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Auto-Weighted Multiple Graph Regularized Non-negative Tensor Tucker Decomposition for Clustering

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Abstract

Non-negative Tucker decomposition (NTD) has received much attention due to its efficient processing of high-dimensional non-negative data. To preserve the intrinsic geometric structure of the data, various graph regularization NTD methods have been proposed. However, most existing methods rely on single graph regularization, limiting their flexibility and adaptability, since a single graph may not adequately capture the intrinsic manifold structure of various datasets. To address this problem, this paper introduces an auto-weighted multiple graph structure as the regularizer for NTD, and then proposes a novel method called auto-weighted multiple graph regularized non-negative Tucker decomposition (AMGRNTD). The AMGRNTD method utilizes a linear combination of multiple simple graphs to more effectively preserve the intrinsic manifold structure of the original data, offering greater applicability to practical problems than single graph-based methods. Furthermore, the AMGRNTD method automatically learns an optimal weight for each graph without additional parameters. Experimental results on four real-world datasets demonstrate that the proposed method achieves better performance in image clustering than some existing state-of-the-art graph-based regularization methods.

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Data Availability

The datasets generated during the current study are available from the corresponding author upon reasonable request.

Code Availability

The code is available upon reasonable request and addressed to the corresponding author.

Notes

  1. Available at https://www.cs.columbia.edu/CAVE/software/softlib/coil-20.php.

  2. Available at https://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html.

  3. Available at https://www.anefian.com/research/face_reco.htm.

  4. Available at http://www.cad.zju.edu.cn/home/dengcai/Data/MLData.html.

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Acknowledgements

The authors are very grateful to the two anonymous referees for their helpful comments and suggestions.

Funding

This work was supported by the National Natural Science Foundation of China (Nos. 12471353, 12201267), the Natural Science Foundation of Gansu Province (No. 22JR5RA559).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Guimin Liu, Bing Zheng & Fanyin Yang

  2. School of Information Engineering and Artificial Intelligence, Lanzhou University of Finance and Economics, Lanzhou, 730000, People’s Republic of China

    Ruijuan Zhao

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  1. Guimin Liu
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Correspondence to Bing Zheng.

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Liu, G., Zhao, R., Zheng, B. et al. Auto-Weighted Multiple Graph Regularized Non-negative Tensor Tucker Decomposition for Clustering. J Sci Comput 102, 86 (2025). https://doi.org/10.1007/s10915-025-02817-0

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