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Multi-view subspace similarity learning based on t-SVD

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Abstract

Multi-view clustering is extensively applied to practical applications. The similarity matrix acquired by most of the existing approaches is obtained by using original multi-view data. However, when dealing with data in a nonlinear subspace, the results of existing methods are not satisfactory. In addition, the existing methods cannot solve the high order relevance of multi-view data. To solve these problems, we present a novel multi-view subspace similarity learning method, MSSLt-SVD, on the basis of tensor singular value decomposition (t-SVD). First, we map each view of the data to the Hilbert space through a Gaussian kernel and then minimize the reconstruction error of the obtained kernel matrix. Second, we use the t-SVD-based tensor nuclear norm (TNN) instead of the matrix-kernel norm as the regularization term to capture the high-order relevance of multi-view data. Then, we incorporate these two steps into a framework and design the corresponding goal function, which can be solved by using the augmented lagrange multiplier (ALM) method. Experiments on some datasets show that the performance of MSSLt-SVD algorithm is better than some representative ones.

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Acknowledgements

This research is supported by the NSFC (No. 61976005); the Anhui Natural Science Foundation (No. 1908085MF183); the Safety-Critical Software Key Laboratory Research Program (Grant No. NJ2018014); the Training Program for Young and Middle-aged Top Talents of Anhui Polytechnic University (No. 201812); the State Key Laboratory for Novel Software Technology (Nanjing University) Research Program (No. KFKT2019B23); and the Major Project of Natural Science Research in Colleges and Universities of Anhui Province (No. KJ2019ZD15).

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  1. School of Electrical Engineering, AnHui Polytechnic University, WuHu, 241000, AnHui, China

    Rong Tang

  2. School of Computer Science and Information, AnHui Polytechnic University, WuHu, 241000, AnHui, China

    Gui-Fu Lu

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  1. Rong Tang
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Correspondence to Gui-Fu Lu.

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Tang, R., Lu, GF. Multi-view subspace similarity learning based on t-SVD. Multimed Tools Appl 82, 45605–45620 (2023). https://doi.org/10.1007/s11042-023-15645-x

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