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基于一步张量学习的多视图子空间聚类

赵晓佳 徐婷婷 陈勇勇 徐勇

赵晓佳, 徐婷婷, 陈勇勇, 徐勇. 基于一步张量学习的多视图子空间聚类. 自动化学报, 2022, 48(x): 1−14 doi: 10.16383/j.aas.c220138
引用本文: 赵晓佳, 徐婷婷, 陈勇勇, 徐勇. 基于一步张量学习的多视图子空间聚类. 自动化学报, 2022, 48(x): 1−14 doi: 10.16383/j.aas.c220138
Zhao Xiao-Jia, Xu Ting-Ting, Chen Yong-Yong, Xu Yong. One-step tensor learning for multi-view subspace clustering. Acta Automatica Sinica, 2022, 48(x): 1−14 doi: 10.16383/j.aas.c220138
Citation: Zhao Xiao-Jia, Xu Ting-Ting, Chen Yong-Yong, Xu Yong. One-step tensor learning for multi-view subspace clustering. Acta Automatica Sinica, 2022, 48(x): 1−14 doi: 10.16383/j.aas.c220138

基于一步张量学习的多视图子空间聚类

doi: 10.16383/j.aas.c220138
基金项目: 广东省自然科学基金 (2022A1515010819), 国家自然科学基金 (62106063), 深圳市科技创新委员会 (GJHZ20210705141812038) 资助
详细信息
    作者简介:

    赵晓佳:哈尔滨工业大学(深圳)计算机科学与技术学院硕士研究生, 主要研究方向为多视图聚类. E-mail: 21S151152@stu.hit.edu.cn

    徐婷婷:哈尔滨工业大学(深圳)计算机科学与技术学院硕士研究生, 主要研究方向为低秩张量近似. E-mail: 21S151168@stu.hit.edu.cn

    陈勇勇: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. 本文通信作者. E-mail: YongyongChen.cn@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, 模式学习, 生物信息学和视频分析. E-mail: yongxu@ymail.com

One-step Tensor Learning for Multi-view Subspace Clustering

Funds: Supported by Guangdong Natural Science Foundation (2022A1515010819), National Natural Science Foundation of China (62106063), Shenzhen Science and Technology Innovation Committee (GJHZ20210705141812038)
More Information
    Author Bio:

    ZHAO Xiao-Jia Master student at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. Her research interest covers multi-view clustering

    XU Ting-Ting Master student at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. Her research interest covers low-rank tensor approximation

    CHEN Yong-Yong Assistant Professor at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. His research interest covers machine learning and pattern recognition. Corresponding author of this paper

    XU Yong Professor at School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen. His research interest covers machine learning, pattern recognition, biometrics, and video analysis

  • 摘要: 现有多视图子空间聚类算法通常先进行张量表示学习, 进而将学习到的表示张量融合为统一的亲和度矩阵. 然而, 因其独立地学习表示张量和亲和度矩阵, 忽略了两者之间的高度相关性. 为了解决此问题, 提出一种基于一步张量学习的多视图子空间聚类方法, 联合学习表示张量和亲和度矩阵. 具体地, 该方法对表示张量施加低秩张量约束, 以挖掘视图的高阶相关性. 利用自适应最近邻法对亲和度矩阵进行灵活重建. 使用交替方向乘子法对模型进行优化求解, 通过对真实多视图数据的实验表明, 较于最新的多视图聚类方法, 提出的算法具有更好的聚类准确性.
  • 图  1  多视图数据示例

    Fig.  1  Examples of multi-view data

    图  2  张量奇异值分解示例

    Fig.  2  Examples of t-SVD

    图  3  基于一步张量学习的多视图子空间聚类结构图

    Fig.  3  The framework of the one-step tensor learning for multi-view subspace clustering (OTSC).

    图  4  OTSC性能的消融实验

    Fig.  4  Ablation experiment of OTSC performance

    图  5  根据$ACC$$NMI$调整数据集ORL参数$\alpha$$\gamma$

    Fig.  5  Parameters tuning in terms of $ACC$ and $NMI$ on ORL

    图  6  参数$K$对数据集ORL的$ACC$影响

    Fig.  6  The effect of parameter $K$ on the $ACC$ of ORL.

