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基于低秩张量图学习的不完整多视角聚类

文杰 颜珂 张正 徐勇

文杰, 颜珂, 张正, 徐勇. 基于低秩张量图学习的不完整多视角聚类. 自动化学报, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c200519
引用本文: 文杰, 颜珂, 张正, 徐勇. 基于低秩张量图学习的不完整多视角聚类. 自动化学报, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c200519
Wen Jie, Yan Ke, Zhang Zheng, Xu Yong. Low-rank tensor graph learning based incomplete multi-view clustering. Acta Automatica Sinica, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c200519
Citation: Wen Jie, Yan Ke, Zhang Zheng, Xu Yong. Low-rank tensor graph learning based incomplete multi-view clustering. Acta Automatica Sinica, 2021, 47(x): 1−13 doi: 10.16383/j.aas.c200519

基于低秩张量图学习的不完整多视角聚类

doi: 10.16383/j.aas.c200519
基金项目: 深圳市基础研究项目(JCYJ20190806142416685), 国家自然科学基金(62006059, 62002085), 中国博士后科学基金(2020M681099), 中国博士后创新人才支持计划(BX20190100), 深圳市科技创新委员会重点实验室组建项目(ZDSYS20190902093015527)资助
详细信息
    作者简介:

    文杰:哈尔滨工业大学(深圳)计算机科学与技术学院助理教授, 主要研究方向为机器学习和模式识别. Email: jiewen_pr@126.com

    颜珂:北京理工大学计算机科学与技术学院博士后, 主要研究方向为生物信息学和模式识别. Email: yanke401@163.com

    张正:哈尔滨工业大学(深圳)计算机科学与技术学院助理教授, 主要研究方向为机器学习、计算机视觉和多媒体分析. Email: darrenzz219@gmail.com

    徐勇:哈尔滨工业大学(深圳)计算机科学与技术学院教授, 主要研究方向为机器学习、模式识别、生物信息学和视频分析. Email: yongxu@ymail.com

Low-rank Tensor Graph Learning Based Incomplete Multi-view Clustering

Funds: Supported by Shenzhen Fundamental Research Fund (JCYJ20190806142416685), National Natural Science Foundation of P. R. China (62006059, 62002085), China Postdoctoral Science Foundation (2020M681099), China National Postdoctoral Program for Innovative Talents (BX20190100), and Establishment of Key Laboratory of Shenzhen Science and Technology Innovation Committee (ZDSYS20190902093015527)
More Information
    Author Bio:

    WEN Jie Assistant professor at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. His main reasearch interestes are machine learning and pattern recognition

    YAN Ke Post-doctoral at School of Computer Science and Technology, Beijing Institute of Technology. His main research interestes are Bioinformatics and pattern recognition

    ZHANG Zheng Assistant professor at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. His main reasearch interestes are machine learning, computer vision, and multimedia analytics

    XU Yong Professor at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. His main reasearch interestes are machine learning, pattern recognition, biometrics, and video analysis

  • 摘要: 传统多视角聚类都基于视角完备假设, 要求所有样本的视角信息完整, 不能处理存在部分视角缺失情形下的不完整多视角聚类任务. 为解决该问题, 本文提出一种基于低秩张量图学习的不完整多视角聚类方法. 为了恢复相似图中缺失视角所对应的样本关联信息, 该方法将低秩张量图约束和视角内在图保持约束融入到多视角谱聚类模型. 通过在一个统一模型中同时挖掘视角间的互补信息和视角内未缺失样例的关联信息, 所提出的方法能够得到表征样例邻接关系的完整相似图和视角间一致的最优聚类指示矩阵. 与12种不完整多视角聚类方法进行实验对比, 实验结果表明所提出的方法在多种视角缺失率下的五个数据集上获得了最好的聚类性能.
  • 图  1  基于低秩张量图学习的不完整多视角聚类框图

    Fig.  1  The flow chart of the low-rank tensor graph learning based incomplete multi-view clustering

