›› 2013, Vol. 28 ›› Issue (2): 311-321.doi: 10.1007/s11390-013-1331-7

Special Issue: Artificial Intelligence and Pattern Recognition

• Artificial Intelligence and Pattern Recognition • Previous Articles     Next Articles

Possibilistic Exponential Fuzzy Clustering

Kiatichai Treerattanapitak and Chuleerat Jaruskulchai   

  1. Department of Computer Science, Kasetsart University, 50 Ngamwongwan Rd., Jatuchak, Bangkok, Thailand
  • Received:2012-03-06 Revised:2012-11-02 Online:2013-03-05 Published:2013-03-05

Generally, abnormal points (noise and outliers) cause cluster analysis to produce low accuracy especially in fuzzy clustering. These data not only stay in clusters but also deviate the centroids from their true positions. Traditional fuzzy clustering like Fuzzy C-Means (FCM) always assigns data to all clusters which is not reasonable in some circumstances. By reformulating objective function in exponential equation, the algorithm aggressively selects data into the clusters. However noisy data and outliers cannot be properly handled by clustering process therefore they are forced to be included in a cluster because of a general probabilistic constraint that the sum of the membership degrees across all clusters is one. In order to improve this weakness, possibilistic approach relaxes this condition to improve membership assignment. Nevertheless, possibilistic clustering algorithms generally suffer from coincident clusters because their membership equations ignore the distance to other clusters. Although there are some possibilistic clustering approaches that do not generate coincident clusters, most of them require the right combination of multiple parameters for the algorithms to work. In this paper, we theoretically study Possibilistic Exponential Fuzzy Clustering (PXFCM) that integrates possibilistic approach with exponential fuzzy clustering. PXFCM has only one parameter and not only partitions the data but also filters noisy data or detects them as outliers. The comprehensive experiments show that PXFCM produces high accuracy in both clustering results and outlier detection without generating coincident problems.

[1] MacQueen J B. Some methods for classification and analy-sis of multivariate observations. In Proc. the 5th BerkeleySymp. Mathematical Statistics and Probability, June 21-July18, 1965 and Dec.27, 1965-Jan.7, 1966, Vol.1, pp.281-297.

[2] Dunn J C. A fuzzy relative of the ISODATA process and itsuse in detecting compact well-separated clusters. J. Cyber-netics., 1973, 3(3): 32-57.

[3] Bezdek J C. Pattern Recognition with Fuzzy Objective Func-tion Algoritms. New York: Plenum Press, 1993.

[4] Krishnapuram R, Keller J M. A possibilistic approach to clus-tering. IEEE Trans. Fuzzy Systems, 1993, 1(2): 98-110.

[5] Treerattanapitak K, Juruskulchai C. Exponential fuzzy C-means for collaborative filtering. Journal of Computer Sci-ence & Technology, 2012, 27(3): 567-576.

[6] Chandola V, Banerjee A, Kumar V. Anomaly detection: Asurvey. ACM Comput. Surveys, 2009, 41(3): Article No. 15.

[7] Treerattanapitak K, Juruskulchai C. Outlier detection withpossibilistic exponential fuzzy clustering. In Proc. the 8thFSKD, Jul. 2011, pp.453-457.

[8] Barni M, Cappellini V, Mecocci A. Comments on "A possi-bilistic approach to clustering". IEEE Trans. Fuzzy Systems,1996, 4(3): 393-396.

[9] Pal N R, Pal K, Bezdek J C. A mixed c-means clusteringmodel. In Proc. the 6th IEEE Int. Conf. Fuzzy Systems,Jul. 1997, pp.11-21.

[10] Pal N R, Pal K, Keller J M, Bezdek J C. A possibilistic fuzzyc-means clustering algorithm. IEEE Trans. Fuzzy Systems,2005, 13(4): 517-530.

[11] Wachs J, Shapira O, Stern H. A method to enhance the "Pos-sibilistic C-means with repulsion" algorithm based on clustervalidity index. In Proc. the 9th Word Conf. Soft Computingin Industry Application, Sept. 20-Oct. 8, 2004, pp.77-87.

[12] Yang M, Wu K. Unsupervised possibilistic clustering. J. Pat-tern Recognition, 2006, 39(1): 5-21.

[13] Wu X, Wu B, Sun J, Fu H. Unsupervised possibilistic fuzzyclustering. J. Info. and Comp. Sci., 2010, 7(5): 1075-1080.

[14] Hawkins S, He H, Williams G J et al. Outlier detection usingreplicator neural networks. In Proc. the 4th DaWaK, Sept.2002, pp.170-180.

[15] Davy M, Godsill S. Detection of abrupt spectral changes us-ing support vector machines, an application to audio signalsegmentation. In Proc. the 2002 IEEE Int. Conf. Acoustics,Speech, and Signal Processing, May. 2002, pp.1313-1316.

[16] Ramaswamy S, Rastogi R, Shim K. Efficient algorithms formining outliers from large data sets. In Proc. the 6th SIG-MOD Int. Conf. Management of Data, Jun. 2000, pp.427-438.

[17] Breunig M, Kriegel H, Ng R T et al. LOF: Identifying density-based local outliers. In Proc. the 6th ACM SIGMOD Int.Conf. Management of Data, Jun. 2000, pp.93-104.

