Kernel robust singular value decomposition

Abstract

Singular value decomposition (SVD) is one of the most widely used algorithms for dimensionality reduction and performing principal component analysis, which represents an important tool used in many pattern recognition problems. However, in the case of data contamination with outlying observations, the classical SVD is not appropriate. To overcome this limitation, several robust SVD algorithms have been proposed, usually based on different types of norms or projection strategies. In this paper, we propose a kernel robust SVD algorithm based on the exponential-type Gaussian kernel, where four estimators are considered for the width hyper-parameters. Differently from the existing approaches that deal with kernel in principal component analysis and SVD, our proposal operates in the original space, instead of the feature space, being the kernel applied in a robust linear regression framework to obtain the robust estimates for the singular values and left and right singular vectors. Simulations show that the proposed algorithm outperforms the classical and robust SVD algorithms under consideration. We also illustrate the merits of the proposed algorithm in an application to image recovery due to the presence of noise.