Robust subspace learning-based low-rank representation for manifold clustering

Abstract

Spectral clustering-based subspace clustering methods have attracted broad interest in recent years. This kind of methods usually uses the self-representation in the original space to extract the affinity between the data points. However, we can usually find a subspace where the affinity of the projected data points can be extracted by self-representation more effectively. Moreover, only using the self-representation in the original space cannot handle nonlinear manifold clustering well. In this paper, we present robust subspace learning-based low-rank representation learning a subspace favoring the affinity extraction for the low-rank representation. The process of learning the subspace and yielding the representation is conducted simultaneously, and thus, they can benefit from each other. After extending the linear projection to nonlinear mapping, our method can handle manifold clustering problem which can be viewed as a general case of subspace clustering. In addition, the $$\ell _{2,1}$$ -norm used in our model can increase the robustness of our method. Extensive experimental results demonstrate the effectiveness of our method on manifold clustering.