Tensor subspace clustering using consensus tensor low-rank representation

Abstract

Recently, subspace clustering (SC) has received an increasing amount of attention. Generally, SC methods are implemented on sample data in matrix form. Even for multiway or tensor data, which is prevalent in reality, traditional SC methods should convert each sample to a vector and then form a data matrix. However, the vectorization process will damage the underlying inherent spatial structure of the data. To address this problem, in this paper, we propose a novel consensus tensor low-rank representation (CTLRR) method, which is directly implemented on tensor data. First, the tensor nuclear norm (TNN) and t-product, which is defined as the multiplication of two tensors, are employed to model the data and obtain the low-rank representation tensor. Second, spectral clustering is unified into CTLRR to explore the consensus information among the low-rank representation tensor, which helps obtain the final fusion similarity matrix with the k connected components, where k is the number of clusters. Third, the cluster structure is characterized, and the clustering performance is substantially improved. Last, an optimization procedure for CTLRR is presented. Experimental results on certain challenging datasets show that the proposed CTLRR method outperforms the state-of-the-art methods.