for real-world applications including handling multidimensional data and evaluating classification boundaries.