KPCA Algorithm MATLAB Implementation with Kernel-Based Principal Component Analysis

In this document, you will find MATLAB source code implementing the KPCA (Kernel Principal Component Analysis) algorithm. To better understand this algorithm, let's first review the standard Principal Component Analysis (PCA) algorithm. PCA is a dimensionality reduction technique that transforms high-dimensional datasets into lower-dimensional representations while preserving maximum data variance. However, when dealing with nonlinear datasets, PCA's effectiveness may be limited. This is where Kernel PCA comes into play - it maintains variance preservation while effectively handling nonlinear data structures through kernel methods. The provided MATLAB implementation includes key functions for kernel computation (such as Gaussian RBF or polynomial kernels), eigenvalue decomposition for feature extraction, and data projection into kernel-induced feature spaces. The code demonstrates how to map original data to a higher-dimensional space using kernel functions without explicit computation of coordinates in that space, thus enabling nonlinear dimensionality reduction through linear PCA in the transformed space. This implementation serves as both an educational resource and practical tool for understanding kernel methods in machine learning, featuring comments on algorithmic steps including kernel matrix calculation, centering in feature space, and eigenvalue analysis for principal component selection.