MATLAB Code Implementation for Principal Component Analysis (PCA)

This documentation presents a high-performance Principal Component Analysis (PCA) program implemented in MATLAB. The algorithm first standardizes input data by centering it around the mean, then computes the covariance matrix to identify orthogonal directions of maximum variance. Through eigenvalue decomposition of the covariance matrix, the program automatically sorts and selects principal components based on explained variance thresholds. Key functions include data normalization, Singular Value Decomposition (SVD) for efficient computation, and component projection for transformed datasets. The program supports multiple applications including: data dimensionality reduction by projecting high-dimensional data onto lower-dimensional subspaces; noise filtering through reconstruction using significant components only; and feature extraction by identifying dominant patterns in datasets. Additional applications include data visualization through 2D/3D projections of multivariate data, as well as preprocessing for classification and clustering tasks by creating decorrelated features. This implementation provides configurable parameters for variance retention percentage and automatic component selection, making it suitable for various dataset sizes and types. The toolbox-style design allows easy integration with existing MATLAB workflows, featuring clear output formats for transformed data, component coefficients, and explained variance metrics.