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Semi-supervised sparse subspace clustering with manifold regularization

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Abstract

For sparse subspace clustering methods, it is crucial to develop a good representation matrix to capture the data structure. In this paper, we incorporated the label information into sparse representation and proposed a new semi-supervised sparse subspace clustering method, named semi-supervised sparse subspace clustering with manifold regularization (S\(^4\)CMR). When developing the sparse self-expressive matrix, the S\(^4\)CMR method utilized the label information to constrain the development of expressiveness coefficients. The local manifold regularization was also integrated to enhance clustering stability and local consistency. By utilizing the Alternating Direction Method of Multipliers (ADMM), the convex optimization problem associated with linear constraints can be easily resolved. The developed similarity matrix can provide strong discriminant information, making it more effective for semi-supervised tasks. The effectiveness of the proposed algorithm is demonstrated through experiments on benchmark data sets, such as motion segmentation and image clustering.

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All data used in this study are public, and all data analyzed during this study will be made available on request.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant 12031003, Grant 12101477.

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Authors and Affiliations

  1. School of Science, Xi’an Polytechnic University, Xi’an, 710048, People’s Republic of China

    Zhiwei Xing, Xingshi He & Mengnan Tian

  2. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Jigen Peng

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  1. Zhiwei Xing
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  2. Jigen Peng
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Contributions

Zhiwei Xing: Conceptualization and writing-Original Draft. Jigen Peng: Methodology, supervision, formal analysis. Xingshi He: Methodology, supervision, and writing-review. Mengnan Tian: Formal analysis and editing. All authors have read and agreed to the submitted version of the manuscript.

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Correspondence to Zhiwei Xing.

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Xing, Z., Peng, J., He, X. et al. Semi-supervised sparse subspace clustering with manifold regularization. Appl Intell 54, 6836–6845 (2024). https://doi.org/10.1007/s10489-024-05535-6

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