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基于密度峰值的聚类集成

褚睿鸿 王红军 杨燕 李天瑞

褚睿鸿, 王红军, 杨燕, 李天瑞. 基于密度峰值的聚类集成. 自动化学报, 2016, 42(9): 1401-1412. doi: 10.16383/j.aas.2016.c150864
引用本文: 褚睿鸿, 王红军, 杨燕, 李天瑞. 基于密度峰值的聚类集成. 自动化学报, 2016, 42(9): 1401-1412. doi: 10.16383/j.aas.2016.c150864
CHU Rui-Hong, WANG Hong-Jun, YANG Yan, LI Tian-Rui. Clustering Ensemble Based on Density Peaks. ACTA AUTOMATICA SINICA, 2016, 42(9): 1401-1412. doi: 10.16383/j.aas.2016.c150864
Citation: CHU Rui-Hong, WANG Hong-Jun, YANG Yan, LI Tian-Rui. Clustering Ensemble Based on Density Peaks. ACTA AUTOMATICA SINICA, 2016, 42(9): 1401-1412. doi: 10.16383/j.aas.2016.c150864

基于密度峰值的聚类集成

doi: 10.16383/j.aas.2016.c150864
基金项目: 

西南交通大学中央高校基本科研业务费专项基金 A0920502051515-12

教育部在线教育研究中心在线教育研究基金(全通教育) 2016YB158

国家自然科学基金 61262058

国家自然科学基金 61572407

国家科技支撑计划课题 2015BAH19F02

详细信息
    作者简介:

    褚睿鸿 西南交通大学信息科学与技术学院硕士研究生.2014年获得西南交通大学信息科学与技术学院学士学位.主要研究方向为集成学习, 数据挖掘.E-mail:rhchu@my.swjtu.edu.cn

    杨燕 西南交通大学信息科学与技术学院教授.2007年在西南交通大学获得博士学位.主要研究方向为数据挖掘, 集成学习, 云计算.E-mail:yyang@swjtu.edu.cn

    李天瑞 西南交通大学信息科学与技术学院教授.主要研究方向为大数据, 云计算, 粗糙集与粒计算.E-mail:trli@swjtu.edu.cn

    通讯作者:

    王红军 西南交通大学信息科学与技术学院副研究员.2009年获得四川大学计算机学院博士学位.主要研究方向为机器学习, 集成学习与数据挖掘.本文通信作者.E-mail:wanghongjun@swjtu.edu.cn

Clustering Ensemble Based on Density Peaks

Funds: 

Fundamental Research Funds for the Central Universities of Southwest Jiaotong University A0920502051515-12

Online Education Research Center of the Ministry of Education Online Education Research Fund (Full Education) 2016YB158

National Natural Science Foundation of China 61262058

National Natural Science Foundation of China 61572407

National Science and Technology Support Program 2015BAH19F02

More Information
    Author Bio:

    Master student at the School of Information Science and Technology, Southwest Jiaotong University. She received her bachelor degree from Southwest Jiaotong University in 2014. Her research interest covers ensemble learning and data mining. E-mail:

    Professor at the School of Information Science and Technology, Southwest Jiaotong University. She received her Ph.D. degree from Southwest Jiaotong University in 2007. Her research interest covers data mining, ensemble learning and cloud computing. E-mail:

    quad Professor at the School of Information Science and Technology, Southwest Jiaotong University. His research interest covers big data, cloud computing, rough set and granular computing. E-mail:

    Corresponding author: WANG Hong-Jun Associate professor at the School of Information Science and Technology, Southwest Jiaotong University. He received his Ph.D. degree from Sichuan University in 2009. His research interest covers machine learning, ensemble learning and data mining. Corresponding author of this paper. E-mail:wanghongjun@swjtu.edu.cn
  • 摘要: 聚类集成的目的是为了提高聚类结果的准确性、稳定性和鲁棒性.通过集成多个基聚类结果可以产生一个较优的结果.本文提出了一个基于密度峰值的聚类集成模型,主要完成三个方面的工作: 1)在研究已有的各聚类集成算法和模型后发现各基聚类结果可以用密度表示; 2)使用改进的最大信息系数(Rapid computation of the maximal information coefficient,RapidMic)表示各基聚类结果之间的相关性,使用这种相关性来衡量原始数据在经过基聚类器聚类后相互之间的密度关系; 3)改进密度峰值(Density peaks,DP)算法进行聚类集成.最后,使用一些标准数据集对所设计的模型进行评估.实验结果表明,相比经典的聚类集成模型,本文提出的模型聚类集成效果更佳.
  • 图  1  基于基聚类结果获取原始数据二维关系映射图的过程

