Robust principal component analysis via feature self-representation

There exists lots of redundant features in high-dimensional data. Generally, PCA devotes to using all the original features for reconstruction, where the redundant features may have significant adverse effect on learning performance. In this paper, we integrate feature selection into PCA framework through using the selected key features for reconstruction. Unlike the traditional PCA-like methods, we first learn the ℓ_2,1-norm sparse projection matrix to span a feature subspace and then use an orthogonal projection matrix to reconstruct the original data from the spanned feature subspace. In this way, the original data, especially its key components (e.g., the eyes, nose, mouth and contours), can be well represented by using the key features characterized by the learned ℓ_2,1-norm sparse projection matrix. Furthermore, when data suffers from the outliers, the outliers would be selected inevitably where the outliers contain the variations appeared in the original images such as pose and illumination, and the added random noise onto the original images. To this end, we exploit the ℓ_2,1-norm on the error term to fit the corruptions, which further provides a robust PCA version. A simple yet effective optimization algorithm with the application of Augmented Lagrange Multiplier is given to solve the resulting optimization problem. Experiments on the dataset demonstrate the effectiveness of the proposed method.