PCA Principal Component Analysis Algorithm Implementation

This article introduces the principles of the PCA principal component analysis algorithm and provides MATLAB source code for its implementation. Let's first understand the basic concepts of PCA: it is a widely used dimensionality reduction technique that transforms high-dimensional data into lower-dimensional space through linear transformations. PCA is commonly applied in fields like image processing, signal analysis, and pattern recognition. The MATLAB implementation includes key functions such as data standardization using z-score normalization, covariance matrix computation, eigenvalue decomposition via MATLAB's eig() function, and principal component selection based on variance thresholds. The code demonstrates how to calculate eigenvectors and eigenvalues, sort components by explained variance, and project data onto the principal component space. This implementation helps deepen understanding of PCA's mathematical foundation while providing valuable reference for research projects and practical applications.