Improved Low-Rank Matrix Approximation in Multivariate Case

The low-rank matrix approximation (LRMA) algorithm is an important method in signal processing. This algorithm is usually used in many tasks such as the matrix estimation and machine learning algorithms. In the past, many convex regularizers, such as the absolute-value norm, were presented for LRMA. Recently, many works show that LRMA on many nonconvex regularizers, such as the quadratic and logarithmic regularizers, can give better efficiency than the convex regularizer. Furthermore, many traditional works present LRMA in the univariate case, and do not consider in the multivariate case. Therefore, LRMA in the multivariate case on the nonconvex regularizer is presented in this work. Note that our proposed method is based on the singular value decomposition (SVD) algorithm. The relationship between singular values is considered by this multivariate case. We also present the novel nonconvex regularizer for LRMA. The simple solution for our method can be obtained from this regularizer. In many random signals, our proposed method is evaluated with the state-of-the-art algorithms. Experimental results show that the best results can be obtained from the proposed method.