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Soft Subspace Fuzzy Clustering with Dimension Affinity Constraint

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Abstract

For high-dimensional data, the cluster structure often exists in a feature subset instead of the whole feature space. Soft subspace clustering can efficiently extract the important subspace by allocating a weight to each dimension on the basis of the contribution of this dimension to the cluster identification. However, this kind of method does not consider the correlations between data dimensions in the clustering process. In high-dimensional data, when two dimensions are closely correlated, they should have similar weight assignments, and vice versa. Inspired by the way of clustering with graph embedding technique, we present a novel soft subspace clustering algorithm with considering the correlations between data dimensions. In this method, a novel dimension affinity regularization term is included into the objective function to further highlight those correlated dimensions that are important to the formation of clusters and compress the feature subspaces. Moreover, the alternating direction method of multipliers is adopted to solve the linear optimization problem regarding the dimension weight lasso regularization. In addition, as an extension, the kernelized version is explored to address the non-linear data clustering. Experiments on the real-world datasets demonstrate the efficiency of the presented algorithms in comparison with the conventional clustering methods.

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Acknowledgements

This work was funded in part by the National Natural Science Foundation of China under Grants with Nos. 61873324, 61903156, and 61872419, the Natural Science Foundation of Shandong Province under Grant with No. ZR2019MF040, the Higher Educational Science and Technology Program of Jinan City under Grant with No. 2020GXRC057, the University Innovation Team Project of Jinan under Grant No. 2019GXRC015, and the Key Science & Technology Innovation Project of Shandong Province under Grants Nos. 2019JZZY010324 and 2019JZZY010448.

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Author notes

  1. Yingying Guo and Rongrong Wang have contributed equally to this work.

Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Network based Intelligent Computing, University of Jinan, Jinan, 250022, China

    Yingying Guo, Rongrong Wang, Jin Zhou, Yuehui Chen, Shiyuan Han, Lin Wang, Tao Du, Ke Ji, Ya-ou Zhao & Kun Zhang

  2. Development and Test Center, Chinabond Fintech Information Technology Co. Ltd., Beijing, 100032, China

    Hui Jiang

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  1. Yingying Guo
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  2. Rongrong Wang
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  3. Jin Zhou
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Correspondence to Jin Zhou.

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Guo, Y., Wang, R., Zhou, J. et al. Soft Subspace Fuzzy Clustering with Dimension Affinity Constraint. Int. J. Fuzzy Syst. 24, 2283–2301 (2022). https://doi.org/10.1007/s40815-022-01271-6

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  • DOI: https://doi.org/10.1007/s40815-022-01271-6

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