一种改进隶属度函数的FCM聚类算法
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摘要
传统模糊??-均值(FCM)算法要求一个样本对于各个聚类的隶属度之和满足归一化条件,从而导致算法对噪声和孤立点敏感,对非均衡分布样本的聚类有效性降低.针对该问题,提出一种改进模糊隶属函数约束的FCM聚类算法,通过放松归一化条件,推导出新的隶属度划分公式,并在聚类过程中不断进行隶属度修正,从而达到消除噪声样本、提高聚类有效性的目的.最后通过实验结果对比验证了改进算法的正确性.
Since the general fuzzy ??-means(FCM) algorithm requires sum of membership satisfying the normalization condition for a sample to each cluster, and thus results algorithm sensitive to noise or outliers and reducing the validity of the clustering on non-equilibrium distribution samples. Therefore, an FCM clustering algorithm with the improved fuzzy membership constraint function is proposed. By relaxing the normalization condition, a new formula of membership division is deduced, and the membership is constantly corrected in the clustering process, so that it will eliminate the noise sample,and improve the validity of clustering. Finally, the comparison of the experimental result verifies the correctness of the improved algorithm.
Since the general fuzzy ??-means(FCM) algorithm requires sum of membership satisfying the normalization condition for a sample to each cluster, and thus results algorithm sensitive to noise or outliers and reducing the validity of the clustering on non-equilibrium distribution samples. Therefore, an FCM clustering algorithm with the improved fuzzy membership constraint function is proposed. By relaxing the normalization condition, a new formula of membership division is deduced, and the membership is constantly corrected in the clustering process, so that it will eliminate the noise sample,and improve the validity of clustering. Finally, the comparison of the experimental result verifies the correctness of the improved algorithm.
引文
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[14]Trygve Randen.Brodatz textures[EB/OL].[2007-08-01].http://www.ux.uis.no/～tranden/brodatz.htm.
[2]Jiashun Chen,Dechang Pi,Zhipeng Liu.An insensitivity fuzzy??-means clustering algorithm based on penalty factor[J].J of Software,2013,8(9):2379-2384.
[3]Hopper F,Klawonn F.Improved fuzzy partitions for fuzzy regression models[J].J of Approximate Reasoning,2003,33(2):85-102.
[4]朱林,王士同,邓赵红.改进模糊划分的FCM聚类算法的一般化研究[J].计算机研究与发展,2009,46(5):814-822.(Zhu L,Wang S T,Deng Z H.Research on generalized fuzzy??-means clustering algorithm with improved fuzzy partitions[J].J of Computer Research and Development,2009,46(5):814-822.)
[5]Li J,Gao X B,Jiao L C.A new feature weighted fuzzy clustering algorithm[J].Acta Electronic Sinica,2006,34(1):412-420.
[6]贺思艳,李鹏,刘澄玉,等.互模糊熵中隶属度函数的改进和影响分析[J].山东大学学报:工学版,2014,44(1):63-68.(He S Y,Li P,Liu C Y,et al.Refining of the membership function in cross fuzzy entropy and its influence[J].J of Shandong University:Engineering Science,2014,44(1):63-68.)
[7]魏延,李晓虹,邬啸.后验概率加权的模糊隶属度函数[J].重庆大学学报,2012,35(8):127-133.(Wei Y,Li X H,Wu X.Design fuzzy membership functions based on the posterior probability weighting[J].J of Chongqing University,2012,35(8):127-133.)
[8]肖满生,汪新凡,朱永平.非均衡原型结构模式模糊类方法研究[J].小型微型计算机系统,2013,34(4):868-871.(Xiao M S,Wang X F,Zhu Y P.Fuzzy clustering method research based on disequilibrium prototype pattern[J].J of Chinese Computer Systems,2013,34(4):868-871.)
[9]Qing Niu,Xinjian Huang.An improved fuzzy??-means clustering algorithm based on PSO[J].J of Software,2011,6(5):873-879.
[10]李弼程,彭天强,彭波,等.智能图像处理技术[M].北京:电子工业出版社,2004:302-304.(Li B C,Peng T Q,Peng B,et al.Intelligent image processing technology[M].Beijing:Publishing House of Electronics Industry,2004:302-304.)
[11]Dong-hyuck Park,Sang H Lee,Eui-Ho Song,et al.Similarity computation of fuzzy membership function pairs with similarity MEASURE[C].Proc of the 3rd Int Conf on Intelligent Computing.Qingdao,2007:485-492.
[12]Xiao Mansheng,Xiao Zhe,Liu Zhi.A method of feature automatic selection based on mutual information grouping and clustering[C].Proc of 2014 Int Conf on Vehicle&Mechanical Engineering and Information Technology.Beijing,2014:1613-1618.
[13]Frank A,Asuncion A.UCI machine learning repository[EB/OL].[2012-02-01].http://archive.ics.uci.edu/ml/datasets.html.
[14]Trygve Randen.Brodatz textures[EB/OL].[2007-08-01].http://www.ux.uis.no/～tranden/brodatz.htm.