    图  2  多视角样本分布典型范例, 其中${{S}}_{a,b}^{\left( v \right)}$表示a、b两样本的第$v$个视角特征的相似度

    Fig.  2  Example of the distribution of multi-view samples, where ${{S}}_{a,b}^{\left( v \right)}$ denotes the similarity degree of samples $a$ and $b$ in the $v$th view

    图  3  各方法在(a)不同视角缺失率下的Handwritten、(b)不同视角配对率下的Animal和(c)不同视角配对率下的Reuters数据集上的聚类Purity (%)

    Fig.  3  The clustering Purities (%) of different methods on the (a) Handwritten dataset with different missing-view rates, (b) Animal dataset with different paired-view rates, and (c) Reuters dataset with different paired-view rates

    图  4  在视角缺失率为30%的(a) Handwritten和(b) Caltech7数据集上, 所提出LASAR方法的聚类NMI (%) 与超参数${\lambda _1}$${\lambda _2}$的关系

    Fig.  4  Clustering NMI (%) of the proposed LASAR v.s. hyper-parameters ${\lambda _1}$ and ${\lambda _2}$ on the (a) Handwritten and (b) Caltech7 datasets with a missing-view rate of 30%

    图  5  本文模型和其两种退化模型在视角缺失率或配对率均为30%的四个数据集上的 (a) 聚类NMI和 (b) 聚类ACC

    Fig.  5  Clustering (a) NMIs and (b) ACCs of the proposed method and two degraded models on the four datasets with a missing-view rate or paired-view rate of 30%

    图  6  在视角缺失率为30%的(a) Handwritten和(b) Caltech7数据集上, LASAR的目标函数值和聚类NMI(%)与迭代步数之间的关系

    Fig.  6  Objective function value and NMI (%) of LASAR v.s. the iterations on the (a) Handwritten and (b) Caltech7 datasets with a missing-view rate of 30%

    图  7  本文方法在视角缺失率为70%的Handwritten数据集上得到的 (a) 第一个视角和 (b) 第五个视角的相似图

    Fig.  7  Two similarity graphs, corresponding to the (a) 1st view and (b) fifth view, obtained by the proposed method on the Handwritten dataset with a missing-view rate of 70%

    表  1  各方法在不同视角缺失率下的Caltech7和BBCSport数据集上的实验结果

    Table  1  Experimental results of different methods on the Caltech7 and BBCSport datasets with different missing-view rates

    NMI (%)ACC (%)Purity (%)
    数据集方法0.10.30.50.10.30.50.10.30.5
    Caltech7MultiNMF+均值30.1628.5228.8846.3940.6137.9279.8078.4378.03
    MultiNMF+KNN36.3834.2734.1950.7143.9842.6680.6880.8880.17
    CCo_MVSC+零值35.5334.1831.5238.4738.1637.3578.3377.8976.21
    CCo_MVSC+KNN37.3837.1837.3339.0639.6237.3480.2580.3681.45
    MIC33.7127.3520.4444.0738.0135.8078.1273.3168.26
    OMVC28.1325.3218.7640.8836.8233.2879.2177.7374.05
    DAIMC44.6138.4536.2848.2947.4644.8983.3276.8375.50
    OPIMC42.9841.5435.9849.2448.3444.1284.8983.7080.64
    UEAF39.4431.0724.0250.8242.7136.3281.4978.2676.29
    IMKKM-IK-MKC24.0923.4522.9136.5434.8736.0572.9873.8272.52
    IMVSC_AGL44.0542.6137.3554.7254.6151.7884.2783.9882.31
    GM-PMVC60.2652.3547.9562.6554.9547.6591.2684.4983.93
    LASAR66.0862.8052.7670.2969.0266.4692.7690.2784.84
    BBCSportMultiNMF+均值23.4818.2514.7948.5842.7540.3447.1744.6643.10
    MultiNMF+KNN33.4129.1732.6656.0354.1454.6658.6255.5158.27
    CCo_MVSC+零值62.7957.6939.5572.7670.0661.3881.4978.6266.72
    CCo_MVSC+KNN59.2456.2538.9769.0269.8360.0680.9278.5668.62
    MIC29.9025.8424.0151.2146.2146.0355.0051.7252.41
    OMVC30.6441.5740.6353.3351.3848.7956.4959.2057.47
    DAIMC56.6250.1737.8968.6263.4556.8976.9071.7261.03
    OPIMC35.6631.5621.7554.1452.9345.6958.2856.7250.86
    UEAF70.7168.2555.1378.2277.2469.3187.4187.0777.07
    IMKKM-IK-MKC72.9164.4253.5277.5575.6667.0788.7684.0377.00
    IMVSC_AGL70.4666.1154.5776.4174.4869.3187.4185.0078.10
    GM-PMVC70.3466.2648.9374.6673.4860.0785.1784.4872.68
    LASAR77.0970.3057.0485.0077.4173.2890.0088.6278.79
    下载: 导出CSV

