Optimal Mean Robust Principal Component Analysis

Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduction approach. In recent research, several robust PCA algorithms were presented to enhance the robustness of PCA model. However, the existing robust PCA methods incorrectly center the data using the l(2)-norm distance to calculate the mean, which actually is not the optimal mean due to the l(1)-norm used in the objective functions. In this paper, we propose novel robust PCA objective functions with removing optimal mean automatically. Both theoretical analysis and empirical studies demonstrate our new methods can more effectively reduce data dimensionality than previous robust PCA methods.