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Multi-view subspace clustering with Kronecker-basis-representation-based tensor sparsity measure

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Abstract

Multi-view data are popular in many machine learning and computer vision applications. For example, in computer vision fields, one object can be described with images, text or videos. Recently, multi-view subspace clustering approaches, which can make use of the complementary information among different views to improve the performance of clustering, have attracted much attention. In this paper, we propose a novel multi-view subspace clustering method with Kronecker-basis-representation-based tensor sparsity measure (MSC-KBR) to address multi-view subspace clustering problem. In the MSC-KBR model, we first construct a tensor based on the subspace representation matrices of different views, and, then the high-order correlations underlying different views can be explored. We also adopt a novel Kronecker-basis-representation-based tensor sparsity measure (KBR) to the constructed tensor to reduce the redundancy of the learned subspace representations and improve the accuracy of clustering. Different from the traditional unfolding-based tensor norm, KBR can encode both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC decompositions for a general tensor. By using the augmented Lagrangian method, an efficient algorithm is presented to solve the optimization problem of the MSC-KBR model. The experimental results on some datasets show that the proposed MSC-KBR model outperforms many state-of-the-art multi-view clustering approaches.

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Notes

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Acknowledgements

This research is supported by NSFC of China (Nos. 61976005, 61772277); 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 Computer Science and Information, AnHui Polytechnic University, WuHu, 241000, AnHui, China

    Gui-Fu Lu, Hua Li, Yong Wang & Ganyi Tang

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  1. Gui-Fu Lu
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  2. Hua Li
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Lu, GF., Li, H., Wang, Y. et al. Multi-view subspace clustering with Kronecker-basis-representation-based tensor sparsity measure. Machine Vision and Applications 32, 123 (2021). https://doi.org/10.1007/s00138-021-01247-w

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