融合密度峰值和空间邻域信息的FCM聚类算法
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摘要
针对模糊C均值(FCM)算法聚类结果对初始中心点敏感以及聚类过程中没有考虑到不同密度样本点在聚类过程中影响力不同的缺陷,提出了一种密度峰值和样本点空间邻域信息优化的FCM算法。改进后的算法选择数据集中具有局部密度峰值的样本点或者局部密度较大的样本点作为初始聚类中心,充分考虑样本点邻域之间的关系,增加局部密度值大的样本点在聚类中心迭代计算过程中的影响力,从而达到优化FCM算法聚类效果的目的。理论分析和在人造数据集、加州大学欧文分校(UCI)机器学习数据库中真实数据上的实验结果表明,改进后算法的抗噪性、聚类效果和全局收敛能力均优于传统FCM算法。
In fuzzy C-means( FCM) algorithm,the clustering result is sensitive to the initial center points and the clustering process does not take into account the influences of different density points. Thus,an improved FCM algorithm based on density peak and spatial neighborhood information is proposed. The improved algorithm selects the points with local density peaks or large local density values as the initial center points,and highlights high density points' influence in the clustering. The theoretical analysis and experiments on both synthetic and real-world datasets from the UCI machine learning repository demonstrate that,the proposed algorithm has better antinoise,clustering performance and global convergence ability than traditional FCM algorithm.
In fuzzy C-means( FCM) algorithm,the clustering result is sensitive to the initial center points and the clustering process does not take into account the influences of different density points. Thus,an improved FCM algorithm based on density peak and spatial neighborhood information is proposed. The improved algorithm selects the points with local density peaks or large local density values as the initial center points,and highlights high density points' influence in the clustering. The theoretical analysis and experiments on both synthetic and real-world datasets from the UCI machine learning repository demonstrate that,the proposed algorithm has better antinoise,clustering performance and global convergence ability than traditional FCM algorithm.
引文
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[15]肖满生,肖哲,文志诚,等.一种空间相关性与隶属度平滑的FCM改进算法[J].电子与信息学报,2017(5):1123-1129.XIAO M SH,XIAO ZH,WEN ZH CH,et al. Improved FCM clustering algorithm based on spatial correlation and membership smoothing[J]. Journal of Electronics&Information Technology,2017(5):1123-1129.
[16] LIU Y,CHEN H P,SHEN X J,et al. Gamma correction FCM algorithm with conditional spatial information for image segmentation[J]. KSII Transactions on Internet and Information Systems,2018,12(9):4336-4354.
[17]余晓东,雷英杰,宋亚飞,等.基于核距离的直觉模糊C均值聚类算法[J].电子学报,2016,44(10):2530-2534.YU X D,LEI Y J,SONG Y F,et al. Intuitionistic fuzzy C-means clustering algorithm based on kernelled distance[J]. Acta Electronica Sinica,2016,44(10):2530-2534.
[18]肖满生,肖哲,文志强,等.模糊C均值聚类区间型模糊化参数模型[J].系统工程与电子技术,2015,37(4):868-873.XIAO M SH,XIAO Z,WEN ZH Q,et al. Interval type fuzzifier parameter model in fuzzy C-means clustering[J]. Systems Engineering and Electronic,2015,37(4):868-873.
[19]周开乐,杨善林,王晓佳,等.基于自适应模糊度参数选择改进FCM算法的负荷分类[J].系统工程理论与实践,2014(5):1283-1289.ZHOU K L,YANG SH L,WANG X J,et al. Load classification based on improved FCM algorithm with adaptive fuzziness parameter selection[J]. System Engineering-Theory&Practice,2014(5):1283-1289.
[20]宫改云,高新波,伍忠东. FCM聚类算法中模糊加权指数m的优选方法[J].模糊系统与数学,2005,19(1):143-148.GONG G Y,GAO X B,WU ZH D. An optimal choice method of parameter m in FCM clustering algorithm[J].Fuzzy Systems and Mathematics,2005,19(1):143-148.
