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基于低秩约束的熵加权多视角模糊聚类算法

张嘉旭 王骏 张春香 林得富 周塔 王士同

张嘉旭, 王骏, 张春香, 林得富, 周塔, 王士同. 基于低秩约束的熵加权多视角模糊聚类算法. 自动化学报, 2022, 48(7): 1760−1770 doi: 10.16383/j.aas.c190350
引用本文: 张嘉旭, 王骏, 张春香, 林得富, 周塔, 王士同. 基于低秩约束的熵加权多视角模糊聚类算法. 自动化学报, 2022, 48(7): 1760−1770 doi: 10.16383/j.aas.c190350
Zhang Jia-Xu, Wang Jun, Zhang Chun-Xiang, Lin De-Fu, Zhou Ta, Wang Shi-Tong. Entropy-weighting multi-view fuzzy C-means with low rank constraint. Acta Automatica Sinica, 2022, 48(7): 1760−1770 doi: 10.16383/j.aas.c190350
Citation: Zhang Jia-Xu, Wang Jun, Zhang Chun-Xiang, Lin De-Fu, Zhou Ta, Wang Shi-Tong. Entropy-weighting multi-view fuzzy C-means with low rank constraint. Acta Automatica Sinica, 2022, 48(7): 1760−1770 doi: 10.16383/j.aas.c190350

基于低秩约束的熵加权多视角模糊聚类算法

doi: 10.16383/j.aas.c190350
基金项目: 国家自然科学基金(61772239), 江苏省自然科学基金(BK20181339)资助
详细信息
    作者简介:

    张嘉旭:江南大学数字媒体学院硕士研究生. 主要研究方向为人工智能和模式识别. E-mail: zhangjiaxu@hl.chinamobile.com

    王骏:上海大学通信与信息工程学院副教授. 主要研究方向为人工智能, 模糊聚类和医学图像分类. 本文通信作者. E-mail: wangjun_sytu@hotmail.com

    张春香:江南大学数字媒体学院硕士研究生. 主要研究方向为人工智能和模式识别. E-mail: 17851308360@163.com

    林得富:江南大学数字媒体学院硕士研究生. 主要研究方向为人工智能和模式识别. E-mail: jiangnandaxu_2022@yeah.net

    周塔:江苏科技大学电子信息学院副教授. 主要研究方向为人工智能, 模式识别与智能系统. E-mail: jkdzhout@just.edu.cn

    王士同:江南大学数字媒体学院教授. 主要研究方向为人工智能和模式识别. E-mail: wxwangst@aliyun.com

Entropy-weighting Multi-view Fuzzy C-means With Low Rank Constraint

Funds: Supported by National Natural Science Foundation of China (61772239) and Natural Science Foundation of Jiangsu Province (BK20181339)
More Information
    Author Bio:

    ZHANG Jia-Xu Master student at the School of Digital Media, Jiangnan University. His research interest covers artificial intelligence and data mining

    WANG Jun Associate professor at the School of Communication and Information Engineering,Shanghai University. His research interest covers artificial intelligence, fuzzy clustering, and medical image classification. Corresponding author of this paper

    ZHANG Chun-Xiang Master student at the School of Digital Media, Jiangnan University. Her research interest covers artificial intelligence and data mining

    LIN De-Fu Master student at the School of Digital Media, Jiangnan University. His research interest covers artificial intelligence and data mining

    ZHOU Ta Associate professor at the School of Electronic Information, Jiangsu University of Science and Technology. His research interest covers artificial intelligence, pattern recognition, and intelligent systems

    WANG Shi-Tong Professor at the School of Digital Media, Jiangnan University. His research interest covers artificial intelligence and data mining

  • 摘要: 如何有效挖掘多视角数据内部的一致性以及差异性是构建多视角模糊聚类算法的两个重要问题. 本文在Co-FKM算法框架上, 提出了基于低秩约束的熵加权多视角模糊聚类算法(Entropy-weighting multi-view fuzzy C-means with low rank constraint, LR-MVEWFCM). 一方面, 从视角之间的一致性出发, 引入核范数对多个视角之间的模糊隶属度矩阵进行低秩约束; 另一方面, 基于香农熵理论引入视角权重自适应调整策略, 使算法根据各视角的重要程度来处理视角间的差异性. 本文使用交替方向乘子法(Alternating direction method of multipliers, ADMM)进行目标函数的优化. 最后, 人工模拟数据集和UCI (University of California Irvine)数据集上进行的实验结果验证了该方法的有效性.
  • 图  1  Co-FKM算法处理多视角聚类任务工作流程

