Learning an Optimal Bipartite Graph for Subspace Clustering via Constrained Laplacian Rank

In this article, we focus on utilizing the idea of co-clustering algorithms to address the subspace clustering problem. In recent years, co-clustering methods have been developed greatly with many important applications, such as document clustering and gene expression analysis. Different from the traditional graph-based methods, co-clustering can utilize the bipartite graph to extract the duality relationship between samples and features. It means that the bipartite graph can obtain more information than other traditional graph methods. Therefore, we proposed a novel method to handle the subspace clustering problem by combining dictionary learning with a bipartite graph under the constraint of the (normalized) Laplacian rank. Besides, to avoid the effect of redundant information hiding in the data, the original data matrix is not used as the static dictionary in our model. By updating the dictionary matrix under the sparse constraint, we can obtain a better coefficient matrix to construct the bipartite graph. Based on Theorem 2 and Lemma 1, we further speed up our algorithm. Experimental results on both synthetic and benchmark datasets demonstrate the superior effectiveness and stability of our model.

Automated summary

This article focuses on the utilization of co-clustering algorithms to solve the subspace clustering problem. Co-clustering methods, unlike traditional graph-based approaches, can extract the duality relationship between samples and features using bipartite graphs, leading to more information extraction. The proposed novel method combines dictionary learning with a bipartite graph under the constraint of the (normalized) Laplacian rank to address the subspace clustering problem. Experimental results demonstrate the effectiveness and stability of the model.