Abstract
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.
Highlights
In the era of big data, the data are usually generated from different sources or collected from different views, these data are called multi-view data [1]
The main contributions of our work are summarized as follows: 1) Our proposed algorithm stacks the subspace representation matrices of different views into a tensor and uses low-rank constraints on the constructed tensor to capture the global structure of the data, and the hyper-Laplacian graph regularization term is used to capture the local geometry structure of the data, which effectively utilizes the relevant information between different views
These two methods are most related to our method, which shows that our method uses graph regularization term to capture the local structure of the data and uses weighted tensor nuclear norm to treat singular values differently, which is effective for improving clustering performance
Summary
In the era of big data, the data are usually generated from different sources or collected from different views, these data are called multi-view data [1]. Author et al.: Preparation of Papers for IEEE TRANSACTIONS and JOURNALS tensor constructed by the representation matrices of different views, and effectively utilizes the relevant information between different views It ignores the local geometric structure of the data samples embedded in the highdimensional ambient space. In order to solve the above problems, in this paper, we propose hyper-Laplacian regularized multi-view subspace clustering with a new weighted tensor nuclear norm (WHLRMSC) method. The main contributions of our work are summarized as follows: 1) Our proposed algorithm stacks the subspace representation matrices of different views into a tensor and uses low-rank constraints on the constructed tensor to capture the global structure of the data, and the hyper-Laplacian graph regularization term is used to capture the local geometry structure of the data, which effectively utilizes the relevant information between different views.
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