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基于加权锚点的多视图聚类算法

刘溯源 王思为 唐厂 周思航 王思齐 刘新旺

刘溯源, 王思为, 唐厂, 周思航, 王思齐, 刘新旺. 基于加权锚点的多视图聚类算法. 自动化学报, 2024, 50(6): 1160−1170 doi: 10.16383/j.aas.c220531
引用本文: 刘溯源, 王思为, 唐厂, 周思航, 王思齐, 刘新旺. 基于加权锚点的多视图聚类算法. 自动化学报, 2024, 50(6): 1160−1170 doi: 10.16383/j.aas.c220531
Liu Su-Yuan, Wang Si-Wei, Tang Chang, Zhou Si-Hang, Wang Si-Qi, Liu Xin-Wang. Multi-view clustering with weighted anchors. Acta Automatica Sinica, 2024, 50(6): 1160−1170 doi: 10.16383/j.aas.c220531
Citation: Liu Su-Yuan, Wang Si-Wei, Tang Chang, Zhou Si-Hang, Wang Si-Qi, Liu Xin-Wang. Multi-view clustering with weighted anchors. Acta Automatica Sinica, 2024, 50(6): 1160−1170 doi: 10.16383/j.aas.c220531

基于加权锚点的多视图聚类算法

doi: 10.16383/j.aas.c220531
基金项目: 国家自然科学基金(61922088, 62006236, 62006237), 国防科技大学科研计划项目(ZK21-23, ZK20-10), 高性能计算国家重点实验室自主课题(202101-15)资助
详细信息
    作者简介:

    刘溯源:国防科技大学计算机学院硕士研究生. 主要研究方向为多视图学习. E-mail: suyuanliu@nudt.edu.cn

    王思为:国防科技大学计算机学院博士研究生. 主要研究方向为无监督多视图学习, 大规模聚类和深度无监督学习. E-mail: wangsiwei13@nudt.edu.cn

    唐厂:中国地质大学计算机学院教授. 主要研究方向为多视图学习. E-mail: tangchang@cug.edu.cn

    周思航:国防科技大学智能科学学院讲师. 主要研究方向为机器学习, 医学图像分析. E-mail: sihangjoe@gmail.com

    王思齐:国防科技大学计算机学院高性能计算国家重点实验室助理研究员. 主要研究方向为机器学习, 异常检测. 本文通信作者. E-mail: wangsiqi10c@gmail.com

    刘新旺:国防科技大学计算机学院教授. 主要研究方向为核学习, 无监督特征学习. E-mail: xinwangliu@nudt.edu.cn

Multi-view Clustering With Weighted Anchors

Funds: Supported by National Natural Science Foundation of China (61922088, 62006236, 62006237), Research Project of National University of Defense Technology (ZK21-23, ZK20-10), and Autonomous Project of State Key Laboratory of High Performance Computing (202101-15)
More Information
    Author Bio:

    LIU Su-Yuan Master student at the College of Computer, National University of Defense Technology. His main research interest is multi-view learning

    WANG Si-Wei Ph.D. candidate at the College of Computer, National University of Defense Technology. His research interest covers unsupervised multi-view learning, scalable clustering, and deep unsupervised learning

    TANG Chang Professor at the College of Computer, China University of Geosciences. His main research interest is multi-view learning

    ZHOU Si-Hang Lecturer at the College of Intelligent Science and Technology, National University of Defense Technology. His research interest covers machine learning and medical image analysis

    WANG Si-Qi Assistant professor at the State Key Laboratory of High Performance Computing, College of Computer, National University of Defense Technology. His research interest covers machine learning and outlier/anomaly detection. Corresponding author of this paper

    LIU Xin-Wang Professor at the College of Computer, National University of Defense Technology. His research interest covers kernel learning and unsupervised feature learning

