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Structured block diagonal representation for subspace clustering

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Abstract

The aim of the subspace clustering is to segment the high-dimensional data into the corresponding subspace. The structured sparse subspace clustering and the block diagonal representation clustering are quite advanced spectral-type subspace clustering algorithms when handling to the linear subspaces. In this paper, the respective advantages of these two algorithms are fully exploited, and the structured block diagonal representation (SBDR) subspace clustering is proposed. In many classical spectral-type subspace clustering algorithms, the affinity matrix which obeys the block diagonal property can not necessarily bring satisfying clustering results. However, the k-block diagonal regularizer of the SBDR algorithm directly pursues the block diagonal matrix, and this regularizer is obviously more effective. On the other hand, the general procedure of the spectral-type subspace clustering algorithm is to get the affinity matrix firstly and next perform the spectral clustering. The SBDR algorithm considers the intrinsic relationship of the two seemingly separate steps, the subspace structure matrix obtained by the spectral clustering is used iteratively to facilitate a better initialization for the representation matrix. The experimental results on the synthetic dataset and the real dataset have demonstrated the superior performance of the proposed algorithm over other prevalent subspace clustering algorithms.

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Acknowledgements

This work was supported by the National Key R&D Program of China (Project Number: 2018YFB1701903) and the National Natural Science Foundation of China (Project Numbers: 61973138, 61672263).

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Authors and Affiliations

  1. Engineering Research Center of Internet of Things Technology Applications, Ministry of Education, Jiangnan University, No 1800, Lihu Avenue, Wuxi, Jiangsu, 214122, China

    Maoshan Liu, Yan Wang & Zhicheng Ji

  2. Jiangsu Provincial Engineering Laboratory of Pattern Recognition and Computational Intelligence, Jiangnan University, No 1800, Lihu Avenue, Wuxi, Jiangsu, 214122, China

    Jun Sun

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  1. Maoshan Liu
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  2. Yan Wang
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  3. Jun Sun
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  4. Zhicheng Ji
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Correspondence to Yan Wang.

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Liu, M., Wang, Y., Sun, J. et al. Structured block diagonal representation for subspace clustering. Appl Intell 50, 2523–2536 (2020). https://doi.org/10.1007/s10489-020-01629-z

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