One-Step Multiview Subspace Segmentation via Joint Skinny Tensor Learning and Latent Clustering

Multiview subspace clustering (MSC) has attracted growing attention due to the extensive value in various applications, such as natural language processing, face recognition, and time-series analysis. In this article, we are devoted to address two crucial issues in MSC: 1) high computational cost and 2) cumbersome multistage clustering. Existing MSC approaches, including tensor singular value decomposition (t-SVD)-MSC that has achieved promising performance, generally utilize the dataset itself as the dictionary and regard representation learning and clustering process as two separate parts, thus leading to the high computational overhead and unsatisfactory clustering performance. To remedy these two issues, we propose a novel MSC model called joint skinny tensor learning and latent clustering (JSTC), which can learn high-order skinny tensor representations and corresponding latent clustering assignments simultaneously. Through such a joint optimization strategy, the multiview complementary information and latent clustering structure can be exploited thoroughly to improve the clustering performance. An alternating direction minimization algorithm, which owns low computational complexity and can be run in parallel when solving several key subproblems, is carefully designed to optimize the JSTC model. Such a nice property makes our JSTC an appealing solution for large-scale MSC problems. We conduct extensive experiments on ten popular datasets and compare our JSTC with 12 competitors. Five commonly used metrics, including four external measures (NMI, ACC, F-score, and RI) and one internal metric (SI), are adopted to evaluate the clustering quality. The experimental results with the Wilcoxon statistical test demonstrate the superiority of the proposed method in both clustering performance and operational efficiency.