    图  7  收敛性曲线 ((a) BBCSport; (b) Extended YaleB)

    Fig.  7  The convergence curves and ACC versus iterations on ((a) BBCSport; (b) Extended YaleB)

    表  1  符号与定义

    Table  1  Notations and definitions

    符号定义
    $\boldsymbol{x}, X, {\cal{X}}$向量, 矩阵, 张量
    1单位向量
    $I$单位矩阵
    ${\cal{I}}$单位张量
    $n$样本个数
    $V$视图个数
    $d_v$第$v$个视图的特征维度
    $X^v\in {\bf{R}}^{d_v \times n}$第$v$个视图的特征矩阵
    ${\cal{Z}}\in{\bf{R}}^{n\times n\times V}$表示张量
    $A\in {\bf{R}}^{n \times n}$亲和度矩阵
    $E^v\in {\bf{R}}^{n \times n}$噪声矩阵
    $\|\cdot\|_{2,1}$$l_{2,1}$范数
    $\|\cdot\|_{\rm{F}}$Frobenius范数
    $\|\cdot\|_\infty$无穷范数
    $\|\cdot\|_{*}$矩阵核范数
    $\|\cdot\|_{\circledast}$张量核范数
    $fft$快速傅里叶分解
    下载: 导出CSV

    表  2  真实多视图数据集信息

    Table  2  Summary of all real-world multi-view databases

    数据集样本数量类别视图种类
    Extended YaleB640383面部图像
    ORL400403面部图像
    3Sources16963新闻故事
    BBCSport54452新闻故事
    UCI-Digits2000103手写数字
    COIL_201440203通用对象
    下载: 导出CSV

    表  3  参数设置

    Table  3  Parameter setting

    数据集$\alpha$$\gamma$$K$
    Extended YaleB10.0055
    ORL0.10.0512
    3Sources0.1508
    BBCSport0.0558
    UCI-Digits0.2215
    COIL_200.0515
    下载: 导出CSV

    表  4  数据集Extended YaleB、ORL的聚类结果

    Table  4  Clustering results (mean$ \pm $standard deviation) on Extended YaleB and ORL.

    数据类型方法$ACC$$NMI$$AR$$F$-$score$$Precision$$Recall$
    Extended YaleB单视图方法SSCbest0.587±0.0030.534±0.0030.430±0.0050.487±0.0040.451±0.0020.509±0.007
    LRRbest0.615±0.0130.627±0.0400.451±0.0020.508±0.0040.481±0.0020.539±0.001
    RSSbest0.742±0.0010.787±0.0000.685±0.0010.717±0.0010.704±0.0010.730±0.000
    多视图方法RMSC0.210±0.0130.157±0.0190.060±0.0140.155±0.0120.151±0.0120.159±0.013
    DiMSC0.615±0.0030.636±0.0020.453±0.0050.504±0.0060.481±0.0040.534±0.004
    LT-MSC0.626±0.0100.637±0.0030.459±0.0300.521±0.0060.485±0.0010.539±0.002
    MLAN0.346±0.0110.352±0.0150.093±0.0090.213±0.0230.159±0.0180.321±0.013
    t-SVD0.652±0.0000.667±0.0040.500±0.0030.550±0.0020.514±0.0040.590±0.004
    GMC0.434±0.0000.449±0.0000.157±0.0000.265±0.0000.204±0.0000.378±0.000
    LMSC0.598±0.0050.568±0.0040.354±0.0070.423±0.0060.390±0.0060.463±0.005
    SCMV-3DT0.410±0.0010.413±0.0020.185±0.0020.276±0.0010.244±0.0020.318±0.001
    LRTG0.954±0.0000.905±0.0000.899±0.0000.909±0.0000.908±0.0000.911±0.000
    WTNNM0.648±0.0050.661±0.0020.501±0.0000.552±0.0000.533±0.0000.573±0.000
    GLTA0.571±0.0020.630±0.0050.510±0.0050.560±0.0040.544±0.0040.576±0.006
    本方法OTSC0.969±0.0010.934±0.0010.931±0.0020.937±0.0020.935±0.0020.939±0.002
    WOTSC0.972±0.0000.943±0.0000.938±0.0000.944±0.0000.942±0.0000.946±0.000
    ORL单视图方法SSCbest0.765±0.0080.893±0.0070.694±0.0130.682±0.0120.673±0.0070.764±0.005
    LRRbest0.773±0.0030.895±0.0060.724±0.0200.731±0.0040.701±0.0010.754±0.002
    RSSbest0.846±0.0240.938±0.0070.798±0.0230.803±0.0230.759±0.0300.852±0.017
    多视图方法RMSC0.723±0.0070.872±0.0120.645±0.0030.654±0.0070.607±0.0090.709±0.004
    DiMSC0.838±0.0010.940±0.0030.802±0.0000.807±0.0030.764±0.0120.856±0.004
    LT-MSC0.795±0.0070.930±0.0030.750±0.0030.768±0.0040.766±0.0090.837±0.005
    MLAN0.705±0.020.854±0.0180.384±0.0100.376±0.0150.254±0.0210.721±0.020
    t-SVD0.970±0.0030.993±0.0020.967±0.0020.968±0.0030.946±0.0040.991±0.003
    GMC0.633±0.0000.857±0.0000.337±0.0000.360±0.0000.232±0.0000.801±0.000
    LMSC0.877±0.0240.949±0.0060.839±0.0220.843±0.0210.806±0.0270.884±0.017
    SCMV-3DT0.839±0.0120.908±0.0070.763±0.0180.769±0.0170.747±0.0200.792±0.016
    LRTG0.933±0.0030.970±0.0020.905±0.0050.908±0.0050.888±0.0040.928±0.007
    WTNNM0.967±0.0000.992±0.0000.960±0.0000.952±0.0000.946±0.0000.968±0.000
    GLTA0.976±0.0020.994±0.0060.958±0.0240.963±0.0190.952±0.0350.989±0.012
    本方法OTSC0.983±0.0020.988±0.0010.964±0.0030.965±0.0030.958±0.0040.972±0.001
    WOTSC0.938±0.0000.972±0.0000.907±0.0000.909±0.0000.885±0.0000.936±0.000
    下载: 导出CSV