  • 摘要: 大规模多视图聚类旨在解决传统多视图聚类算法中计算速度慢、空间复杂度高, 以致无法扩展到大规模数据的问题. 其中, 基于锚点的多视图聚类方法通过使用整体数据集合的锚点集构建后者对于前者的重构矩阵, 利用重构矩阵进行聚类, 有效地降低了算法的时间和空间复杂度. 然而, 现有的方法忽视了锚点之间的差异, 均等地看待所有锚点, 导致聚类结果受到低质量锚点的限制. 为定位更具有判别性的锚点, 加强高质量锚点对聚类的影响, 提出一种基于加权锚点的大规模多视图聚类算法(Multi-view clustering with weighted anchors, MVC-WA). 通过引入自适应锚点加权机制, 所提方法在统一框架下确定锚点的权重, 进行锚图的构建. 同时, 为增加锚点的多样性, 根据锚点之间的相似度进一步调整锚点的权重. 在9个基准数据集上与现有最先进的大规模多视图聚类算法的对比实验结果验证了所提方法的高效性与有效性.
    1)  11 http://mkl.ucsd.edu/dataset/protein-fold-prediction/2 http://archive.ics.uci.edu/ml/datasets/Multiple+Features3 https://www.fruitfly.org/4 http://svcl.ucsd.edu/projects/crossmodal/5 https://www.ee.columbia.edu/ln/dvmm/CCV/6 http://staff.science.uva.nl/aloi/7 https://www.cs.tau.ac.il/wolf/ytfaces/
    2)  2http://archive.ics.uci.edu/ml/datasets/Multiple+Features
    3)  3https://www.fruitfly.org/
    4)  4http://svcl.ucsd.edu/projects/crossmodal/
    5)  5https://www.ee.columbia.edu/ln/dvmm/CCV/
    6)  6http://staff.science.uva.nl/aloi/
    7)  7https://www.cs.tau.ac.il/wolf/ytfaces/
  • 图  1  4个数据集上学习到的锚点权重

    Fig.  1  Learned anchor weights on four datasets

    图  2  目标函数值随迭代次数增长的变化曲线

    Fig.  2  The variation curves the objective function value with the increase of the number of iterations

    图  3  参数调整对聚类性能的影响

    Fig.  3  The influence of parameter tuning on clustering performance

    表  1  本文使用的主要符号

    Table  1  Summary of notations

    符号 定义
    $n$ 数据点数量
    $k$ 类别数
    $v$ 视图数
    $m$ 锚点数
    $d^{(p)}$ 第$p$个视图上数据的维度
    ${\boldsymbol{X}}^{(p)} \in \mathbf{R}^{d^{(p)} \times n}$ 第$p$个视图的数据矩阵
    ${\boldsymbol{A}}^{(p)} \in \mathbf{R}^{d^{(p)} \times m}$ 第$p$个视图的锚点矩阵
    ${\boldsymbol{Z}}^{(p)} \in \mathbf{R}^{m \times n}$ 第$p$个视图上的锚图
    ${\boldsymbol{W}}^{(p)} \in \mathbf{R}^{m \times m}$ 第$p$个视图上的权重矩阵
    ${\boldsymbol{M}}^{(p)} \in \mathbf{R}^{m \times m}$ 第$p$个视图上锚点的相关性矩阵
    下载: 导出CSV

    表  2  实验中使用的数据集

    Table  2  Description of datasets

    数据集 样本数 视图数 类别数
    ProteinFold 694 12 27
    Mfeat 2 000 6 10
    BDGP 2 500 3 5
    Wiki 2 866 2 10
    CCV 6 773 3 20
    ALOI 10 800 4 100
    YTF10 38 654 4 10
    YTF20 63 896 4 20
    YTF50 126 054 4 50
    下载: 导出CSV

    表  3  对比算法在所有数据集上的聚类性能 (%)

    Table  3  Clustering performance of compared methods on all datasets (%)

