Robust Principal Component Analysis Based on Welsch Loss and Half-Quadratic Optimization

Principal component analysis (PCA) stands as one of the most extensively utilized techniques in dimensionality reduction. However, PCA uses least squares (LS) loss which may yield poor performance in the presence of the data contaminated by outliers. To enhance the robustness of PCA, this paper proposes a Welsch robust principal component analysis (WRPCA) method based on bounded, smooth, and nonconvex Welsch loss function to robustly learn the low-dimensional subspace. Moreover, due to the non-convexity of the proposed model caused by Welsch loss, we design an effective iterative algorithm via half-quadratic (HQ) theory to optimize the problem of WRPCA. The experiments on practical databases demonstrate the efficacy of WRPCA.