    表  5  数据集3Sources、UCI-Digits的聚类结果

    Table  5  Clustering results (mean $ \pm $ standard deviation) on 3Sources and UCI-Digits.

    数据类型方法$ACC$$NMI$$AR$$F$-$score$$Precision$$Recall$
    3Sources单视图方法SSCbest0.762±0.0030.694±0.0030.658±0.0040.743±0.0030.769±0.0010.719±0.005
    LRRbest0.647±0.0330.542±0.0180.486±0.0280.608±0.0330.594±0.0310.636±0.096
    RSSbest0.722±0.0000.601±0.0000.533±0.0000.634±0.0000.679±0.0000.595±0.000
    多视图方法RMSC0.583±0.0220.630±0.0110.455±0.0310.557±0.0250.635±0.0290.497±0.028
    DiMSC0.795±0.0040.727±0.0100.661±0.0050.748±0.0040.711±0.0050.788±0.003
    LT-MSC0.781±0.0000.698±0.0030.651±0.0030.734±0.0020.716±0.0080.754±0.005
    MLAN0.775±0.0150.676±0.0050.580±0.0080.666±0.0070.756±0.0030.594±0.009
    t-SVD0.781±0.0000.678±0.0000.658±0.0000.745±0.0000.683±0.0000.818±0.000
    GMC0.693±0.0000.622±0.0000.443±0.0000.605±0.0000.484±0.0000.804±0.000
    LMSC0.912±0.0060.826±0.0070.842±0.0110.887±0.0080.873±0.0070.877±0.012
    SCMV-3DT0.440±0.0200.386±0.0090.226±0.0120.411±0.0090.399±0.0120.425±0.016
    LRTG0.947±0.0000.865±0.0000.881±0.0000.909±0.0000.911±0.0000.906±0.000
    WTNNM0.793±0.0000.692±0.0000.679±0.0000.761±0.0100.693±0.0000.845±0.000
    GLTA0.859±0.0080.753±0.0150.713±0.0140.775±0.0110.827±0.0090.730±0.013
    本方法OTSC0.953±0.0000.880±0.0000.893±0.0000.918±0.0000.914±0.0000.922±0.000
    WOTSC0.947±0.0000.867±0.0000.888±0.0000.914±0.0000.909±0.0000.920±0.000
    UCI-Digits单视图方法SSCbest0.815±0.0110.840±0.0010.770±0.0050.794±0.0040.747±0.0100.848±0.004
    LRRbest0.871±0.0010.768±0.0020.736±0.0020.763±0.0020.759±0.0020.767±0.002
    RSSbest0.819±0.0000.863±0.0000.787±0.0000.810±0.0000.756±0.0000.872±0.000
    多视图方法RMSC0.915±0.0240.822±0.0080.789±0.0140.811±0.0120.797±0.0170.826±0.006
    DiMSC0.703±0.0100.772±0.0060.652±0.0060.695±0.0060.673±0.0050.718±0.007
    LT-MSC0.803±0.0010.775±0.0010.725±0.0010.753±0.0010.739±0.0010.767±0.001
    MLAN0.874±0.0000.910±0.0000.847±0.0000.864±0.0000.797±0.0000.943±0.000
    t-SVD0.955±0.0000.932±0.0000.924±0.0000.932±0.0000.930±0.0000.934±0.000
    GMC0.736±0.0000.815±0.0000.678±0.0000.713±0.0000.644±0.0000.799±0.000
    LMSC0.893±0.0000.815±0.0000.783±0.0000.805±0.0000.798±0.0000.812±0.000
    SCMV-3DT0.930±0.0010.861±0.0010.846±0.0010.861±0.0010.859±0.0010.864±0.001
    LRTG0.981±0.0000.953±0.0000.957±0.0000.961±0.0000.961±0.0000.962±0.000
    WTNNM0.998±0.0000.993±0.0000.994±0.0000.995±0.0100.998±0.0000.995±0.000
    GLTA0.997±0.0000.992±0.0000.993±0.0000.994±0.0000.994±0.0000.994±0.000
    本方法OTSC0.983±0.0010.958±0.0010.962±0.0010.966±0.0010.965±0.0000.966±0.002
    WOTSC0.983±0.0000.958±0.0000.962±0.0000.966±0.0000.965±0.0000.966±0.000
    下载: 导出CSV

    表  6  数据集BBCSport、COIL-20的聚类结果

    Table  6  Clustering results (mean $ \pm $ standard deviation) on BBCSport and COIL-20.

