Labeled-Robust Regression: Simultaneous Data Recovery and Classification

Rank minimization is widely used to extract low-dimensional subspaces. As a convex relaxation of the rank minimization, the problem of nuclear norm minimization has been attracting widespread attention. However, the standard nuclear norm minimization usually results in overcompression of data in all subspaces and eliminates the discrimination information between different categories of data. To overcome these drawbacks, in this article, we introduce the label information into the nuclear norm minimization problem and propose a labeled-robust principal component analysis (L-RPCA) to realize nuclear norm minimization on multisubspace data. Compared with the standard nuclear norm minimization, our method can effectively utilize the discriminant information in multisubspace rank minimization and avoid excessive elimination of local information and multisubspace characteristics of the data. Then, an effective labeled-robust regression (L-RR) method is proposed to simultaneously recover the data and labels of the observed data. Experiments on real datasets show that our proposed methods are superior to other state-of-the-art methods.