Semi-Supervised Kernel Principal Component Analysis

Semi-Supervised Kernel Principal Component Analysis (SS-KPCA) MATLAB code implements a dimensionality reduction algorithm that preserves critical data information while handling large-scale datasets. The algorithm utilizes kernel methods to map data into higher-dimensional feature spaces, where it performs principal component analysis to capture nonlinear relationships. By incorporating unlabeled data during the training phase, the algorithm more accurately identifies underlying data structures and relationships through the kernel trick implementation using MATLAB's matrix operations. This approach employs MATLAB functions like kernel matrix computation and eigenvalue decomposition to handle nonlinear transformations. The SS-KPCA code can be applied across various domains including image processing (feature extraction from images) and natural language processing (text data dimensionality reduction). The semi-supervised version specifically uses partially labeled data that acts as "guidance" in the algorithm, helping it better learn data structures through supervised constraints combined with unsupervised learning components. The implementation typically involves constructing labeled and unlabeled data matrices, computing kernel matrices using Gaussian or polynomial kernels, and solving generalized eigenvalue problems to obtain principal components.