MATLAB Implementation of Kernel Fisher Discriminant Analysis

The Kernel Fisher classifier is a nonlinear classification algorithm based on kernel methods, which maps original data into a high-dimensional feature space, making linearly non-separable data become linearly separable in the new space.

The fundamental approach to implementing the Kernel Fisher classifier in MATLAB involves these key steps: Data Preprocessing: Initially, input data requires standardization to ensure features across different dimensions share the same scale. In MATLAB, this can be implemented using functions like zscore or through manual normalization. Kernel Matrix Computation: An appropriate kernel function (such as Gaussian/RBF kernel, polynomial kernel, or linear kernel) must be selected to calculate the kernel matrix between samples, replacing the original inner product operations. MATLAB implementation typically involves creating a kernel function handle and computing pairwise similarities using vectorized operations. Projection Direction Solution: In the high-dimensional feature space, compute between-class and within-class scatter matrices, then solve the generalized eigenvalue problem to find the optimal projection direction. This can be implemented using MATLAB's eig function for eigenvalue decomposition. Classification Decision: Map test samples to the projection space and perform classification by comparing their distances to class centers. This involves computing kernel evaluations for test points and applying the trained projection matrix.

The Kernel Fisher classifier is suitable for nonlinear classification tasks such as handwritten digit recognition and face recognition. Compared to linear Fisher discriminant analysis, the kernel version can handle more complex decision boundaries but requires higher computational complexity, particularly on large-scale datasets. Implementation considerations include kernel parameter selection through cross-validation and potential dimensionality reduction techniques for computational efficiency.