Robust Subspace Clustering Based on Latent Low-rank Representation with Weighted Schatten-p Norm Minimization

Abstract

AbstractSubspace clustering, which aims to cluster the high-dimensional data samples drawn from a union of multiple subspaces, has drawn much attention in machine learning and computer vision. As a typical subspace clustering method, latent low-rank representation (LLRR) can handle high-dimensional data efficiently. However, the nuclear norm in its formulation is not the optimal approximation of the rank function, which may lead to a suboptimal solution for the original rank minimization problem. In this paper, a weighted Schatten-p norm (WSN), which can better induce low rank, is used to replace the nuclear norm in LLRR, resulting in a novel latent low-rank representation model (WSN-LLRR) for subspace clustering. Furthermore, considering both the accuracy and convergence rate, we present an efficient optimization algorithm by using the alternating direction method of multipliers (ADMM) to solve the proposed model. Finally, experimental results on several real-world subspace clustering datasets show that the performance of our proposed method is better than several state-of-the-art methods, which demonstrates that WSN-LLRR can get a better accurate low-rank solution.KeywordsSubspace clusteringLatent low-rank representationWeighted schatten-[spsdollar1dollarsps] norm