MATLAB Code Implementation of PCA Steps

In this article, we provide a detailed explanation of PCA implementation steps. First, we need to center the data through mean normalization, which simplifies covariance calculations by removing the mean from each feature. In MATLAB, this can be implemented using X_centered = X - mean(X). Next, we compute the covariance matrix to analyze feature relationships, achievable via MATLAB's cov() function or manual calculation (X_centered' * X_centered)/(size(X,1)-1). We then calculate eigenvalues and eigenvectors using [eigenvectors, eigenvalues] = eig(cov_matrix), where eigenvalues represent variance explained and eigenvectors indicate principal component directions.

Subsequently, we sort eigenvalues in descending order with corresponding eigenvectors, typically implemented through [sorted_eigenvalues, idx] = sort(diag(eigenvalues), 'descend') and reordering eigenvectors accordingly. For dimensionality reduction to d' dimensions, we select the top d' eigenvectors as projection directions, forming a transformation matrix W = eigenvectors(:, 1:d'). Finally, we obtain reduced-dimensional data through linear projection X_reduced = X_centered * W, which preserves maximum variance while reducing computational complexity. This process enables better data visualization and more efficient machine learning model training.