    数据集
    MSC-IAS PMSC MVSC FMR SFMC MLRSSC AMGL RMKM BMVC LMVSC SMVSC FPMVS 本文算法
    ACC
    ProteinFold 28.45±1.31 12.06±0.41 24.83±1.35 32.85±1.75 26.22±0 11.10±0 10.96±1.23 23.63±0 26.22±0 28.29±1.57 29.26±1.52 30.03±1.06 32.57±1.88
    Mfeat 85.95±6.81 32.48±2.11 45.40±3.03 59.63±3.21 85.85±0 20.00±0 83.08±7.58 67.10±0 58.45±0 81.50±5.30 67.64±3.86 46.34±3.11 88.97±6.42
    BDGP 52.10±4.59 26.44±0.19 35.36±2.45 24.93±0.28 20.08±0 36.12±0 32.33±1.82 41.44±0 29.48±0 50.16±0.29 37.22±2.03 32.62±0.71 60.04±1.89
    Wiki 23.91±0.58 49.93±3.46 20.99±0.50 41.97±1.26 35.45±0 15.77±0 12.21±0.16 17.34±0 15.11±0 56.05±2.65 52.47±3.53 51.18±2.54 56.55±2.03
    CCV 11.93±0.26 12.52±0 10.44±0 13.71±0.31 11.94±0 15.50±0 20.28±0.60 22.98±0.58 22.88±0.74 22.60±0.67
    ALOI 1.01±0 60.26±1.69 33.74±0 59.67±0 40.27±1.55 48.34±1.49 21.72±0.65 71.29±1.80
    YTF10 75.68±0 60.43±0 66.74±3.69 72.93±3.96 67.09±2.80 79.15±8.39
    YTF20 57.62±0 60.09±0 60.64±4.18 67.13±4.20 63.08±2.39 68.16±4.82
    YTF50 66.00±0 68.32±2.45 67.13±3.68 64.24±2.97 66.97±3.08
    NMI
    ProteinFold 36.91±0.89 6.71±0.58 34.45±1.58 40.69±1.13 31.02±0 0±0 20.02±2.19 34.83±0 29.53±0 37.43±1.14 39.94±1.40 37.75±0.99 43.34±1.19
    Mfeat 87.68±2.85 40.14±2.76 42.49±3.30 49.19±1.37 91.77±0 28.63±0 87.29±3.84 65.33±0 68.88±0 79.35±1.95 62.18±1.77 56.46±1.81 86.74±2.26
    BDGP 33.07±2.81 3.70±0.20 10.25±2.15 0.99±0.08 2.25±0 26.33±0 13.42±2.29 28.12±0 4.60±0 25.41±0.15 9.85±1.22 10.02±0.38 33.78±0.43
    Wiki 8.65±0.27 52.01±1.51 7.28±0.67 33.09±1.09 34.18±0 0.08±0 0.82±0.10 4.34±0 2.46±0 51.57±2.17 50.05±3.79 49.34±2.95 49.47±1.77
    CCV 7.04±0.32 5.44±0 0±0 12.52±0.40 7.76±0 11.70±0 16.28±0.46 17.55±0.32 16.96±0.68 17.02±0.49
    ALOI 0.02±0 75.29±0.90 63.55±0 75.67±0 54.38±1.88 72.51±0.50 55.39±0.29 83.15±0.53
    YTF10 80.22±0 58.91±0 73.75±2.25 78.57±4.61 76.11±5.78 83.15±4.01
    YTF20 73.84±0 71.67±0 75.57±1.88 78.36±3.96 74.30±5.99 78.63±1.90
    YTF50 81.90±0 82.43±0.78 82.56±1.42 82.08±1.07 83.19±0.90
