Enhanced face recognition with nuclear norm-based angle 2D-PCA using QR decomposition

Abstract

Several approaches based on two-dimensional principal component analysis (2DPCA) have shown limitations in terms of classification performance. To enhance its robustness, an angular variant of 2DPCA has been proposed, establishing a relationship between reconstruction error and data variance through the Frobenius norm. However, this technique still encounters certain challenges. To overcome these shortcomings and further strengthen resilience to data variations, we propose a novel framework: nuclear norm-based angular 2DPCA using QR-decomposition (AN2DPCA-QR). This new formulation leverages the nuclear norm to optimize a variance-related criterion by maximizing the ratio of projected to original variance, aiming to improve the discriminative capacity of the projection space. The method employs a non-greedy iterative algorithm to solve the optimization problem, incorporating adaptive mean centralization for bias reduction, and QR decomposition instead of singular value decomposition (SVD) for numerical stability and reduced complexity. Compared to its predecessor, AN2DPCA-QR offers enhanced robustness, and interpretability. Results obtained on various public benchmark datasets clearly demonstrate the practical relevance and resilience of the proposed method.