    表  2  各方法在不同视角缺失率下的Handwritten及不同视角配对率下的Animal和Reuters数据集上的实验结果

    Table  2  Experimental results of different methods on the Handwritten dataset with different missing-view rates, Animal and Reuters datasets with different paired-view rates

    NMI (%)ACC (%)
    数据集方法0.10.30.50.70.10.30.50.7
    HandwrittenMultiNMF+均值72.0560.1141.9920.8882.3571.7452.0331.85
    MultiNMF+KNN74.2374.7773.8167.9383.6483.8983.5378.33
    CCo_MVSC+零值70.8968.2362.8653.1474.6173.1770.1564.62
    CCo_MVSC+KNN73.0373.7773.0667.6676.7676.7976.2075.52
    MIC70.8465.3952.9534.7177.5973.2961.2741.34
    OMVC56.7244.9935.1625.8365.0455.0036.4029.80
    DAIMC79.7876.6568.7747.1088.8686.7381.9260.44
    OPIMC77.2673.7466.5751.8680.2076.4569.5056.66
    UEAF77.7469.3755.0950.5685.8076.1165.3961.11
    IMKKM-IK-MKC69.4365.4259.0447.3671.7869.0766.0855.55
    IMVSC_AGL93.6890.5586.3975.4497.1595.5093.1984.08
    GM-PMVC99.8499.6499.1297.1499.9499.8799.6698.87
    LASAR99.9299.8199.3299.1399.9799.9399.7399.68
    AnimalMultiNMF+均值48.2553.5156.3061.4842.0446.3348.6252.92
    MultiNMF+KNN53.6855.5858.8560.6845.1547.8951.5153.16
    CCo_MVSC+零值52.1955.3158.3161.7148.1252.0354.7256.73
    CCo_MVSC+KNN49.1357.9661.3763.8647.7153.5856.7958.41
    MIC48.9652.7955.6959.3039.4443.3845.8849.15
    OMVC44.6650.7753.1155.3830.6642.5143.9846.39
    DAIMC49.3355.0359.3662.7642.7650.1853.8756.42
    OPIMC44.2952.3458.5162.0437.8646.3353.1453.88
    UEAF54.8862.1064.2768.6246.7652.4558.1562.71
    IMKKM-IK-MKC51.4757.2162.1466.5046.0553.6158.4861.85
    IMVSC_AGL56.3859.6563.2666.7151.6154.9457.9760.73
    GM-PMVC55.5757.6261.2564.5547.8450.8953.9957.81
    LASAR65.7969.6190.2692.9758.0565.6786.2888.05
    ReutersMultiNMF+均值19.5818.8218.5619.5137.6838.3137.2737.58
    MultiNMF+KNN19.9123.1722.5022.2137.9538.0837.4737.35
    CCo_MVSC+零值17.0418.6618.1020.1134.6637.3937.4640.01
    CCo_MVSC+KNN17.6419.3319.6720.9535.4237.7939.4141.06
    MIC18.7221.3022.7824.3438.4740.8541.3743.05
    OMVC18.0519.7721.3722.9736.7837.4439.4541.09
    DAIMC26.5329.9830.2731.5543.3246.6747.7848.89
    OPIMC19.0222.4723.8225.3940.5842.1943.8744.43
    UEAF24.7726.8527.1428.3641.4544.9546.8747.92
    IMKKM-IK-MKC24.3026.7526.8828.6741.1345.7146.4047.29
    IMVSC_AGL25.7528.4128.3929.7942.3846.2947.8248.91
    GM-PMVC26.2229.3530.7130.8943.1546.8848.1950.44
    LASAR28.3432.0131.2732.7745.3848.1450.8052.77
    下载: 导出CSV