    Fig.  1  Co-FKM algorithm for multi-view clustering task

    图  2  LR-MVEWFCM算法处理多视角聚类任务工作流程

    Fig.  2  LR-MVEWFCM algorithm for multi-view clustering task

    图  3  模拟数据集及各视角数据集

    Fig.  3  Simulated data under multiple views

    图  4  低秩约束对算法性能的影响(横坐标为数据集编号, 纵坐标为聚类性能指标)

    Fig.  4  The influence of low rank constraints on the performance of the algorithm (the X-coordinate is the data set number and the Y-coordinate is the clustering performance index)

    图  5  LR-MVEWFCM算法的收敛曲线

    Fig.  5  Convergence curve of LR-MVEWFCM algorithm

    图  6  模拟数据集7上参数敏感性分析

    Fig.  6  Sensitivity analysis of parameters on simulated dataset 7

    表  1  参数定义和设置

    Table  1  Parameter setting in the experiments

    算法算法说明参数设置
    FCM经典的单视角模糊聚类算法模糊指数$m=\frac{\min (N, D-1)}{\min (N, D-1)-2}$,
    其中, $N$表示样本数, $D$表示样本维数
    CombKM组合${\rm{K}}\text{-}{\rm{means}}$算法
    Co-FKM多视角协同划分的模糊聚类算法模糊指数$m=\frac{\min (N, D-1)}{\min (N, D-1)-2}$, 协同学习系数$\eta{}\in{}\frac{K-1}{K}$,
    其中, $K$为视角数, 步长$\rho{}=0.01$
    Co-Clustering基于样本与特征空间的协同聚类算法正则化系数$\lambda \in\left\{10^{-3}, 10^{-2}, \cdots, 10^{3}\right\}$,
    正则化系数$\mu \in\left\{10^{-3}, 10^{-2}, \cdots, 10^{3}\right\}$
    LR-MVEWFCM基于低秩约束的熵加权多视角模糊聚类算法视角权重平衡因子$\lambda{}\in{}\left\{{10}^{-5}, {10}^{-4}, \cdots{}, {10}^5\right\}$, 低秩约束正则项系数$\theta{}\in{}\left\{{10}^{-3}, 10^{-2}, \cdots{}, {10}^3\right\}$, 模糊指数$m=2$
    MVEWFCMLR-MVEWFCM 算法中低秩约束正则项系数$\theta{}=0$视角权重平衡因子$\lambda{}\in{}\left\{{10}^{-5}, {10}^{-4}, \cdots{}, {10}^5\right\}$, 模糊指数$m=2$
    下载: 导出CSV

    表  2  模拟数据集特征组成

    Table  2  Characteristic composition of simulated dataset

    视角包含特征
    视角 1$x,y$
    视角 2$y,z$
    视角 3$x,z$
    下载: 导出CSV

    表  3  模拟数据实验算法性能对比

    Table  3  Performance comparison of the proposed algorithms on simulated dataset

    编号包含特征NMIRI
    1视角11.0000 ± 0.00001.0000 ± 0.0000
    2视角20.7453 ± 0.00750.8796 ± 0.0081
    3视角30.8750 ± 0.00810.9555 ± 0.0006
    4视角1, 视角21.0000 ± 0.00001.0000 ± 0.0000
    5视角1, 视角31.0000 ± 0.00001.0000 ± 0.0000
    6视角2, 视角30.9104 ± 0.03960.9634 ± 0.0192
    7视角2, 视角31.0000 ± 0.00001.0000 ± 0.0000
    下载: 导出CSV

    表  4  模拟数据集7上各算法的性能比较

    Table  4  Performance comparison of the proposed algorithms on simulated dataset 7

    数据集指标Co-ClusteringCombKMFCMCo-FKMLR-MVEWFCM
    ANMI-mean1.00000.93051.00001.00001.0000
    NMI-std0.00000.14640.00000.00000.0000
    RI-mean1.00000.94451.00001.00001.0000
    RI-std0.00000.11710.00000.00000.0000
    下载: 导出CSV

    表  5  基于UCI数据集构造的多视角数据

    Table  5  Multi-view data constructded based on UCI dataset

    编号原数据集说明视角特征样本视角类别
    8ISShape92 31027
    RGB9
    9IrisSepal长度215023
    Sepal宽度
    Petal长度2
    Petal宽度
    10Balance天平左臂重量262523
    天平左臂长度
    天平右臂重量2
    天平右臂长度
    11IrisSepal长度115043
    Sepal宽度1
    Petal长度1
    Petal宽度1
    12Balance天平左臂重量162543
    天平左臂长度1
    天平右臂重量1
    天平右臂长度1
    13Ionosphere每个特征单独
    作为一个视角
    1351342
    14Wine每个特征单独
    作为一个视角
    1178133
    下载: 导出CSV