    Purity
    ProteinFold 32.99±1.37 14.37±0.41 31.26±1.19 38.46±1.60 28.96±0 11.10±0 11.71±1.20 33.86±0 28.53±0 35.90±1.63 36.00±1.16 34.95±0.66 39.21±1.56
    Mfeat 87.20±6.10 33.27±2.29 47.92±3.08 60.99±2.47 88.25±0 20.00±0 83.94±6.13 75.95±0 74.98±0 82.08±4.59 68.80±2.87 49.44±2.92 89.97±5.26
    BDGP 53.52±3.70 28.59±0.23 35.67±3.06 25.17±0.21 21.12±0 36.12±0 33.46±2.10 51.00±0 29.48±0 50.17±0.23 37.80±1.17 34.82±1.33 60.13±1.24
    Wiki 26.68±0.76 51.85±2.91 24.03±0.94 46.06±1.31 37.68±0 15.77±0 12.46±0.19 24.08±0 17.62±0 60.45±2.69 57.63±4.19 55.97±3.30 59.54±1.68
    CCV 15.92±0.31 13.04±0 10.44±0 14.12±0.33 17.04±0 19.18±0 23.62±0.47 25.91±0.51 25.09±0.78 25.34±0.67
    ALOI 1.01±0 63.92±1.26 64.02±0 62.35±0 42.32±1.55 51.46±1.41 23.67±0.72 73.81±1.42
    YTF10 80.70±0 60.43±0 71.52±3.25 77.35±5.70 69.43±3.06 83.57±5.78
    YTF20 68.78±0 64.83±0 68.20±3.02 72.40±3.79 64.92±1.95 74.40±3.32
    YTF50 73.64±0 73.21±2.18 70.09±3.61 66.84±3.02 73.65±2.50
    F-score
    ProteinFold 14.07±0.62 9.44±0.01 14.28±0.85 18.57±1.38 11.68±0 9.64±0 7.84±0.79 12.92±0 16.41±0 15.58±1.17 16.76±0.96 17.09±0.94 19.61±1.62
    Mfeat 83.66±6.35 26.94±1.09 37.46±2.69 41.49±1.51 85.52±0 27.39±0 81.39±7.35 59.22±0 62.59±0 74.42±4.13 56.50±2.45 46.57±1.33 85.05±5.09
    BDGP 40.44±2.22 29.55±0.10 29.08±0.61 21.00±0.07 33.15±0 41.19±0 32.62±0.81 36.28±0 26.51±0 37.81±0.06 28.81±1.23 28.79±0.58 45.31±0.50
    Wiki 15.44±0.25 41.83±2.91 14.91±0.54 30.34±0.78 21.38±0 19.46±0 12.48±0.69 13.04±0 11.15±0 48.71±2.18 45.76±4.69 44.91±3.43 47.17±1.64
    CCV 7.50±0.07 10.81±0 10.84±0 10.93±0.41 8.66±0 9.79±0 11.43±0.31 12.93±0.21 13.16±0.31 12.51±0.30
    ALOI 1.96±0 13.58±2.28 28.82±0 48.29±0 29.91±1.49 31.22±0.85 10.21±0.13 61.96±1.48
    YTF10 73.27±0 53.15±0 62.24±3.70 68.34±5.88 66.10±5.06 75.78±8.28
    YTF20 53.89±0 48.06±0 55.39±4.25 61.68±3.83 57.81±4.00 63.66±4.34
    YTF50 57.09±0 62.49±2.45 57.97±5.08 56.89±3.18 60.54±3.26
    下载: 导出CSV

