Principal Component Analysis (PCA) Algorithm Implementation

The following MATLAB program code implements the Principal Component Analysis (PCA) algorithm. The code structure includes these key computational steps: Step 1: Data Standardization Implementation approach: Normalize the input data by subtracting the mean and scaling by standard deviation using MATLAB's zscore function or manual calculation to ensure all features have zero mean and unit variance Step 2: Covariance Matrix Computation Algorithm explanation: Compute the covariance matrix of standardized data using MATLAB's cov function, which measures how variables change together and forms the basis for principal component extraction Step 3: Eigenvalue and Eigenvector Calculation Key function description: Utilize MATLAB's eig function to solve the eigenvalue problem, where eigenvalues represent the variance explained by each principal component and eigenvectors define the directions of maximum variance Step 4: Variance Contribution Rate Calculation Implementation detail: Calculate the proportion of total variance explained by each principal component by normalizing eigenvalues, typically expressed as percentages to determine the optimal number of components to retain In Principal Component Analysis, the PCA algorithm serves as a powerful dimensionality reduction technique that eliminates redundant information while preserving essential data characteristics. This approach facilitates better data comprehension and more efficient analysis. By implementing this program code in MATLAB, researchers and data analysts can easily perform principal component analysis and gain deeper insights into their datasets through systematic dimensionality reduction and feature extraction.