Double Layer Robust 2DPCA: Joint Flexible Cut Norm and Adaptive Weighted Learning for Small Sample Size Image Recognition

Recently, many 2D principal component analysis (2DPCA) methods with different distance metric mechanisms have been successfully proposed and applied to improve the robustness of information perception based on image data. However, these methods ignore the possibility of minimizing reconstruction errors in a real sense. To overcome this shortcoming, we propose a method called double layer robust 2DPCA (DLR-2DPCA), which is a novel formulation of 2DPCA with robustness. DLR-2DPCA uses the cut l2, p -norm as the similarity measure criterion between data in the first layer, which not only effectively utilizes a flexible distance metric mechanism with rotational invariance, but also fully suppresses the amplification of reconstruction errors caused by p-value selection, greatly improving the robustness of the method. Moreover, we introduce an adaptive weighted learning strategy in the second layer, which can adaptively assign different weights to the reconstruction errors obtained from each sample in the first layer, clearly considering the difference in the contribution of each sample to the reconstruction error. Finally, we design a novel iterative algorithm with nongreedy properties to seek the DLR-2DPCA expected solution. Numerous experimental results have effectively validated the theoretical analysis and fully demonstrated the excellent performance of our method.