[21]王骏,王士同.基于混合距离学习的双指数模糊C均值算法[J].软件学报,2010,21(8):1878-1888.WANG J,WANG SH T. Double indices FCM algorithm based on hybrid distance metric learning[J]. Journal of Software,2010,21(8):1878-1888.
[22] RODRIGUEZ A,LAIO A. Clustering by fast search and find of density peaks[J]. Science,2014,344(6191):1492-1496.
[23] JIANG J,HAO D,CHEN Y. GDPC:Gravitation-based density peaks clustering algorithm[J]. Physica A:Statistical Mechanics and its Applications, 2018,502(7):345-355.
[24]江克勤,施培蓓.优化初始中心的模糊C-均值(FCM)算法[J].合肥工业大学学报(自然科学版),2009,32(5):762-764.JIANG K Q,SHI P B. Optimized initial centers for fuzzy C-means algorithm[J]. Journal of Hefei University of Technology,2009,32(5):762-764.
[25] PAL N R,BEZDEK J C. On cluster validity for the fuzzy C-mean model[J]. IEEE Transactions on Fuzzy Systems,1995,3(3):370-379.
[2]霍冠英,刘静,李庆武,等.空间约束FCM与MRF结合的侧扫声呐图像分割算法[J].仪器仪表学报,2017,38(1):226-235.HUO G Y,LIU J,LI Q W,et al. Side-scan sonar image segmentation algorithm based on space-constrained FCM and MRF[J]. Chinese Journal of Scientific Instrument,2017,38(1):226-235.
[3]田再克,李洪儒,孙健,等.基于改进MF-DFA和SSM-FCM的液压泵退化状态识别方法[J].仪器仪表学报,2016,37(8):1851-1860.TIAN Z K,LI H R,SUN J,et al. Degradation state identification method of hydraulic pump based on improved MF-DFA and SSM-FCM[J]. Chinese Journal of Scientific Instrument,2016,37(8):1851-1860.
[4]张淑清,孙国秀,李亮,等.基于LMD近似熵和FCM聚类的机械故障诊断研究[J].仪器仪表学报,2013,34(3):714-720.ZHANG SH Q, SUN G X, LI L, et al. Study on mechanical fault diagnosis method based on LMD approximate entropy and fuzzy C-means clustering[J].Chinese Journal of Scientific Instrument,2013,34(3):714-720.
[5]袁帅,郭艳茹,宫巍,等.基于DSm T的室内环境轮廓超声检测模型研究[J].仪器仪表学报,2018,39(10):142-149.YUAN SH,GUO Y R,GONG W,et al. Research of the ultrasonic detection model for indoor environment contour based on DSm T[J]. Chinese Journal of Scientific Instrument,2018,39(10):142-149.
[6] BEZDEK J C. Pattern recognition with fuzzy objective function algorithms[J]. Advanced Applications in Pattern Recognition,1981,22(1171):203-239.
[7]李洪波.基于减法聚类和快速紧密性函数的SF-FCM[J].控制与决策,2011,26(7):1074-1078.LI H B. SF-FCM based on fast close function and subtractive clustering[J]. Control and Decision,2011,26(7):1074-1078.
[8] WU Z,WU Z,ZHANG J. An improved FCM algorithm with adaptive weights based on SA-PSO[J]. Neural Computing and Applications,2017,28(12):3113-3118.
[9] KHALILIA M A,BEZDEK J,POPESCU M,et al.Improvements to the relational fuzzy C-means clustering algorithm[J]. Pattern Recognition, 2014, 47(12):3920-3930.
[10] SHI Y L,NAN J Z. Improved FCM algorithm based on initial center optimization method[J]. Journal of Intelligent&Fuzzy Systems,2017,32(5):3487-3494.
[11] RICHARD J H,HU Y K. Density-weighted fuzzy Cmeans clustering[J]. IEEE Transactions on Fuzzy Systems,2009,17(1):243-252.
[12]周世波,徐维祥,柴田.基于数据加权策略的模糊C均值聚类算法[J].系统工程与电子技术,2012,36(11):2314-2319.ZHOU SH B,XU W X,CHAI T. Data-weighted fuzzy C-means clustering algorithm[J],Systems Engineering and Electronic,2012,36(11):2314-2319.
