SVM Kernel Principal Component Analysis with Implementation

This paper introduces a method called Support Vector Machine Kernel Principal Component Analysis (SVM-KPCA), which processes high-dimensional data by reducing it to a lower-dimensional space for improved visualization and comprehension. The approach specifically utilizes support vector machines to identify principal components in data while employing kernel tricks to handle nonlinear data structures. The implementation follows a straightforward methodology using key computational steps: first applying kernel functions (such as RBF or polynomial kernels) to transform data into higher-dimensional feature spaces, then performing principal component analysis on the resulting kernel matrix. The algorithm implementation involves computing the kernel matrix, centering it in feature space, solving eigenvalue problems, and projecting data onto principal components. We provide a comprehensive program code package that includes critical functions for kernel computation, eigenvalue decomposition, and dimensionality reduction, making it easily reproducible for academic research and practical applications. The complete thesis code demonstrates proper parameter tuning, visualization techniques, and performance evaluation metrics to facilitate deeper understanding of method implementation and practical usage scenarios.