Tensor low-rank representation combined with consistency and diversity exploration

In recent years, many tensor data processing methods have been proposed. Tensor low-rank representation (TLRR) is a recently proposed tensor-based clustering method that has shown good clustering performance in some applications. However, TLRR does not make full use of the consistency and diversity information hidden in different similarity matrices. Therefore, we propose the TLRR combined with consistency and diversity exploration (TLRR-CD) method. First, the tensor Frobenius norm and tensor product (t-product), which is defined as the multiplication of two tensors, are used to obtain the low-rank representation tensor, which can be seen as being composed of many similarity matrices. Second, the low-rank representation tensor is further decomposed into a consistent tensor, which contains the common structural information contained in the different similarity matrices, and a diversity tensor, which contains the locally specific structural information of different similarity matrices. Finally, the Hilbert–Schmidt Independence Criterion (HSIC), which is used to measure the relevance of local specific structural information, and spectral clustering are unified into the final objective function to improve clustering performance. In addition, the optimization process of TLRR-CD is also given. The experimental results show the good performance of TLRR-CD.