Robust generalized two-dimensional principal component analysis with optimal bias learning.

Two-dimensional principal component analysis (2DPCA) performs feature extraction directly in the matrix space and has shown high efficiency in image recognition. However, existing robust 2DPCA methods still have limited ability to handle occlusion, noise, and outliers, and it remains difficult to simultaneously achieve strong discriminative ability and data recoverability. To address this issue, this paper extends the robust generalized principal component analysis model (RGPCA-OB) to the two-dimensional matrix setting and proposes model RG2DPCA-OB. The proposed method separates the projection matrix from the recovery matrix. This gives more flexible feature learning and better reconstruction. An optimal bias term is learned adaptively instead of using the conventional sample mean. This improves robustness and representation ability. In addition, generalized norm loss and row-sparse regularization are introduced to suppress outliers and remove redundant features. A truncated reweighting strategy is further used to filter severely corrupted samples and improve noise resistance. An efficient alternating iterative algorithm is developed, and the monotonic decrease and convergence of the objective function values are theoretically established. Experiments on multiple image datasets demonstrate that, under different noise levels, RG2DPCA-OB improves classification accuracy by an average of approximately 0.44 percentage points and reduces reconstruction error by an average of approximately 1.28% compared with the best competing methods.