Multi-View Clustering by Low-Rank Tensor Decomposition

Abstract

To solve the problem that the traditional multi-view learning methods cannot fully explore the consensus information among different views, a low-rank tensor decomposition multi-view spectral clustering algorithm based on truncated nuclear norm is proposed. The similarity matrix and transition probability matrix of each view are firstly obtained, then a tensor based on multi-view transition probability matrices is constructed. Tensor singular value decomposition based tensor truncated nuclear norm is imposed to preserve the low-rank property of the common tensor. Minimizing the tensor truncated kernel norm, a tensor containing both shared information and high-order correlations can be obtained properly via learning. The proposed method can be efficiently optimized by the alternating direction method of multipliers. Experimental results on 4 datasets show that compared with standard spectral clustering, the value of normalized mutual information is enhanced by 7.9%, 24.9%, 29.5% and 8.1% respectively, and 3.4%, 18.1%, 17.6% and 6.6% respectively compared with LT-MSC. It is found that the performance of the proposed method only has small variations when trade-off parameter is chosen from 0.000 1 to 100, and the best trade-off parameter is ranged from 0.1 to 1. The proposed method has good clustering effect and robustness, and can effectively enhance the complementarity between the various perspectives.