• Optics and Precision Engineering
  • Vol. 32, Issue 7, 1045 (2024)
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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    DOI: 10.37188/OPE.20243207.1045 Cite this Article
    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 Copy Citation Text show less
    Neighborhood information
    Fig. 1. Neighborhood information
    Flowchart of ANFCM algorithm
    Fig. 2. Flowchart of ANFCM algorithm
    Experimental results of parameter sensitivity of clustering accuracy to parameters kx and kv under fixed α condition
    Fig. 3. 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
    Fig. 4. 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
    Fig. 5. 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
    Fig. 6. Changes in objective function values and clustering performance with iteration steps on 6 datasets
    Ablation experimental results on 4 datasets
    Fig. 7. Ablation experimental results on 4 datasets

    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. [in Chinese]
    数据集样本个数特征数类别数
    Ionosphere351342
    Jain37322
    WBC68392
    Air359643
    Appendicitis10672
    Mammographic74842
    Pima76882
    WDBC569302
    Table 1. Description of benchmark datasets

    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. [in Chinese]
    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 2. Accuracy 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. NMI values for each algorithm on 8 datasets

    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 3. [in Chinese]
    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
    Table 4. Purity values for each algorithm on 8 datasets
    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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