[13]贾亚飞,朱永利,高佳程,等.基于样本加权FCM聚类的未知类别局部放电信号识别[J].电力自动化设备,2018(12):107-112.JIA Y F,ZHU Y L,GAO J CH,et al. Recognition of unknown partial discharge signals based on sampleweighted FCM clustering[J]. Electric Power Automation Equipment,2018(12):107-112.
[14]王丽娟,关守义,王晓龙,等基于属性权重的Fuzzy C-Mean算法[J].计算机学报, 2006, 29(10):1797-1803.WANG L J,GUAN S Y,WANG X L,et al. Fuzzy Cmean algorithm based on feature weights[J]. Chinese Journal of Computers,2006,29(10):1797-1803.
[15]肖满生,肖哲,文志诚,等.一种空间相关性与隶属度平滑的FCM改进算法[J].电子与信息学报,2017(5):1123-1129.XIAO M SH,XIAO ZH,WEN ZH CH,et al. Improved FCM clustering algorithm based on spatial correlation and membership smoothing[J]. Journal of Electronics&Information Technology,2017(5):1123-1129.
[16] LIU Y,CHEN H P,SHEN X J,et al. Gamma correction FCM algorithm with conditional spatial information for image segmentation[J]. KSII Transactions on Internet and Information Systems,2018,12(9):4336-4354.
[17]余晓东,雷英杰,宋亚飞,等.基于核距离的直觉模糊C均值聚类算法[J].电子学报,2016,44(10):2530-2534.YU X D,LEI Y J,SONG Y F,et al. Intuitionistic fuzzy C-means clustering algorithm based on kernelled distance[J]. Acta Electronica Sinica,2016,44(10):2530-2534.
[18]肖满生,肖哲,文志强,等.模糊C均值聚类区间型模糊化参数模型[J].系统工程与电子技术,2015,37(4):868-873.XIAO M SH,XIAO Z,WEN ZH Q,et al. Interval type fuzzifier parameter model in fuzzy C-means clustering[J]. Systems Engineering and Electronic,2015,37(4):868-873.
[19]周开乐,杨善林,王晓佳,等.基于自适应模糊度参数选择改进FCM算法的负荷分类[J].系统工程理论与实践,2014(5):1283-1289.ZHOU K L,YANG SH L,WANG X J,et al. Load classification based on improved FCM algorithm with adaptive fuzziness parameter selection[J]. System Engineering-Theory&Practice,2014(5):1283-1289.
[20]宫改云,高新波,伍忠东. FCM聚类算法中模糊加权指数m的优选方法[J].模糊系统与数学,2005,19(1):143-148.GONG G Y,GAO X B,WU ZH D. An optimal choice method of parameter m in FCM clustering algorithm[J].Fuzzy Systems and Mathematics,2005,19(1):143-148.
[21]王骏,王士同.基于混合距离学习的双指数模糊C均值算法[J].软件学报,2010,21(8):1878-1888.WANG J,WANG SH T. Double indices FCM algorithm based on hybrid distance metric learning[J]. Journal of Software,2010,21(8):1878-1888.
[22] RODRIGUEZ A,LAIO A. Clustering by fast search and find of density peaks[J]. Science,2014,344(6191):1492-1496.
[23] JIANG J,HAO D,CHEN Y. GDPC:Gravitation-based density peaks clustering algorithm[J]. Physica A:Statistical Mechanics and its Applications, 2018,502(7):345-355.
[24]江克勤,施培蓓.优化初始中心的模糊C-均值(FCM)算法[J].合肥工业大学学报(自然科学版),2009,32(5):762-764.JIANG K Q,SHI P B. Optimized initial centers for fuzzy C-means algorithm[J]. Journal of Hefei University of Technology,2009,32(5):762-764.
[25] PAL N R,BEZDEK J C. On cluster validity for the fuzzy C-mean model[J]. IEEE Transactions on Fuzzy Systems,1995,3(3):370-379.
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