[18] Ester M, Kriegel H P, Sander J, Xu X. A density-based algo-rithm for discovering clusters in large spatial databases withnoise. In Proc. the 2nd the KDD, Aug. 1996, pp.226-231.

[19] Tang C, Wang S, Xu W. New fuzzy c-means clustering modelbased on the data weighted approach. Data Knowledge En-gineering, 2010, 69(9): 881-900.

[20] Shahi A, Atan R B, Sulaiman M N. Detecting effectiveness ofoutliers and noisy data on fuzzy system using FCM. EuropeanJ. Sci. Research, 2009, 36(4): 627-638.

[21] He Z, Deng S, Xu X. An optimization model for outlier de-tection in categorical data. In Lecture Notes in ComputerScience 3644, Huang D S, Zhang X P, Huang G B (eds.),Springer, 2005, pp.400-409.

[22] Agovic A, Banerjee A, Ganguly A R, Protopopescu V.Anomaly detection in transportation corridors using manifoldembedding. In Proc. the 1st SensorKDD, Aug. 2007.

[23] Jin W, Tung K H, Han J. Mining top-n local outliers in largedatabases. In Proc. the 7th KDD, Aug. 2001, pp.293-298.

[24] Xue Z, Shang Y, Feng A. Semi-supervised outlier detectionbased on fuzzy rough C-means clustering. J. Mathematicsand Computers in Simulation, 2010, 80(9): 1911-1921.

[25] Xie X L, Beni G. A validity measure for fuzzy clustering.TPAMI, 1991, 13(8): 841-847.

[26] Kwon S H. Cluster validity index for fuzzy clustering. Elec-tronics Letters, 1998, 34(22): 2176-2177.

[27] Fukuyama Y, Sugeno M. A new method of choosing the num-ber of clusters for the fuzzy c-means method. In Proc. the5th Fuzzy Systems Symposium, Jun. 1989, pp.247-250.

[28] Gath I, Geva A B. Unsupervised optimal fuzzy clustering.Trans. Pattern Anal. Mach. Intell., 1989, 11(7): 773-781.

[29] Pakhira M K, Bandyopadhyay S, Maulik U. Validity indexfor crisp and fuzzy clusters. Pattern Recognition, 2004, 37(3):487-501.

[30] Wu K L, Yang M S. A cluster validity index for fuzzy cluster-ing. Pattern Recognition Lett., 2005, 26(9): 1275-1291.

[31] Aggarwal C C, Yu P S. Outlier detection for high dimensionaldata. In Proc. the 2001 ACM SIGMOD Int. Conf. Manage-ment of Data, May 2001, pp.37-46.

[32] Williums G J, Baster R A, He H et al. A comparative studyof RNN for outlier detection in data mining. In Proc. the2002 Int. Conf. Data Mining, Dec. 2002, pp.709-712.

[33] He Z, Xu X, Huang J Z, Deng S. A frequent pattern discov-ery method for outlier detection. In Proc. the 5th Int. Conf.Web-Age Info. Management, Jul. 2004, pp.726-732.

[34] He Z, Xu X, Deng S. Discovery cluster-based local outliers.Pattern Recognition Letters, 2003, 24(9/10): 1641-1650.
No related articles found!
Full text



[1] Jin Lan; Yang Yuanyuan;. A Modified Version of Chordal Ring[J]. , 1986, 1(3): 15 -32 .
[2] Fan Zhihua;. Vectorization for Loops with Three-Forked Jumps[J]. , 1988, 3(3): 186 -202 .
[3] Guo Qingping; Y. Paker;. Communication Analysis and Granularity Assessment for a Transputer-Based System[J]. , 1990, 5(4): 347 -362 .
[4] Zhou Yong; Tang Zesheng;. Constructing Isosurfaces from 3D Data Sets Taking Account of Depth Sorting of Polyhedra[J]. , 1994, 9(2): 117 -127 .
[5] Liao Lejian; Shi Zhongzhi;. Minimal Model Semantics for Sorted Constraint Representation[J]. , 1995, 10(5): 439 -446 .
[6] Zhao Yu; Zhang Qiong; Xiang Hui; Shi Jiaosing; He Zhijun;. A Simplified Model for Generating 3D Realistic Sound in the Multimedia and Virtual Reality Systems[J]. , 1996, 11(4): 461 -470 .
[7] Wang Yun; Gu Guanqun; Dui Jiyin;. Research on Protocol Migration[J]. , 1996, 11(6): 601 -606 .
[8] Cheng Qi; Zhu Hong;. MNP: A Class of NP Optimization Problems[J]. , 1997, 12(4): 306 -313 .
[9] Mi Thxi;. Constructive Sets in Computable Sets[J]. , 1997, 12(5): 425 -440 .
[10] CHEN Yangjun;. On the Arc Consistency Problem[J]. , 1999, 14(4): 298 -308 .

ISSN 1000-9000(Print)

CN 11-2296/TP

Editorial Board
Author Guidelines
Journal of Computer Science and Technology
Institute of Computing Technology, Chinese Academy of Sciences
P.O. Box 2704, Beijing 100190 P.R. China
E-mail: jcst@ict.ac.cn
  Copyright ©2015 JCST, All Rights Reserved