Error-robust low-rank tensor approximation for multi-view clustering

Abstract

Multi-view clustering has been widely developed to improve the clustering performance over that of single-view clustering. However, the types of errors vary and behave inconsistently in each view, which results in performance degradation in real applications. To address this limitation, in this paper, we propose a novel Markov chain-based spectral clustering method for multi-view clustering to handle different types of errors. Unlike most of the existing self-representation-based subspace clustering methods, which process each view separately, ignoring complementary information among views, our method first computes the transition probability matrices of all views, then forms each transition probability matrix as a frontal slice of a third-order tensor to capture the multi-view information, and finally decomposes the tensor into an ideal tensor with the tensor nuclear norm constraint and an error term. Furthermore, the proposed method imposes the group l1 and l2,1 norms on the error matrix for error learning such that various errors can be clearly characterized and processed to improve performance. To solve the challenging optimization model, we propose an efficient algorithm using the augmented Lagrangian multiplier method. Experimental results on three real-world datasets show that the proposed method is superior to the state-of-the art methods in various evaluation metrics.