Evaluating geometrically-approximated principal component analysis vs. classical eigenfaces: a quantitative study using image quality metrics

Principal component analysis (PCA) is essential for diminishing the number of dimensions across various fields, preserving data integrity while simplifying complexity. Eigenfaces, a notable application of PCA, illustrates the method's effectiveness in facial recognition. This paper introduces a novel PCA approximation technique based on maximizing distance and compares it with the traditional eigenfaces approach. We employ several image quality metrics including Euclidean distance, mean absolute error (MAE), peak signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), and structural similarity index measure (SSIM) for a quantitative assessment. Experiments conducted on the Brazilian FEI database reveal significant differences between the approximated and classical eigenfaces. Despite these differences, our approximation method demonstrates superior performance in retrieval and search tasks, offering faster and parallelizable implementation. The results underscore the practical advantages of our approach, particularly in scenarios requiring rapid processing and expansion capabilities.