Generalized centered 2-D principal component analysis

Most existing robust principal component analysis (PCA) and 2-D PCA (2DPCA) methods involving the l₂-norm can mitigate the sensitivity to outliers in the domains of image analysis and pattern recognition. However, existing approaches neither preserve the structural information of data in the optimization objective nor have the robustness of generalized performance. To address the above problems, we propose two novel center-weight-based models, namely, centered PCA (C-PCA) and generalized centered 2DPCA with l₂,_p-norm minimization (GC-2DPCA), which are developed for vector- and matrix-based data, respectively. The C-PCA can preserve the structural information of data by measuring the similarity between the data points and can also retain the PCA's original desirable properties such as the rotational invariance. Furthermore, GC-2DPCA can learn efficient and robust projection matrices to suppress outliers by utilizing the variations between each row of the image matrix and employing power p of l₂,₁-norm. We also propose an efficient algorithm to solve the C-PCA model and an iterative optimization algorithm to solve the GC-2DPCA model, and we theoretically analyze their convergence properties. Experiments on three public databases show that our models yield significant improvements over the state-of-the-art PCA and 2DPCA approaches.