Robust Rank-Constrained Sparse Learning: A Graph-Based Framework for Single View and Multiview Clustering
Qi Wang, Ran Liu, Mulin Chen, Xuelong Li
Abstract
Graph-based clustering aims to partition the data according to a similarity graph, which has shown impressive performance on various kinds of tasks. The quality of similarity graph largely determines the clustering results, but it is difficult to produce a high-quality one, especially when data contain noises and outliers. To solve this problem, we propose a robust rank constrained sparse learning (RRCSL) method in this article. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2,1}$ </tex-math></inline-formula> -norm is adopted into the objective function of sparse representation to learn the optimal graph with robustness. To preserve the data structure, we construct an initial graph and search the graph within its neighborhood. By incorporating a rank constraint, the learned graph can be directly used as the cluster indicator, and the final results are obtained without additional postprocessing. In addition, the proposed method cannot only be applied to single-view clustering but also extended to multiview clustering. Plenty of experiments on synthetic and real-world datasets have demonstrated the superiority and robustness of the proposed framework.