    表  3  各方法在五个数据集上的运行时间(秒), 其中视角缺失率或配对率为30%

    Table  3  Running times (seconds) of different methods on the above five datasets with a missing-view rate or paired-view rate of 30%

    方法Caltech7BBCSportHandwrittenAnimalReuters计算复杂度
    MultiNMF+均值60.3828.6235.5413489.1827385.81.$O\left( {\tau T\sum\nolimits_{v = 1}^l {{m_v}cn} } \right)$[10]
    MultiNMF+KNN59.0525.4640.6913499.8827408.45$O\left( {\tau T\sum\nolimits_{v = 1}^l {{m_v}cn} } \right)$[10]
    CCo_MVSC+零值3.010.355.18174.16489.83$O\left( {\tau \left( {l{n^3} + {n^3}} \right)} \right)$
    CCo_MVSC+KNN4.360.467.69243.77699.74$O\left( {\tau \left( {l{n^3} + {n^3}} \right)} \right)$
    MIC225.313.01149.873693.9222499.46$O\left( {\tau T\sum\nolimits_{v = 1}^l {{m_v}cn} } \right)$[10]
    OMVC152.543.1727.773409.0818154.71$O\left( {\tau T\sum\nolimits_{v = 1}^l {{m_v}cn} } \right)$[10]
    DAIMC62.7481.1826.722191.4396628.66$O\left( {\tau \left( {Tnc{m_{\max }} + lm_{\max }^3} \right)} \right)$[17]
    OPIMC0.160.050.093.311.05$O\left( {\tau lcn{m_{\max }}} \right)$[18]
    UEAF4.642.367.05201258.9318599.64$O\left( {\tau \left( {2{n^3} + \sum\nolimits_{v = 1}^l {{m_v}{c^2}} } \right)} \right)$[19]
    IMKKM-IK-MKC23.680.2241.22975.381762.95$O\left( {\tau \left( {{n^3} + l{n^3} + {l^3}} \right)} \right)$[21]
    IMVSC_AGL173.582.5781.135265.9928672.45$O\left( {\tau \left( {l{n^3} + {n^3} + \sum\nolimits_{v = 1}^l {n_v^3} } \right)} \right)$[20]
    GM-PMVC607.4014.63602.8150725.431.78×105$O\left( {\tau l\left( {{n^3} + kdn + {k^3} + {k^2}d} \right)} \right)$[22]
    LASAR73.871.09115.602352.885677.46$O\left( {\tau \left( {l{n^2}\log \left( n \right){\rm{ + }}{l^2}{n^2} + c{n^2}} \right)} \right)$
    备注: 本表未考虑kmeans聚类算法的计算复杂度. 表中“$T$”表示子循环迭代步数, “${m_{\max }}$”表示所有视角的最大特征维度, “${n_v}$”表示第$v$个视角的未缺失样例数, “$d$”表示多视角数据特征的平均维度, “$k$”表示矩阵分解模型中的隐层表征维度.
    下载: 导出CSV
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出版历程
  • 收稿日期:  2020-07-09
  • 修回日期:  2020-11-24
  • 网络出版日期:  2021-03-27

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