Capped L2p-Norm Based 2DPCA with Adaptive Capped Threshold Learning for Image Processing

Two-dimensional principal component analysis (2DPCA) is an effective technique to extract low-dimensional representations for face clustering and recognition. However, it suffers from extreme sensitivity to outliers and noise. To improve the robustness of 2DPCA, we design a novel optimal-mean 2DPCA with adaptive capped L2p-norm minimization, called Adaptive Capped L2p-2DPCA, which adopts capped L2p-norm in the objective function to measure the reconstruction error. Simultaneously, Adaptive Capped L2p-2DPCA integrates the adaptive capped threshold learning during the optimization process, such that the capped threshold can be obtained without human intervention. Furthermore, we develop a non-greedy iterative algorithm to solve Adaptive Capped L2p-2DPCA. The proposed algorithm has a closed-form solution in each iteration and is proven to achieve good convergence. We conduct experiments on four face image datasets, and the recognition rates on the four datasets Extended Yale B, AR, CMU PIE, and ORL are 5.02%, 1.86%, 0.47%, and 5.5% higher than the second best method, respectively, which indicates the effectiveness and superiority of our method.