Robust Sparse PCA via Weighted Elastic Net

In principal component analysis (PCA), `2/`1-norm is widely used to measure coding residual. In this case, it assume that the residual follows Gaussian/Laplacian distribution. However, it may fail to describe the coding errors in practice when there are outliers. Toward this end, this paper propose a Robust Sparse PCA (RSPCA) approach to solve the outlier problem, by modeling the sparse coding as a sparsity-constrained weighted regression problem. By using a series of equivalent transformations, we show the proposed RSPCA is equivalent to the Weighted Elastic Net (WEN) problem and thus the Least Angle Regression Elastic Net (LARS-EN) algorithm is used to yield the optimal solution. Simulation results illustrated the effectiveness of this approach.