Abstract：A clustering algorithm named Fuzzy k-Plane Clustering (FkPC) is proposed by introducing fuzzy membership into the prevalent k-Plane Clustering (kPC). From the view of prototype selection, FkPC substitutes hyperplanes for points as the prototype, which is similar with kPC. Meanwhile, FkPC represents the membership between the points and its central hyperplanes much more clearly than kPC, due to the introduction of fuzzy membership into its objective function. Experimental results of both artificial and UCI datasets have proved the clustering validity of FkPC, and they also reveal that besides the similarity metric, the expression of prototype also plays a crucial role in clustering.
[1] Jain A K, Dubes R C. Algorithms for Clustering Data. Englewood Cliffs, USA: Prentice Hall, 1988 [2] Duda R O, Hart P E. Pattern Classification and Scene Analysis. New York, USA: Wiley, 1973 [3] Hartigan J. Clustering Algorithms. New York, USA: Wiley, 1975 [4] Everitt B S. Cluster Analysis. London, UK: Edward Arnold, 1993 [5] Anderberg M R. Cluster Analysis for Applications. New York, USA: Academic Press, 1973 [6] Bezdek J C. Pattern Recognition with Fuzzy Objective Function Algorithms. Norwell, USA: Kluwer Academic Publishers, 1981 [7] Zhang Honggang, Liu Gang, Guo Jun. An Algorithm of FCM-VKNN Clustering. Acta Automatica Sinica, 2002, 28(4): 631-636 (in Chinese) (张红刚,刘 刚,郭 军.FCM-VKNN聚类算法的研究.自动化学报, 2002, 28(4): 631-636) [8] Belacel N, Hansen P, Mladenovic N. Fuzzy J-Means: A New Heuristic for Fuzzy Clustering. Pattern Recognition, 2002, 35(10): 2193-2200 [9] Zahid N, Abouelala O, Limouri M, et al. Fuzzy Clustering Based on K-Nearest-Neighbours Rule. Fuzzy Sets and Systems, 2001, 120(2): 239-247 [10] Bradley P S, Mangasarian O L. k-Plane Clustering. Journal of Global Optimization, 2000, 16(1): 23-32 [11] Mangasarian O L. Arbitrary-Norm Separating Plane. Operations Research Letters, 1999, 24(1/2): 15-23 [12] Dai Hua. Theory of Matrix. Beijing, China: Science Press, 2003 (in Chinese) (戴 华.矩阵论.北京:科学出版社, 2003) [13] Xu Shufang, Gao Li, Zhang Pingwen. Numerical Linear Algebra. Beijing, China: Peking University Press, 2002 (in Chinese) (徐树方,高 利,张平文.数值线性代数.北京:北京大学出版社, 2002) [14] Blake C, Keogh E, Merz C J. UCI Repository of Machine Learning Databases [DB/OL]. [20060321]. http://www.ics.uci.edu/~mlearn /MLRepository.html [15] Duda R O, Hart P E, Stork D G. Pattern Classification. 2nd Edition. New York, USA: Wiley-Interscience Press, 2000 [16] Stone M. Cross-Validatory Choice and Assessment of Statistical Predictions. Journal of the Royal Statistical Society, 1974, 36(2): 111-147 [17] Zhang Daoqiang, Chen Songcan. Clustering Incomplete Data Using Kernel-Based Fuzzy c-Means Algorithm. Neural Processing Letters, 2003, 18(3): 155-162 [18] Chen Songcan, Zhang Daoqiang. Robust Image Segmentation Using FCM with Spatial Constraints Based on New Kernel-Induced distance Metric. IEEE Trans on System, Man and Cybernetics, 2004, 34(4): 1907-1916
2007, Vol. 20 
