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MSAFC: matrix subspace analysis with fuzzy clustering ability

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Abstract

In this paper, based on the maximum margin criterion (MMC) together with the fuzzy clustering and the tensor theory, a novel matrix based fuzzy maximum margin criterion (MFMMC) is proposed and based upon which a matrix subspace analysis method with fuzzy clustering ability (MSAFC) is derived. Besides, according to the intuitive geometry, a proper method of setting the adjustable parameter \(\gamma \) in the proposed criterion MFMMC is given and its rationale is provided. The proposed method MSAFC can simultaneously realize unsupervised feature extraction and fuzzy clustering for matrix data (e.g. image data). As to the running efficiency of MSAFC, a two-directional orthogonal method of dealing with matrix data without any iteration is developed to improve it. Experimental results on UCI datasets, hand-written digit datasets, face image datasets and gene datasets show the distinctive performance of MSAFC.

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Notes

  1. Although it is also called as 2D-FLD, it is a two-direction two-dimensional feature extraction method in nature. In order to distinguish it from other single-direction two-dimensional feature extraction methods, we take it as \({\hbox {(2D)}}^{2}{\hbox {LDA}}\) in this paper.

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Acknowledgments

This work was supported in part by the Hong Kong Polytechnic University under Grants 1-ZV5V and G-U724, and by the National Natural Science Foundation of China under Grants 61375001,61170122 and 61272210, and by the Natural Science Foundation of Jiangsu Province under Grants BK2011417BK2011003, JiangSu 333 expert engineering Grant (BRA2011142), and 2011, 2012 &2013 Postgraduate Student’s Creative Research Fund of Jiangsu Province. Also, we are very thankful for the referees whose comments help us greatly improve the quality of the paper.

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Authors and Affiliations

  1. School of Information Engineering, Yancheng Institute of Technology, Yancheng, Jiangsu, China

    Jun Gao

  2. School of Digital Media, Jiangnan University, Wuxi, Jiangsu, China

    Jun Gao & Shitong Wang

  3. Department of Computing, Hong Kong Polytechnic University, Hong Kong, China

    Fulai Chung & Shitong Wang

Authors
  1. Jun Gao
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  2. Fulai Chung
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  3. Shitong Wang
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Correspondence to Shitong Wang.

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Communicated by W. Pedrycz.

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Gao, J., Chung, F. & Wang, S. MSAFC: matrix subspace analysis with fuzzy clustering ability. Soft Comput 18, 1143–1163 (2014). https://doi.org/10.1007/s00500-013-1134-3

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