    表  6  5种聚类方法的NMI值比较结果

    Table  6  Comparison of NMI performance of five clustering methods

    编号Co-ClusteringCombKMFCMCo-FKMLR-MVEWFCM
    均值P-value均值P-value均值P-value均值P-value均值
    80.5771 ±
    0.0023
    0.00190.5259 ±
    0.0551
    0.20560.5567 ±
    0.0184
    0.00440.5881 ±
    0.0109
    3.76×10−40.5828 ±
    0.0044
    90.7582 ±
    7.4015 ×10−17
    2.03×10−240.7251 ±
    0.0698
    2.32×10−70.7578 ±
    0.0698
    1.93×10−240.8317 ±
    0.0064
    8.88×10−160.9029 ±
    0.0057
    100.2455 ±
    0.0559
    0.01650.1562 ±
    0.0749
    3.47×10−50.1813 ±
    0.1172
    0.00610.2756 ±
    0.0309
    0.10370.3030 ±
    0.0402
    110.7582 ±
    1.1703×10−16
    2.28×10−160.7468 ±
    0.0079
    5.12×10−160.7578 ±
    1.1703×10−16
    5.04×10−160.8244 ±
    1.1102×10−16
    2.16×10−160.8768 ±
    0.0097
    120.2603 ±
    0.0685
    0.38250.1543 ±
    0.0763
    4.61×10−40.2264 ±
    0.1127
    0.15730.2283 ±
    0.0294
    0.01460.2863 ±
    0.0611
    130.1385 ±
    0.0085
    2.51×10−90.1349 ±
    2.9257×10−17
    2.35×10−130.1299 ±
    0.0984
    2.60×10−100.2097 ±
    0.0329
    0.04830.2608 ±
    0.0251
    140.4288 ±
    1.1703×10−16
    1.26×10−080.4215 ±
    0.0095
    7.97×10−090.4334 ±
    5.8514×10−17
    2.39×10−080.5295 ±
    0.0301
    0.43760.5413 ±
    0.0364
    下载: 导出CSV

    表  7  5种聚类方法的RI值比较结果

    Table  7  Comparison of RI performance of five clustering methods

    编号Co-ClusteringCombKMFCMCo-FKMLR-MVEWFCM
    均值P-value均值P-value均值P-value均值P-value均值
    80.8392 ±
    0.0010
    1.3475 ×10−140.8112 ±
    0.0369
    1.95×10−70.8390 ±
    0.0115
    0.00320.8571 ±
    0.0019
    0.00480.8508 ±
    0.0013
    90.8797 ±
    0.0014
    1.72×10−260.8481 ±
    0.0667
    2.56×10−50.8859 ±
    1.1703×10−16
    6.49×10−260.9358 ±
    0.0037
    3.29×10−140.9665 ±
    0.0026
    100.6515 ±
    0.0231
    3.13×10−40.6059 ±
    0.0340
    1.37×10−60.6186 ±
    0.0624
    0.00160.6772 ±
    0.0227
    0.07610.6958 ±
    0.0215
    110.8797 ±
    0.0014
    1.25×10−180.8755 ±
    0.0029
    5.99×10−120.8859 ±
    0.0243
    2.33×10−180.9267 ±
    2.3406×10−16
    5.19×10−180.9527 ±
    0.0041
    120.6511 ±
    0.0279
    0.01560.6024 ±
    0.0322
    2.24×10−50.6509 ±
    0.0652
    0.11390.6511 ±
    0.0189
    0.0080.6902 ±
    0.0370
    130.5877 ±
    0.0030
    1.35×10−120.5888 ±
    0.0292
    2.10×10−140.5818 ±
    1.1703×10−16
    4.6351 ×10−130.6508 ±
    0.0147
    0.03580.6855 ±
    0.0115
    140.7187 ±
    1.1703×10−16
    3.82×10−60.7056 ±
    0.0168
    1.69×10−60.7099 ±
    1.1703×10−16
    8.45×10−70.7850 ±
    0.0162
    0.59050.7917 ±
    0.0353
    下载: 导出CSV
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出版历程
  • 收稿日期:  2019-05-09
  • 录用日期:  2019-07-17
  • 网络出版日期:  2022-05-31
  • 刊出日期:  2022-07-01

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