Robust Low Rank Subspace Segmentation via Joint $\ell _{21}$-Norm Minimization

Abstract

In the real world, data samples are often contaminated. Using these contaminated data samples for subspace segmentation usually leads to segmentation results distorted. To remove error, many existing subspace segmentation algorithms directly use different regularization to model the error of the corresponding type in the objective. However, the priori of errors is difficult to obtain in practice, which leads to the degradation of segmentation performance. In this work, we propose to jointly learn the representation matrix and eliminate the effect of errors in the low rank projection spaces via joint the nuclear norm and $\ell _{21}$-norm minimization on the representation matrix for subspace segmentation, termed as robust low rank subspace segmentation via joint $\ell _{21}$-norm minimization (LR-L21). Numerical experiments indicate that the proposed method can effectively deal with different types of errors possibly existing in data, even without the priori of errors. A simple and efficient algorithm is presented based on the alternating direction method, which is convergent. Extensive experiments on three real datasets demonstrate the effectiveness of the proposed approach.