Principal Component Analysis MATLAB Source Code Implementation

This article provides fundamental knowledge about Principal Component Analysis (PCA), a widely-used dimensionality reduction technique. PCA transforms high-dimensional data into lower-dimensional representations while preserving the most significant information, enabling more efficient analysis and visualization. We present MATLAB source code implementations to help readers better understand PCA's practical application and implementation mechanics. The implementation typically involves key steps: data standardization using z-score normalization, covariance matrix computation, eigenvalue decomposition via MATLAB's eig() function, and projection of data onto principal components. We also explore PCA variants including Kernel PCA (KPCA) for nonlinear dimensionality reduction through kernel tricks, and Incremental PCA (IPCA) for streaming data applications using iterative updating algorithms. The discussion covers practical considerations such as variance retention thresholds, component selection criteria, and computational efficiency comparisons between batch and incremental approaches. This comprehensive guide aims to provide both theoretical foundations and hands-on implementation experience for PCA and its extensions.