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基于公理化模糊子集的改進(jìn)譜聚類算法

趙小強(qiáng) 劉曉麗

趙小強(qiáng), 劉曉麗. 基于公理化模糊子集的改進(jìn)譜聚類算法[J]. 電子與信息學(xué)報(bào), 2018, 40(8): 1904-1910. doi: 10.11999/IEIT170904
引用本文: 趙小強(qiáng), 劉曉麗. 基于公理化模糊子集的改進(jìn)譜聚類算法[J]. 電子與信息學(xué)報(bào), 2018, 40(8): 1904-1910. doi: 10.11999/IEIT170904
Xiaoqiang ZHAO, Xiaoli LIU. An Improved Spectral Clustering Algorithm Based on Axiomatic Fuzzy Set[J]. Journal of Electronics & Information Technology, 2018, 40(8): 1904-1910. doi: 10.11999/IEIT170904
Citation: Xiaoqiang ZHAO, Xiaoli LIU. An Improved Spectral Clustering Algorithm Based on Axiomatic Fuzzy Set[J]. Journal of Electronics & Information Technology, 2018, 40(8): 1904-1910. doi: 10.11999/IEIT170904

基于公理化模糊子集的改進(jìn)譜聚類算法

doi: 10.11999/IEIT170904
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61763029),甘肅省基礎(chǔ)研究創(chuàng)新群體基金(1506RJIA031)
詳細(xì)信息
    作者簡(jiǎn)介:

    趙小強(qiáng):男,1969年生,博士生導(dǎo)師,教授,主要研究方向?yàn)閿?shù)據(jù)挖掘、故障診斷、圖像處理、污水處理、生產(chǎn)調(diào)度等

    劉曉麗:女,1992年生,碩士生,研究方向?yàn)閿?shù)據(jù)挖掘

    通訊作者:

    趙小強(qiáng) ? xqzhao@lut.cn

  • 中圖分類號(hào): TP181

An Improved Spectral Clustering Algorithm Based on Axiomatic Fuzzy Set

Funds: The National Natural Science Foundation of China (61763029), The Gansu Province Basic Research Innovation Group Fund (1506RJIA031)
  • 摘要: 譜聚類算法通常是采用高斯核作為相似性度量,并利用所有可用的特征來(lái)構(gòu)建具有歐氏距離的相似度矩陣,數(shù)據(jù)集復(fù)雜度會(huì)影響其譜聚類性能,因此該文提出一種基于公理化模糊子集(AFS)的改進(jìn)譜聚類算法。首先結(jié)合AFS算法,利用識(shí)別特征來(lái)衡量更合適的數(shù)據(jù)成對(duì)相似性,生成更強(qiáng)大的親合矩陣;再有效地利用Nystr?m采樣算法,計(jì)算采樣點(diǎn)間以及采樣點(diǎn)和剩余點(diǎn)間的相似度矩陣去降低計(jì)算的復(fù)雜度;最后通過(guò)在不同數(shù)據(jù)集以及圖像分割上進(jìn)行實(shí)驗(yàn),證明了提出算法的有效性。
  • 圖  1  原圖

    圖  2  譜聚類算法分割結(jié)果

    圖  3  本文算法分割結(jié)果

    表  1  數(shù)據(jù)集特征

    數(shù)據(jù)集 數(shù)據(jù)總數(shù) 類數(shù) 維數(shù)
    Iris 150 3 4
    Heart 270 2 13
    Sonar 208 2 60
    Wine 178 3 13
    Protein 552 8 77
    Hepatitis 155 2 19
    Segmentation 2310 7 19
    Pen digits 10992 10 16
    下載: 導(dǎo)出CSV

    表  2  數(shù)據(jù)集的CE(%)

    數(shù)據(jù)集 SC STSC AFS 本文算法
    Iris 10.71 7.46 9.72 7.63
    Heart 20.96 22.13 30.63 12.42
    Sonar 44.53 46.83 38.52 33.60
    Wine 2.92 2.91 3.54 3.13
    Protein 54.70 55.67 55.12 48.87
    Hepatitis 30.76 38.73 32.34 23.20
    Segmentation 22.08 21.35 31.17 18.63
    Pen digits 25.37 24.25 22.16
    下載: 導(dǎo)出CSV

    表  3  數(shù)據(jù)集的NMI(%)

    數(shù)據(jù)集 SC STSC AFS 本文算法
    Iris 75.87 78.63 78.06 85.49
    Heart 28.54 26.23 18.45 40.33
    Sonar 7.32 1.83 15.47 22.38
    Wine 89.30 89.34 85.67 87.96
    Protein 54.43 48.24 36.62 65.80
    Hepatitis 13.75 4.78 3.57 17.42
    Segmentation 65.58 66.72 58.56 72.24
    Pen digits 60.53 61.48 66.52
    下載: 導(dǎo)出CSV

    表  4  SAR圖像分割性能對(duì)比表

    譜聚類算法 本文算法
    運(yùn)行時(shí)間(S) 30.62 3.27
    誤分率(%) 9.53 5.34
    下載: 導(dǎo)出CSV

    表  5  樹圖像分割性能對(duì)比表

    譜聚類算法 本文算法
    運(yùn)行時(shí)間(S) 16.39 4.25
    誤分率(%) 6.87 2.13
    下載: 導(dǎo)出CSV

    表  6  復(fù)雜度分析

    計(jì)算步驟 復(fù)雜度
    計(jì)算矩陣 ${{A}}$ O(n2)
    計(jì)算矩陣 ${{B}}$ O(n(Nn))
    若矩陣 ${{A}}$正定 對(duì) ${{A}}$矩陣分解 O(n3)
    求解矩陣 ${{p}}$ O(n2(Nn))
    矩陣分解 O(n3)
    求解矩陣 ${{Y}}$ O(n2N)
    若矩陣 ${{A}}$非正定 求解矩陣 ${{S}}$ O(n2N)
    對(duì)矩陣 ${{S}$對(duì)角分解 O(n3)
    求解矩陣 ${{Y}}$ O(n2N)
    K-means算法進(jìn)行聚類 O(nK2T)
    下載: 導(dǎo)出CSV
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出版歷程
  • 收稿日期:  2017-09-25
  • 修回日期:  2018-05-02
  • 網(wǎng)絡(luò)出版日期:  2018-05-30
  • 刊出日期:  2018-08-01

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