Robust principal component analysis

Abstract

One of the most famous dimensionality reduction methods is Principal Component Analysis (PCA), which is successfully used worldwide. However this method is sensitive to outliers and hence a few number of them cause bias in the resulting subspace. There are a number of techniques now for the robustification of PCA, but we stick to the version introduced in [ 30 ]. The numerical technique for optimization in [ 30 ] relied on Iteratively Reweighted Least Squares (IRLS) method. In the present paper we adopted the Conjugate Gradient Descent algorithm with orthogonal matrix constraints from [ 18 ] for solving the nonconvex matrix optimization problem. We discuss the arising computational and convergence problems and compare effectiveness of the methods.