The International Arab Journal of Information Technology (IAJIT)

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2008 Optimal Fuzzy Clustering in Overlapping Clusters

, Khadija Slaoui 3,


[1] Ammor O., Lachkar A., Slaoui K., and Rais N., New Efficient Approach to Determine the Optimal Number of Clusters in Overlapping Cases, in P roceedings of the IEEE on Advances in Cybernetic Systems , UK, pp. 26-31, 2006.

[2] Anderson E., The IRISes of the Gaspe Peninsula, Bulletin of the American Iris Society , vol. 59, no. 1935, pp. 2-5, 1959.

[3] Bezdek J., Cluster Validity with Fuzzy Sets, Cybernetics and Systems , vol. 3, no. 3, pp. 58-72, 1975.

[4] Cembrzynski T., Banc D'essai Sur Les Boules Polonaises, Des Trois Crit res de D cision Utilis s Dans La Proc dure de Classification, MNDOPT Pour Choisir un Nombre de Classes, RR-0784 Rapport de recherche de l'INRIA, 1986.

[5] Fukuyama Y. and Sugeno M., A New Method of Choosing the Number of Clusters for the Fuzzy C-Means Method, in Proceedings of the 5 th Fuzzy Systems Symposium , Japan, pp. 247-250, 1989.

[6] Halkidi M., Batistakis Y. , and Vazirgiannis M., Quality Scheme Assessment in the Clustering Process, in Proceedings of the 4 th European Conference on Principles of Data Mining and Knowledge Discovery , London, pp. 265-276, 2000.

[7] Halkidi M. and Vazirgiannis M., Clustering Validity Assessment: Finding the Optimal Partitioning of a Data Set, in Proceedings of 1 st IEEE International Conference on Data Mining (ICDM'2001) , USA, pp. 187-194, 2001.

[8] Halkidi M., Batistakis Y., and Vazirgiannis M., Clustering Validity Checking Methods: Part II, Special Interest Group on Management of Data ( SIGMOD) , vol. 31, no. 3, pp. 19-27, 2002.

[9] Jain A., Murty M., and Flynn P., Data Clustering a Review, ACM Computing Surveys , vol. 31, no. 3 , pp. 264-323, 1999.

[10] Kim D., Park Y., and Park D., A Novel Validity Index for Determination of the Optimal Number of Clusters, IEICE Transactions on Information System , vol. D-E84, no. 2, pp. 281-285, 2001.

[11] Kim D., Kwang A, Lee H. , and Lee D., On Cluster Validity Index for Estimation of the Optimal Number of Fuzzy Clusters, Pattern Recognition , v ol. 37, pp. 2009-2025, 2004.

[12] Kwon S., Cluster Validity Index for Fuzzy Clustering, Pattern Recognition Letters , vol. 34, no. 22, pp. 2176-2177, 1998.

[13] Lachkar A. , Benslimane R., D Orazio L., and Martuscelli E., A System for Textile Design Patterns Retrieval Part 1: Design Patterns Extraction by Adaptive and Efficient Color Image Segmentation Method, Journal of the Textile Institute , no . 10.1533. joti, 124r1, 2005.

[14] Liu J. and Yang Y., Multiresolution Color Image Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence , vol. 16, no. 7, pp. 689-700, 1994.

[15] Liu X. and Beni G., A Validity Measure for Fuzzy Clustering, IEEE Transactions on Pattern Analysis Machine Intelligence , vol. 13, no. 8, pp. 841-847, 1991.

[16] Sharma S., Applied Multivariate Techniques , John Wiley and Sons, 1996.

[17] Trivedi M. and Bezdek J., Low-Level Segmentation of Aerial Images with Fuzzy Clustering, IEEE Transactions on Systems, Man and Cybernetics , vol. 16, no. 4, pp. 589-598, 1986. Ouafae Ammor is a professor in the Department of Mathematics at Faculty of Sciences and Technology of Fes, Morocco. She has obteined her Master s degree in statistics from Polytechnique school of Montreal, Canada. Her research focuses on the clustering in data analysis, pattern recognition, colour image segmentation , Optimal Fuzzy Clustering in Overlapping Clusters 152 medical image processing, fuzzy logic and spatial data analysis. Abdelmonaime Lachkar received the Master degree in automatic and systems analysis in 1999, and his PhD degree from the USMBA, Morocco in 2004. In computer sciences. He is associate professor in Computer Sciences in ESTM at Moulay Ismail University-Morocco. His current research interests include image indexing and retrieval, shape representation, indexing and retrieval in large shapes databases, colour image segmentation, unsupervised clustering, cluster validity index, pattern recognition, arabic and latin handwritten recognition, document clustering and categorisation, medical image processing, image compression and watermarking. Khadija Slaoui is a professor in the Department of Physics at Faculty of Sciences Dhar Mehraz of Fes, Morocco. She has obteined her Master s in image processing at Polytechnique Institute of Toulouse, France, and PHD in data analysis at University Sidi Mohammed Ben Abdellah. Her research focuses on signal processing, clustering, and images processing. Noureddine Rais is full professor at the University of Fez in Morocco. He has a PhD in mathematical statistics from the University of Montreal, Canada and a 3 rd Cycle Doctorate in Statistics and Mathematical Models from University of Paris-sud, Orsay, France. His current research interests covers bootstrap, spatial data, survey sampling, decision theory, data analysis, data mining, experimental design, linear models and analysis of variance, with applications in many fields, specially statistical processing control, arabic handwritten recognition, and medical image processing.