    数据类型方法$ACC$$NMI$$AR$$F$-$score$$Precision$$Recall$
    BBC Sport单视图方法SSCbest0.627±0.0030.534±0.0080.364±0.0070.565±0.0050.427±0.0040.834±0.004
    LRRbest0.836±0.0010.698±0.0020.705±0.0010.776±0.0010.768±0.0010.784±0.001
    RSSbest0.878±0.0000.714±0.0000.717±0.0000.784±0.0000.787±0.0000.782±0.000
    多视图方法RMSC0.826±0.0010.666±0.0010.637±0.0010.719±0.0010.766±0.0010.677±0.001
    DiMSC0.922±0.0000.785±0.0000.813±0.0000.858±0.0000.846±0.0000.872±0.000
    LT-MSC0.460±0.0460.222±0.0280.167±0.0430.428±0.0140.328±0.0280.629±0.053
    MLAN0.721±0.0000.779±0.0000.591±0.0000.714±0.0000.567±0.0000.962±0.000
    t-SVD0.879±0.0000.765±0.0000.784±0.0000.834±0.0000.863±0.0000.807±0.000
    GMC0.807±0.0000.760±0.0000.722±0.0000.794±0.0000.727±0.0000.875±0.000
    LMSC0.847±0.0030.739±0.0010.749±0.0010.810±0.0010.799±0.0010.822±0.001
    SCMV-3DT0.980±0.0000.929±0.0000.935±0.0000.950±0.0000.959±0.0000.942±0.000
    LRTG0.943±0.0050.869±0.0090.840±0.0120.879±0.0000.866±0.0060.892±0.014
    WTNNM0.963±0.0000.900±0.0000.908±0.0000.930±0.0000.950±0.0000.911±0.000
    GLTA1.000±0.0001.000±0.0001.000±0.0001.000±0.0001.000±0.0001.000±0.000
    本方法OTSC0.970±0.0000.914±0.0000.911±0.0000.933±0.0000.928±0.0000.937±0.000
    WOTSC0.985±0.0000.950±0.0000.957±0.0000.967±0.0000.963±0.0000.971±0.000
    COIL-20单视图方法SSCbest0.803±0.0220.935±0.0090.798±0.0220.809±0.0130.734±0.0270.804±0.028
    LRRbest0.761±0.0030.829±0.0060.720±0.0200.734±0.0060.717±0.0030.751±0.002
    RSSbest0.837±0.0120.930±0.0060.789±0.0050.800±0.0050.717±0.0120.897±0.017
    多视图方法RMSC0.685±0.0450.800±0.0170.637±0.0440.656±0.0420.620±0.0570.698±0.026
    DiMSC0.778±0.0220.846±0.0020.732±0.0050.745±0.0050.739±0.0070.751±0.003
    LT-MSC0.804±0.0110.860±0.0020.748±0.0040.760±0.0070.741±0.0090.776±0.006
    MLAN0.862±0.0110.961±0.0040.835±0.0060.844±0.0130.758±0.0080.953±0.007
    t-SVD0.830±0.0000.884±0.0050.786±0.0030.800±0.0040.785±0.0070.808±0.001
    GMC0.791±0.0010.941±0.0000.782±0.0000.794±0.0000.694±0.0000.929±0.000
    LMSC0.806±0.0130.862±0.0070.765±0.0140.776±0.0130.770±0.0130.783±0.013
    SCMV-3DT0.701±0.0280.810±0.0090.635±0.0030.654±0.0290.614±0.0390.702±0.018
    LRTG0.927±0.0000.976±0.0000.928±0.0000.932±0.0000.905±0.0000.961±0.000
    WTNNM0.902±0.0000.945±0.0000.893±0.0000.898±0.0100.897±0.0000.900±0.000
    GLTA0.903±0.0060.946±0.0010.891±0.0070.897±0.0060.893±0.0130.900±0.001
    本方法OTSC0.936±0.0040.983±0.0040.938±0.0060.941±0.0060.906±0.0070.979±0.006
    WOTSC0.960±0.0260.976±0.0040.934±0.0250.938±0.0240.918±0.0420.959±0.004
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-03-04
  • 录用日期:  2022-08-22
  • 网络出版日期:  2022-10-20

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