MATLAB Implementation of PCA Algorithm for Dimensionality Reduction

Using Principal Component Analysis (PCA) algorithm for data dimensionality reduction enables extraction of principal eigenvalues to achieve dimension reduction. This method reduces data dimensionality, thereby decreasing data complexity and computational time requirements. PCA-based dimensionality reduction also helps prevent data overfitting issues, ensuring data reliability and accuracy. In practical applications, PCA algorithm is widely used in fields such as image processing, pattern recognition, speech recognition, and bioinformatics, holding significant application value. Key implementation steps in MATLAB include: 1. Data standardization using zscore() or similar functions to normalize features 2. Computing covariance matrix with cov() function to analyze variable relationships 3. Performing eigenvalue decomposition using eig() or svd() functions to obtain principal components 4. Selecting top k eigenvalues based on variance explanation ratios to determine reduced dimensions 5. Projecting original data onto principal components through matrix multiplication for final reduced dataset The core MATLAB functions involved are pca() for direct implementation or manual coding using eigen decomposition approaches. The algorithm effectively transforms correlated variables into linearly uncorrelated principal components while preserving maximum variance in the data.