ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Fuzzy local coordinate concept factorization with graph regularization

  • 1.

    School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China

  • 2.

    School of Computer Science and Information Security, Guilin University of Electronic Technology, Guilin 541000, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.07.017
  • Received Date: 30 April 2020
  • Accepted Date: 22 June 2020
  • Rev Recd Date: 22 June 2020
  • Publish Date: 31 July 2020
    Abstract

  • Abstract

    Matrix Factorization is an effective and efficient method to solve clustering problems in machine learning. However, for most traditional which factorization based models in clustering, there are two necessary steps to get the final assignments. First, original data can be decomposed to a basis matrix and a coefficient matrix through a certain model. Second, the learned coefficient matrix is fed into K-means to make discretization. This two-step paradigm causes extra computational burden and may have some side effect on the final results due to the sensitivity to initialization of K-means. To this end, a novel model termed fuzzy local coordinate concept factorization with graph regularizer (FLCCF-G) is proposed. Which avoids using K-means by enforcing the sum of each row of the non-negative coefficient matrix to equal to one. Then the final clustering results can obtained directly by checking the maximum value of each row of the coefficient matrix. In addition, through this constraint, our proposed model changes is a fuzzy clustering model rather than hard clustering, indicating that the model has better interpretability to data points in boundaries of different clusters. Extensive experimental results on synthetic and Benchmark data sets indicate the better performance of FLCCF-G on data clustering.

    Abstract

    Matrix Factorization is an effective and efficient method to solve clustering problems in machine learning. However, for most traditional which factorization based models in clustering, there are two necessary steps to get the final assignments. First, original data can be decomposed to a basis matrix and a coefficient matrix through a certain model. Second, the learned coefficient matrix is fed into K-means to make discretization. This two-step paradigm causes extra computational burden and may have some side effect on the final results due to the sensitivity to initialization of K-means. To this end, a novel model termed fuzzy local coordinate concept factorization with graph regularizer (FLCCF-G) is proposed. Which avoids using K-means by enforcing the sum of each row of the non-negative coefficient matrix to equal to one. Then the final clustering results can obtained directly by checking the maximum value of each row of the coefficient matrix. In addition, through this constraint, our proposed model changes is a fuzzy clustering model rather than hard clustering, indicating that the model has better interpretability to data points in boundaries of different clusters. Extensive experimental results on synthetic and Benchmark data sets indicate the better performance of FLCCF-G on data clustering.
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    • References(20)
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    YU K, ZHANG T, GONG Y. Nonlinear learning using local coordinate coding[C]//Advances in Neural Information Processing Systems. 2009: 2223-2231.
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    NIE F, SHI S J, LI X. Semi-supervised learning with auto-weighting feature and adaptive graph[J]. IEEE Transactions on Knowledge and Data Engineering, 2019.
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    [19]
    沈浩,王士同.按风格划分数据的模糊聚类算法[J].模式识别与人工智能,2019,32(3):204-213.
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    SHI J, MALIK J. Normalized cuts and image segmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905.)
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    [1]
    XU W, LIU X, GONG Y. Document clustering based on non-negative matrix factorization[C]//Proceedings of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. 2003: 267-273.
    [2]
    WANG Y X, ZHANG Y J. Nonnegative matrix factorization: A comprehensive review[J]. IEEE Transactions on Knowledge and Data Engineering, 2012, 25(6): 1336-1353.
    [3]
    HE Y C, LU H T, HUANG L, et al. Non-negative matrix factorization with pairwise constraints and graph Laplacian[J]. Neural Processing Letters, 2015, 42(1): 167-185.
    [4]
    XU W, GONG Y. Document clustering by concept factorization[C]//Proceedings of the 27th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval. 2004: 202-209.
    [5]
    CAI D, HE X, HAN J, et al. Graph regularized nonnegative matrix factorization for data representation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 33(8): 1548-1560.
    [6]
    CAI D, HE X, HAN J. Locally consistent concept factorization for document clustering[J]. IEEE Transactions on Knowledge and Data Engineering, 2010, 23(6): 902-913.
    [7]
    CHEN Y, ZHANG J, CAI D, et al. Nonnegative local coordinate factorization for image representation[J]. IEEE Transactions on Image Processing, 2012, 22(3): 969-979.
    [8]
    LIU H, YANG Z, YANG J, et al. Local coordinate concept factorization for image representation[J]. IEEE Transactions on Neural Networks and Learning Systems, 2013, 25(6): 1071-1082.
    [9]
    祁宏宇,吴小俊,王士同,杨静宇.一种协同的FCPM模糊聚类算法[J].模式识别与人工智能,2010,23(01):120-126.
    [10]
    马文萍,黄媛媛,李豪,等. 基于粗糙集与差分免疫模糊聚类算法的图像分割[J]. 软件学报,2014,25(11):2675-2689.
    [11]
    苏冬雪,吴小俊.基于多特征模糊聚类的图像融合方法[J].计算机辅助设计与图形学学报,2006,18(6):838-843.
    [12]
    YANG B, FU X, SIDIROPOULOS N D. Learning from hidden traits: Joint factor analysis and latent clustering[J]. IEEE Transactions on Signal Processing, 2016, 65(1): 256-269.
    [13]
    YU K, ZHANG T, GONG Y. Nonlinear learning using local coordinate coding[C]//Advances in Neural Information Processing Systems. 2009: 2223-2231.
    [14]
    NIE F, SHI S J, LI X. Semi-supervised learning with auto-weighting feature and adaptive graph[J]. IEEE Transactions on Knowledge and Data Engineering, 2019.
    [15]
    KYRILLIDIS A, BECKER S, CEVHER V, et al. Sparse projections onto the simplex[C]//International Conference on Machine Learning. 2013: 235-243.
    [16]
    NIE F, YANG S, ZHANG R, et al. A general framework for auto-weighted feature selection via global redundancyminimization[J]. IEEE Transactions on Image Processing, 2018, 28(5): 2428-2438.
    [17]
    CHEN X, YUAN G, NIE F, et al. Semi-supervised feature selection via sparse rescaled linear square regression[J]. IEEE Transactions on Knowledge and Data Engineering, 2018, 32(1): 165-176.
    [18]
    NIE F, HUANG H, CAI X, et al. Efficient and robust feature selection via joint 2, 1-norms minimization[C]//Advances in neural information processing systems. 2010: 1813-1821.
    [19]
    沈浩,王士同.按风格划分数据的模糊聚类算法[J].模式识别与人工智能,2019,32(3):204-213.
    [20]
    SHI J, MALIK J. Normalized cuts and image segmentation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(8): 888-905.)
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