Fisher Algorithm Source Code
One challenge in applying statistical methods to pattern recognition is the dimensionality issue - classification problems are generally simpler in low-dimensional feature spaces than in high-dimensional ones. This leads to dimensionality reduction techniques, where a fundamental approach projects d-dimensional feature space onto a straight line to create one-dimensional space, which is mathematically straightforward. However, the key challenge is ensuring samples remain linearly separable after projection. While linearly separable samples can always find a projection direction maintaining linear separability after dimensionality reduction, Fisher Linear Discriminant specifically determines the optimal projection direction that maximizes separability by maximizing between-class distance while minimizing within-class variance.