Angle-Aware Weighted 2DPCA for Structure-Preserving Feature Learning

To address the sensitivity of traditional Two-Dimensional Principal Component Analysis (2DPCA) to outliers and the breakdown of variance-reconstruction equivalence under noise, we propose an Angle-Aware Weighted 2DPCA (AW2DPCA) method for robust, structure-preserving feature learning. AW2DPCA fundamentally shifts from the conventional &#x201C;denoise-then-extract&#x201D; paradigm and traditional distance-based weighting schemes by introducing a novel angle-based adaptive weighting mechanism. This mechanism acts as an implicit geometric attention, evaluating sample reliability via the angular deviation between input data and reconstruction residuals. By integrating this mechanism with an <inline-formula> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula>-norm spatial penalty and a tunable power parameter, the proposed unified objective jointly optimizes reconstruction fidelity and projection variance without requiring prior denoising. Furthermore, we develop an efficient, theoretically-guaranteed iterative algorithm that directly computes the optimal projection matrix. Extensive evaluations on six benchmark image and video datasets demonstrate that AW2DPCA achieves superior classification accuracy with exceptionally low variance and rapid convergence. Furthermore, it yields statistically significant improvements in reconstruction fidelity and demonstrates precise anomaly detection, exhibiting remarkable robustness against heavy occlusions and complex noise.