    Fig.  1  The process of obtaining the two-dimensional relational mapping of original dataset based on clustering results

    图  2  原始数据的基聚类结果的二维关系映射

    Fig.  2  The two-dimensional relational mapping of the base clustering results of original dataset

    图  3  基于改进的DP算法的聚类集成过程

    Fig.  3  The process of cluster ensembling based on improved DP algorithm

    表  1  实验数据集的样本、属性和类别数量

    Table  1  The number of instances, features and classes of datasets

    IDDatasetsNumber of instancesNumber of featuresNumber of classes
    1Aerosol9058923
    2Amber8808923
    3Ambulances9308923
    4Aquarium9228923
    5Balloon8308923
    6Banner8608923
    7Baobab9008923
    8Basket8928923
    9Bateau9008923
    10Bathroom9248923
    11Bed8888923
    12Beret8768923
    13Beverage8738923
    14Bicycle8448923
    15Birthdaycake9328923
    16Blog9438923
    17Blood8668923
    18Boat8578923
    19Bonbon8748923
    20Bonsai8678923
    下载: 导出CSV

    表  2  平均准确率和标准差(每个数据集的最大准确率加粗显示.)

    Table  2  Average MPs and standard deviations (The highest MP among different algorithms on each dataset is bolded.)

    ID AP-average AP-max CSPA HGPA MCLA DP EM QMI K-means
    1 0.022±0.015 0.113±0.072 0.379±0.020 0.384±0.003 0.395±0.020 0.484±0.019 0.354±0.004 0.466±0.053 0.369±0.008
    2 0.023±0.016 0.111±0.054 0.472±0.045 0.502±0.020 0.493±0.004 0.571±0.001 0.387±0.025 0.526±0.050 0.595±0.008
    3 0.026±0.016 0.119±0.056 0.392±0.026 0.394±0.021 0.384±0.008 0.596±0.041 0.370±0.022 0.497±0.019 0.442±0.029
    4 0.021±0.013 0.095±0.040 0.401±0.013 0.394±0.027 0.381±0.026 0.653±0.042 0.353±0.011 0.580±0.057 0.361±0.006
    5 0.026±0.020 0.161±0.118 0.410±0.037 0.468±0.017 0.393±0.009 0.554±0.010 0.358±0.032 0.541±0.035 0.445±0.004
    6 0.027±0.017 0.124±0.058 0.346±0.002 0.365±0.010 0.346±0.004 0.805±0.158 0.358±0.004 0.791±0.112 0.462±0.001
    7 0.018±0.015 0.108±0.098 0.432±0.026 0.474±0.008 0.427±0.017 0.534±0.068 0.389±0.050 0.482±0.024 0.503±0.004
    8 0.022±0.017 0.133±0.099 0.362±0.018 0.394±0.020 0.394±0.008 0.538±0.025 0.357±0.023 0.483±0.049 0.409±0.000
    9 0.028±0.018 0.135±0.066 0.401±0.020 0.445±0.039 0.423±0.023 0.511±0.050 0.367±0.017 0.510±0.020 0.441±0.003
    10 0.019±0.012 0.088±0.045 0.351±0.014 0.369±0.001 0.361±0.014 0.756±0.059 0.355±0.011 0.662±0.031 0.394±0.001
    11 0.035±0.021 0.173±0.045 0.371±0.002 0.401±0.025 0.382±0.024 0.617±0.046 0.347±0.006 0.542±0.029 0.459±0.004
    12 0.020±0.012 0.101±0.048 0.368±0.005 0.372±0.018 0.373±0.017 0.629±0.015 0.354±0.007 0.575±0.094 0.417±0.009
    13 0.031±0.023 0.173±0.101 0.419±0.014 0.425±0.019 0.400±0.013 0.531±0.027 0.353±0.004 0.511±0.015 0.396±0.000
    14 0.020±0.015 0.113±0.089 0.410±0.020 0.412±0.025 0.407±0.006 0.522±0.017 0.357±0.008 0.478±0.028 0.452±0.008
    15 0.017±0.013 0.092±0.063 0.392±0.044 0.446±0.032 0.450±0.014 0.576±0.008 0.372±0.005 0.563±0.042 0.491±0.001
    16 0.023±0.015 0.119±0.056 0.347±0.005 0.383±0.010 0.369±0.006 0.685±0.069 0.357±0.003 0.627±0.077 0.411±0.001
    17 0.018±0.011 0.088±0.025 0.349±0.011 0.352±0.013 0.375±0.003 0.776±0.059 0.354±0.017 0.687±0.095 0.473±0.004
    18 0.022±0.014 0.106±0.052 0.388±0.007 0.368±0.020 0.377±0.012 0.587±0.038 0.354±0.008 0.537±0.025 0.404±0.001
    19 0.016±0.011 0.090±0.049 0.397±0.022 0.411±0.019 0.402±0.012 0.508±0.012 0.357±0.013 0.481±0.020 0.465±0.002
    20 0.021±0.012 0.095±0.032 0.383±0.005 0.385±0.024 0.355±0.011 0.642±0.045 0.380±0.039 0.587±0.051 0.443±0.003
    AVG 0.023±0.015 0.117±0.063 0.389±0.018 0.407±0.019 0.394±0.012 0.604±0.040 0.362±0.016 0.556±0.046 0.442±0.005
    下载: 导出CSV

