Optimal mean robust principal component analysis

Principal Component Analysis (PCA) is the most widely used unsupervised dimensionality reduc-tion 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 l2-norm distance to calculate the mean, which actually is not the optimal mean due to the l2-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.