Optics and Precision Engineering, Volume. 32, Issue 7, 1045(2024)

Fuzzy C-means clustering algorithm based on adaptive neighbors information

Yunlong GAO1... Jianpeng LI2, Xingshen ZHENG1, Guifang SHAO1, Qingyuan ZHU1 and Chao CAO3,* |Show fewer author(s)
Author Affiliations
  • 1Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen3602, China
  • 2Department of Automation, Xiamen University, Xiamen36110, China
  • 3Third Institute of Oceanography, Ministry of Natural Resources, Xiamen61005, China
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    Figures & Tables(14)
    Neighborhood information
    Flowchart of ANFCM algorithm
    Experimental results of parameter sensitivity of clustering accuracy to parameters kx and kv under fixed α condition
    Experimental results of parameter sensitivity of clustering accuracy to parameters kv and α under fixed kx condition
    Experimental results of parameter sensitivity of clustering accuracy to parameters kx and α under fixed kv condition
    Changes in objective function values and clustering performance with iteration steps on 6 datasets
    Ablation experimental results on 4 datasets
    • Table 1. [in Chinese]

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      Table 1. [in Chinese]

      算法1样本点近邻信息GX的求解

      输入:数据矩阵XRd×n,类簇数量c,自适应近邻个数k

      输入:自适应近邻信息向量GXR1×n

       1: 开始

       2: 计算 距离矩阵DRn×n,矩阵第j行第k列元素按式(14)定义;

       3:     根据给定自适应近邻个数k,通过式(17)和(18)计算了参数λ

       4:     拉格朗日乘子η根据式(19)计算;

       5:     相似度矩阵SRn×n,矩阵第j行第k列元素按式(20)定义;

       6:     根据ANFCM模块(3.5)中Gxj的定义式计算样本点xj的近邻信息;

       7: 输出 近邻信息向量GX

    • Table 1. Description of benchmark datasets

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      Table 1. Description of benchmark datasets

      数据集样本个数特征数类别数
      Ionosphere351342
      Jain37322
      WBC68392
      Air359643
      Appendicitis10672
      Mammographic74842
      Pima76882
      WDBC569302
    • Table 2. [in Chinese]

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      Table 2. [in Chinese]

      算法2类中心点近邻信息GV的求解

      输入:数据矩阵XRd×n,聚类原型矩阵VRd×c,类簇数量c,自适应近邻个数k

      输入:类中心点自适应近邻信息向量GVR1×c

       1: 开始

       2: 计算 距离矩阵DRc×n,矩阵第i行第k列元素由dik=vi-xk定义;

       3:     根据给定自适应近邻个数k,通过式(17)和(18)计算参数λ

       4:     拉格朗日乘子η根据式(19)计算;

       5:     相似度矩阵SRc×n,矩阵第j行第k列元素按式(20)定义;

       6:     根据ANFCM模块(3.5)中Gvj的定义式计算类中心点vi的近邻信息;

       7: 输出 近邻信息向量GV

    • Table 2. Accuracy values for each algorithm on 8 datasets

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      Table 2. Accuracy values for each algorithm on 8 datasets

      MethodIonosphereJainWBCAirAppendicitisMammographicPimaWDBC
      KM0.705 10.781 00.960 60.404 20.800 90.731 60.660 20.854 1
      FCM0.711 10.589 80.956 10.376 30.792 50.707 20.658 90.854 1
      FCS0.709 40.595 20.956 10.381 60.792 50.707 20.658 90.852 4
      AFKM0.712 30.780 20.972 20.404 50.778 30.762 00.651 40.688 6
      RSFKM l2,10.695 20.766 80.964 90.436 80.826 40.675 10.608 10.868 2
      RSFKM capped2,10.641 00.740 00.774 40.442 30.837 70.762 00.651 00.627 4
      FKPS0.710 50.808 30.973 80.415 90.792 50.673 30.645 40.911 6
      ANFCM0.863 00.963 50.975 10.507 20.851 90.771 40.739 30.924 4
    • Table 3. NMI values for each algorithm on 8 datasets

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      Table 3. NMI values for each algorithm on 8 datasets

      MethodIonosphereJainWBCAirAppendicitisMammographicPimaWDBC
      KM0.118 30.332 10.743 60.010 20.174 00.014 60.026 70.422 3
      FCM0.129 30.283 70.722 30.017 70.162 10.014 80.031 70.422 3
      FCS0.126 40.283 70.722 30.017 90.162 10.014 80.031 30.417 9
      AFKM0.131 20.331 10.806 80.022 10.158 30.008 50.019 70.114 0
      RSFKM l2,10.114 40.315 90.765 10.028 90.210 20.023 40.015 10.458 7
      RSFKM capped2,10.167 80.076 90.360 90.034 10.243 00.000 40.000 00.000 0
      FKPS0.129 50.381 10.816 70.024 80.162 10.026 10.037 20.554 3
      ANFCM0.413 10.761 40.825 50.064 80.196 30.025 90.135 10.597 3
    • Table 3. [in Chinese]

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      Table 3. [in Chinese]

      算法3ANFCM迭代求解法

      输入:数据矩阵XRd×n,类簇数量c,样本点和类中心点近邻个数kxkv

      输入:隶属度矩阵URc×n

       1: 开始

       2: 初始化 随机初始化隶属度矩阵U,使满足0uij1Σiuij=1

       3:     根据式(28)初始化聚类原型矩阵VRd×c

       4: 计算 根据算法1计算样本点的近邻信息GX

       5: While U not converge do:

       6:     根据算法2更新类中心点的近邻信息GV

       7:     根据式(25)更新隶属度矩阵U

       8:     根据式(28)更新聚类原型矩阵V

       9: End while

       10: 输出 近邻信息向量GV

    • Table 4. Purity values for each algorithm on 8 datasets

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      Table 4. Purity values for each algorithm on 8 datasets

      MethodIonosphereJainWBCAirAppendicitisMammographicPimaWDBC
      KM0.705 10.781 00.960 60.420 60.807 50.762 00.660 20.854 1
      FCM0.711 10.895 40.956 10.427 00.801 90.762 00.658 90.854 1
      FCS0.709 40.895 40.956 10.424 20.801 90.762 00.658 90.852 4
      AFKM0.712 30.793 80.972 20.424 00.816 00.763 10.657 70.688 6
      RSFKM l2,10.695 20.766 80.964 90.439 60.826 40.762 00.651 00.868 2
      RSFKM capped2,10.657 60.759 50.774 40.445 40.837 70.762 00.651 00.627 4
      FKPS0.710 50.811 50.973 80.438 70.801 90.762 00.664 10.911 6
      ANFCM0.863 00.963 50.975 10.507 20.851 90.771 40.739 30.924 4
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    Yunlong GAO, Jianpeng LI, Xingshen ZHENG, Guifang SHAO, Qingyuan ZHU, Chao CAO. Fuzzy C-means clustering algorithm based on adaptive neighbors information[J]. Optics and Precision Engineering, 2024, 32(7): 1045

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    Paper Information

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    Received: Aug. 28, 2023

    Accepted: --

    Published Online: May. 28, 2024

    The Author Email: CAO Chao (caochao@tio.org.cn)

    DOI:10.37188/OPE.20243207.1045

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