    表  3  平均纯度值和标准差(每个数据集的最大纯度值加粗显示.)

    Table  3  Average purities and standard deviations (The highest purity among different algorithms on each dataset is bolded.)

    ID AP-average AP-max CSPA HGPA MCLA DP EM QMI K-means
    1 0.315±0.159 0.743±0.251 0.796±0.006 0.796±0.004 0.795±0.004 0.797±0.005 0.803±0.000 0.790±0.009 0.795±0.002
    2 0.233±0.127 0.591±0.231 0.704±0.046 0.667±0.011 0.684±0.007 0.769±0.007 0.764±0.007 0.741±0.017 0.633±0.005
    3 0.274±0.149 0.707±0.290 0.753±0.009 0.755±0.005 0.755±0.002 0.767±0.001 0.764±0.003 0.754±0.012 0.749±0.013
    4 0.252±0.137 0.651±0.244 0.702±0.013 0.706±0.006 0.711±0.008 0.717±0.003 0.719±0.002 0.707±0.003 0.697±0.002
    5 0.316±0.170 0.802±0.317 0.863±0.016 0.843±0.007 0.868±0.003 0.878±0.004 0.881±0.004 0.876±0.005 0.840±0.008
    6 0.079±0.043 0.202±0.077 0.215±0.001 0.212±0.000 0.215±0.002 0.216±0.002 0.216±0.001 0.216±0.000 0.213±0.000
    7 0.270±0.140 0.678±0.240 0.764±0.007 0.761±0.001 0.779±0.005 0.806±0.004 0.801±0.010 0.800±0.007 0.764±0.002
    8 0.336±0.179 0.809±0.325 0.861±0.002 0.853±0.005 0.857±0.001 0.868±0.001 0.866±0.002 0.861±0.006 0.842±0.001
    9 0.339±0.177 0.775±0.300 0.836±0.023 0.839±0.013 0.825±0.012 0.866±0.002 0.864±0.005 0.849±0.003 0.837±0.003
    10 0.239±0.129 0.551±0.223 0.575±0.003 0.578±0.002 0.576±0.000 0.581±0.000 0.580±0.002 0.576±0.002 0.578±0.000
    11 0.345±0.177 0.726±0.284 0.769±0.010 0.752±0.003 0.775±0.006 0.782±0.004 0.786±0.001 0.775±0.009 0.752±0.007
    12 0.250±0.134 0.658±0.237 0.716±0.003 0.717±0.003 0.718±0.001 0.721±0.003 0.722±0.001 0.718±0.003 0.705±0.004
    13 0.325±0.166 0.731±0.274 0.776±0.007 0.777±0.004 0.786±0.003 0.801±0.000 0.800±0.001 0.789±0.014 0.766±0.000
    14 0.325±0.166 0.731±0.274 0.776±0.007 0.777±0.004 0.786±0.003 0.801±0.000 0.800±0.001 0.789±0.014 0.877±0.003
    15 0.289±0.150 0.713±0.270 0.820±0.027 0.779±0.012 0.784±0.020 0.839±0.001 0.839±0.000 0.818±0.015 0.735±0.002
    16 0.265±0.141 0.654±0.265 0.680±0.002 0.674±0.002 0.675±0.002 0.680±0.003 0.681±0.001 0.679±0.002 0.673±0.000
    17 0.171±0.090 0.425±0.158 0.465±0.000 0.460±0.006 0.464±0.001 0.471±0.001 0.471±0.001 0.468±0.001 0.459±0.001
    18 0.306±0.167 0.784±0.329 0.817±0.006 0.823±0.005 0.817±0.005 0.827±0.002 0.828±0.001 0.824±0.002 0.807±0.002
    19 0.316±0.167 0.807±0.316 0.845±0.010 0.844±0.006 0.848±0.005 0.862±0.002 0.863±0.002 0.861±0.000 0.835±0.001
    20 0.295±0.156 0.709±0.276 0.750±0.001 0.750±0.007 0.755±0.001 0.759±0.001 0.755±0.003 0.752±0.004 0.752±0.000
    AVG 0.277±0.146 0.672±0.259 0.724±0.010 0.718±0.005 0.724±0.005 0.740±0.002 0.740±0.002 0.732±0.006 0.715±0.003
    下载: 导出CSV

