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一種基于屬性空間相似性的模糊聚類算法

施偉鋒 卓金寶 蘭瑩

施偉鋒, 卓金寶, 蘭瑩. 一種基于屬性空間相似性的模糊聚類算法[J]. 電子與信息學(xué)報(bào), 2019, 41(11): 2722-2728. doi: 10.11999/JEIT180974
引用本文: 施偉鋒, 卓金寶, 蘭瑩. 一種基于屬性空間相似性的模糊聚類算法[J]. 電子與信息學(xué)報(bào), 2019, 41(11): 2722-2728. doi: 10.11999/JEIT180974
Weifeng SHI, Jinbao ZHUO, Ying LAN. A Novel Fuzzy Clustering Algorithm Based on Similarity of Attribute Space[J]. Journal of Electronics & Information Technology, 2019, 41(11): 2722-2728. doi: 10.11999/JEIT180974
Citation: Weifeng SHI, Jinbao ZHUO, Ying LAN. A Novel Fuzzy Clustering Algorithm Based on Similarity of Attribute Space[J]. Journal of Electronics & Information Technology, 2019, 41(11): 2722-2728. doi: 10.11999/JEIT180974

一種基于屬性空間相似性的模糊聚類算法

doi: 10.11999/JEIT180974
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61503240),上海海事大學(xué)研究生創(chuàng)新基金(2016ycx078)
詳細(xì)信息
    作者簡(jiǎn)介:

    施偉鋒:男,1963年生,博士,教授,主要研究方向?yàn)殡娏ο到y(tǒng)自動(dòng)化

    卓金寶:男,1991年生,博士生,研究方向?yàn)橹悄芄收显\斷與預(yù)測(cè)

    蘭瑩:女,1985年生,博士,講師,研究方向?yàn)槎嘧灾黧w與混雜系統(tǒng)研究

    通訊作者:

    施偉鋒 wfshi@shmtu.edu.cn

  • 中圖分類號(hào): TP391

A Novel Fuzzy Clustering Algorithm Based on Similarity of Attribute Space

Funds: The National Natural Science Foundation of China (61503240), Shanghai Maritime University Graduate Student Innovation Fund Project (2016ycx078)
  • 摘要: 模糊C均值(FCM)聚類算法及其相關(guān)改進(jìn)算法基于最大模糊隸屬度原則確定聚類結(jié)果,沒有充分利用迭代后的模糊隸屬度矩陣和簇類中心的樣本屬性特征信息,影響聚類準(zhǔn)確度。針對(duì)這個(gè)問題,該文提出一種新的改進(jìn)思路:改進(jìn)FCM算法輸出定類原則。給出二元屬性拓?fù)渥涌臻g中屬性相似度的定義,最終提出一種基于屬性空間相似性的改進(jìn)FCM算法(FCM-SAS):首先,選擇FCM算法聚類后模糊隸屬度低于聚類置信度的樣本作為存疑樣本;然后,計(jì)算存疑樣本與聚類后聚類中心的屬性相似度;最后,基于最大屬性相似度原則更新存疑樣本的簇類標(biāo)簽。通過UCI數(shù)據(jù)集實(shí)驗(yàn),證明算法不僅有效,還較一些基于最大模糊隸屬度原則定類的改進(jìn)算法具有更優(yōu)的聚類評(píng)價(jià)指標(biāo)。
  • 表  1  FCM-SAS算法具體步驟