    表  4  对比算法在所有数据集上的运行时间 (s)

    Table  4  Running time of compared methods on all datasets (s)

    数据集 MSC-IAS PMSC MVSC FMR SFMC MLRSSC AMGL RMKM BMVC LMVSC SMVSC FPMVS 本文算法
    ProteinFold 2.44 1 512.10 408.89 16.43 6.86 2.12 1.66 1.21 12.64 2.55 2.82 3.97 6.91
    Mfeat 16.81 3 300.30 11 528.00 251.03 88.62 27.94 19.62 3.95 0.43 2.96 1.38 1.43 9.20
    BDGP 13.26 15 215.00 34 800.00 1 070.40 39.00 26.89 73.71 7.53 0.35 2.86 1.63 3.38 7.18
    Wiki 15.92 14 386.00 9 991.70 1 068.80 9.84 30.72 180.62 6.27 0.11 3.57 3.15 20.16 4.89
    CCV 10 287.00 39.51 486.68 1 250.00 25.00 0.88 20.46 13.79 10.54 47.37
    ALOI 3 358.90 10 594.00 202.32 8.41 68.53 66.24 61.46 581.28
    YTF10 675.42 108.22 196.70 253.21 998.23 495.83
    YTF20 1 780.50 80.53 513.52 720.15 1 680.34 1 516.70
    YTF50 65.71 3 535.72 2 254.48 9 175.31 4 868.40
    下载: 导出CSV

    表  5  消融实验结果 (%)

    Table  5  Results of ablation experiments (%)

    聚类指标 对比方法 数据集
    ProteinFold Mfeat BDGP Wiki CCV ALOI YTF10 YTF20
    ACC 最优单视图 31.48±1.22 77.62±5.85 49.98±2.95 52.01±3.70 20.03±0.32 55.79±1.40 72.08±5.27 63.52±3.80
    未加权 27.83±1.66 82.55±6.64 46.32±3.19 52.05±2.38 18.10±0.53 70.14±2.04 70.72±8.29 66.36±4.72
    无正则化项 30.57±1.57 86.54±7.40 47.37±2.16 47.49±2.35 21.75±0.74 66.26±1.82 68.95±8.83 62.18±4.49
    本文方法 32.57±1.88 88.97±6.42 60.04±1.89 56.55±2.03 22.60±0.67 71.29±1.80 79.15±8.39 68.16±4.82
    NMI 最优单视图 41.08±0.82 74.73±2.25 27.61±2.33 50.01±3.12 16.67±0.40 73.59±0.44 74.87±2.52 69.70±1.55
    未加权 36.98±1.18 84.10±2.64 24.28±3.34 49.25±1.88 13.90±0.36 83.17±0.51 76.34±4.74 75.09±1.74
    无正则化项 42.10±1.08 87.26±2.59 26.89±2.87 36.51±2.07 16.83±0.49 79.91±0.51 76.77±4.39 75.65±1.70
    本文方法 43.34±1.19 86.74±2.26 33.78±0.43 49.47±1.77 17.02±0.49 83.15±0.53 83.15±4.01 78.63±1.90
    Purity 最优单视图 36.97±0.97 79.67±4.38 51.69±2.83 57.39±3.90 23.59±0.32 58.86±1.22 76.85±3.66 68.07±2.33
    未加权 35.17±1.46 84.32±5.43 47.12±3.11 58.34±2.52 21.10±0.40 72.77±1.71 76.89±6.26 71.52±3.27
    无正则化项 38.73±1.27 88.55±5.55 47.45±2.04 50.37±1.98 24.76±0.63 69.02±1.47 76.11±6.23 70.25±3.64
    本文方法 39.21±1.56 89.97±5.26 60.13±1.24 59.54±1.68 25.34±0.67 73.81±1.42 83.57±5.78 74.40±3.32
    F-score 最优单视图 19.63±1.10 69.72±4.28 37.83±2.14 45.07±3.62 11.50±0.20 43.10±1.38 67.00±4.92 52.49±3.96
    未加权 15.68±1.38 78.80±5.59 35.78±2.64 44.79±2.01 10.64±0.23 60.72±1.60 66.43±8.78 58.07±4.43
    无正则化项 18.65±1.24 83.90±5.96 38.61±2.13 37.17±1.75 12.06±0.32 54.92±1.47 67.00±8.70 54.88±3.74
    本文方法 19.61±1.62 85.05±5.09 45.31±0.50 47.17±1.64 12.51±0.30 61.96±1.48 75.78±8.28 63.66±4.34
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-06-27
  • 录用日期:  2022-11-12
  • 网络出版日期:  2022-12-19
  • 刊出日期:  2024-06-20

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