Kernel Principal Component Analysis (KPCA) Algorithm Source Code Implementation

This document provides the complete MATLAB source code implementation for the Kernel Principal Component Analysis (KPCA) algorithm. KPCA represents a powerful non-linear extension of traditional Principal Component Analysis (PCA), serving as a fundamental dimensionality reduction technique in data analysis that preserves maximum information while reducing data complexity. The KPCA algorithm implementation operates by transforming original data into a higher-dimensional feature space using kernel functions, where data separation becomes more feasible. The code incorporates various kernel functions (such as Gaussian RBF or polynomial kernels) that compute similarity measures between data points in this transformed space. The implementation follows these key computational steps: first, it constructs the kernel matrix using the selected kernel function; then, it centers the kernel matrix in the feature space; finally, it performs eigenvalue decomposition on the kernel matrix to extract principal components. Key MATLAB functions in this implementation include kernel matrix computation, eigenvalue decomposition using built-in functions like 'eig', and principal component projection routines. The algorithm handles data normalization and kernel parameter optimization to ensure robust performance across different datasets. KPCA finds extensive applications in multiple domains including image recognition systems, data compression algorithms, and signal processing pipelines. This source code enables researchers and practitioners to directly apply KPCA to their specific datasets, customize kernel parameters, and explore the algorithm's capabilities for non-linear pattern recognition and feature extraction tasks. The code includes comprehensive comments and follows MATLAB best practices for clear understanding and easy modification.