Hyper-Laplacian Regularized Multi-View Subspace Clustering With a New Weighted Tensor Nuclear Norm

In this paper, we present a hyper-Laplacian regularized method WHLR-MSC with a new weighted tensor nuclear norm for multi-view subspace clustering. Specifically, we firstly stack the subspace representation matrices of the different views into a tensor, which neatly captures the higher-order correlations between the different views. Secondly, in order to make all the singular values have different contributions in tensor nuclear norm based on tensor-Singular Value Decomposition (t-SVD), we use weighted tensor nuclear norm to constrain the constructed tensor, which can obtain the class discrimination information of the sample distribution more accurately. Third, from a geometric point of view, the data are usually sampled from a low-dimensional manifold embedded in a high-dimensional ambient space, the WHLR-MSC model uses hyper-Laplacian graph regularization to capture the local geometric structure of the data. An effective algorithm for solving the optimization problem of WHLR-MSC model is proposed. Extensive experiments on five benchmark image datasets show the effectiveness of our proposed WHLR-MSC method.