What PCA Actually Does to Your Data, Explained Clearly

Principal Component Analysis (PCA) is a dimensionality reduction technique that works by finding the directions of greatest variance in data using eigenvectors of the covariance matrix. The covariance matrix captures how features vary individually and together, and is the sole input PCA uses — meaning it is blind to any other data properties. Eigenvectors of this matrix identify axes along which data varies independently, with corresponding eigenvalues indicating how much variance each axis holds. Sorting these eigenvectors by eigenvalue ranks the principal components from most to least informative, allowing analysts to retain only the top few. Unlike feature selection, PCA performs feature extraction, creating entirely new uncorrelated variables that are weighted combinations of the originals rather than preserving any original columns.