    輸入:樣本集${\text{X}}$、樣本數(shù)$n$,聚類個(gè)數(shù)$c$、加權(quán)指數(shù)$m$、迭代閾
    值$\varepsilon $、最大迭代次數(shù)T、聚類存疑率$\xi $、屬性占比率$\kappa $;
    輸出:樣本標(biāo)簽集${{\text{X}}_l}'$;
    1表1的傳統(tǒng)FCM算法步驟得到迭代后模糊隸屬度矩陣${\text{U}}$、簇類中心${\text{V}}$和樣本標(biāo)簽集${{\text{X}}_l}$,令$j = 0$;
    2計(jì)算所有樣本點(diǎn)${\text{x}}$的模糊隸屬度最大值,按遞增順序排序并組成數(shù)組,選出此數(shù)組中第$\left[ {\xi \times n} \right]$個(gè)元素的數(shù)值作為聚類置信度$\eta $;
    3令$j = j + 1$,判斷第$j$個(gè)樣本的模糊隸屬度$\max \left( {\left\{ {{u_{ij}}\left| {i = 1, 2, ·\!·\!· , c} \right.} \right\}} \right)$是否不大于聚類置信度$\eta $,若是則此樣本為存疑樣本,轉(zhuǎn)步驟4;否則轉(zhuǎn)步驟8;
    4按式(8)計(jì)算第$j$個(gè)樣本與各個(gè)簇類中心在2元屬性拓?fù)渥涌臻g中的拓?fù)湎嗨贫燃?\gamma \left( {{{\text{x}}_j}, {{\text{v}}_i}} \right)$,將所有集合中的元素取絕對(duì)值后按遞增的順序排序并組成數(shù)組,計(jì)算此數(shù)組中第$\left[ {n \times {\gamma _{dis}} \times \kappa } \right]$個(gè)元素與數(shù)值1之間差的絕對(duì)值作為鄰域半徑$\delta $;
    5以$\delta $為鄰域半徑,按式(10)計(jì)算第$j$個(gè)樣本與各個(gè)簇類中心的屬性相似度$\psi \left( {{{\text{x}}_j}, {{\text{v}}_i}} \right)$;
    6若最大屬性相似度$\max \left( {\psi \left( {{{\text{x}}_j}, {{\text{v}}_i}} \right)} \right)$只有一個(gè),則選出最大屬性相似度時(shí)的簇類中心所在的類別作為此樣本更新后的標(biāo)簽$x_{lj}'$,轉(zhuǎn)步驟8;否則,轉(zhuǎn)步驟7;
    7若最大屬性相似度不止一個(gè),則選擇這些簇類中最大拓?fù)湎嗨贫燃现?\widehat S = \max \left( {\Sigma \gamma \left( {{{\text{x}}_j}, {{\text{v}}_i}} \right)} \right)$時(shí)的簇類中心所在的類別作為$x_{lj}'$;
    8判斷$j < n$,若是則轉(zhuǎn)步驟3,否則輸出更新后的樣本標(biāo)簽集${{\text{X}}_l}'$。
    下載: 導(dǎo)出CSV

    表  2  算法輸入?yún)?shù)設(shè)置

    參數(shù)數(shù)值
    加權(quán)指數(shù)$m$2
    迭代閾值$\varepsilon $${10^{ - 3}}$
    最大迭代次數(shù)$T\;$$100$
    聚類存疑率$\xi $$0.3$
    屬性占比率$\kappa $$0.5$
    下載: 導(dǎo)出CSV

    表  3  UCI數(shù)據(jù)集的統(tǒng)計(jì)描述

    數(shù)據(jù)集樣本數(shù)維數(shù)簇類各類占比
    Iris1504350:50:50
    Wine17813359:71:48
    Seeds2107370:70:70
    Breast68392444:239
    Glass2149670:17:76:13:9:29
    下載: 導(dǎo)出CSV

    表  4  UCI數(shù)據(jù)集聚類結(jié)果評(píng)價(jià)指標(biāo)對(duì)比(1)

    FCMRL-FCMRCAWFCMFRCMFCM-SAS(標(biāo)準(zhǔn)化樣本)FCM-SAS(未標(biāo)準(zhǔn)化樣本)
    IrisAR0.8930.9070.9670.9570.9600.9870.953
    RI0.8800.8920.9580.9340.9520.9830.942
    NMI0.7500.8310.8730.9490.8498
    SeedsAR0.8950.8950.9030.8950.8950.9190.900
    RI0.8740.8740.8840.8730.8760.8990.877
    NMI0.6950.6770.6970.7170.671
    BreastAR0.9370.9530.6550.9380.9470.9650.946
    RI0.8760.9100.5480.8840.9110.9320.897
    NMI0.7300.7360.7550.7820.688
    下載: 導(dǎo)出CSV

    表  5  UCI數(shù)據(jù)集聚類結(jié)果評(píng)價(jià)指標(biāo)對(duì)比(2)

    FCMPSO-IFCMGA-IFCMABC-IFCMKFCMWGFCMFCM-SAS(標(biāo)準(zhǔn)化樣本)FCM-SAS(未標(biāo)準(zhǔn)化樣本)
    IrisAR0.8930.8070.8490.7870.8950.9730.9870.953
    WineAR0.9490.6550.6520.6420.9420.9660.9550.781
    GlassAR0.4210.4190.3930.4670.4600.7330.5330.472
    下載: 導(dǎo)出CSV

    表  6  FCM-SAS算法聚類過程統(tǒng)計(jì)數(shù)據(jù)

    樣本集1次定類錯(cuò)誤樣本數(shù)1次定類正確的存疑樣本數(shù)1次定類錯(cuò)誤的存疑樣本數(shù)存疑樣本數(shù)2次定類正確樣本數(shù)2次定類錯(cuò)誤樣本數(shù)
    Iris16291645432
    Seeds214419634815
    Breast43173272001919
    Wine945853476
    Glass1262142634518
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2018-10-17
  • 修回日期:  2019-02-28
  • 網(wǎng)絡(luò)出版日期:  2019-04-25
  • 刊出日期:  2019-11-01

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