    表  4  实验选择的6种算法的调整后观察值(括号中的调整秩次用于Friedman调整秩和检验的计算.最小代表最好.)

    Table  4  Aligned observations of six algorithms selected in the experimental study (The ranks in the parentheses are used in the computation of the Friedman aligned ranks test. The smallest one is the best.)

    ID CSPA HGPA MCLA DP EM QMI Total
    1 0.000(68) 0.000(60) -0.001(70) 0.001(57) 0.007(26) -0.006(97) 378
    2 -0.017(111) -0.054(120) -0.038(119) 0.048(1) 0.042(2) 0.019(7) 360
    3 -0.005(93) -0.003(83) -0.002(79) 0.009(21) 0.006(29) -0.004(88) 393
    4 -0.009(104) -0.004(91) 0.001(55) 0.007(28) 0.009(19) -0.003(84) 381
    5 -0.005(94) -0.025(116) 0.000(65) 0.01(17) 0.013(11) 0.007(23) 326
    6 0.000(63) -0.003(80) 0.000(61) 0.001(56) 0.001(52) 0.000(58) 370
    7 -0.021(112) -0.025(115) -0.007(99) 0.021(5) 0.016(9) 0.015(10) 350
    8 0.000(67) -0.008(102) -0.004(90) 0.007(24) 0.005(32) 0.000(62) 377
    9 -0.010(106) -0.008(101) -0.022(114) 0.019(6) 0.018(8) 0.003(40) 375
    10 -0.003(82) 0.000(59) -0.002(74) 0.004(37) 0.002(41) -0.001(71) 364
    11 -0.004(92) -0.021(113) 0.002(42) 0.009(18) 0.013(12) 0.002(43) 320
    12 -0.003(81) -0.001(73) 0.000(66) 0.002(44) 0.003(38) -0.001(69) 371
    13 -0.012(109.5) -0.011(107.5) -0.002(77.5) 0.013(13.5) 0.012(15.5) 0.001(53.5) 377
    14 -0.012(109.5) -0.011(107.5) -0.002(77.5) 0.013(13.5) 0.012(15.5) 0.001(53.5) 377
    15 0.007(27) -0.034(118) -0.029(117) 0.026(4) 0.026(3) 0.005(33) 302
    16 0.001(49) -0.004(89) -0.003(87) 0.002(45) 0.003(39) 0.001(50) 359
    17 -0.001(72) -0.007(100) -0.002(76) 0.004(35) 0.004(36) 0.001(48) 367
    18 -0.006(96) 0.000(64) -0.006(95) 0.004(34) 0.005(31) 0.002(47) 367
    19 -0.008(103) -0.010(105) -0.006(98) 0.008(22) 0.009(20) 0.007(25) 373
    20 -0.003(86) -0.003(85) 0.001(51) 0.006(30) 0.002(46) -0.002(75) 373
    Total 1725 1889 1613 511 485 1037
    AVG 86.25 94.45 80.65 25.55 24.25 51.85
    下载: 导出CSV
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  • 收稿日期:  2015-12-25
  • 录用日期:  2016-04-18
  • 刊出日期:  2016-09-01

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