MATLAB Implementation and Explanation of KPCA Algorithm

This article explores the MATLAB implementation and technical documentation of the Kernel Principal Component Analysis (KPCA) algorithm. KPCA is a fundamental data analysis technique commonly used for dimensionality reduction of high-dimensional datasets, simplifying data complexity and enhancing analytical efficiency. We will demonstrate how to implement KPCA in MATLAB using kernel functions and matrix operations, with detailed explanations of key computational steps including kernel matrix construction, eigenvalue decomposition, and projection calculations. The implementation typically involves MATLAB functions like 'eig' for eigenvalue computation and custom kernel functions (e.g., Gaussian RBF kernel) for nonlinear mapping. Additionally, we will discuss practical application scenarios for KPCA and provide case studies showcasing its real-world utility in pattern recognition and data preprocessing. Through this article, readers will gain comprehensive understanding of KPCA's mathematical foundation and master its practical application for data analysis in MATLAB environment, including parameter selection for kernel functions and interpretation of reduced-dimensional features.