Validity Index and number of clusters
Clustering (or cluster analysis) has been used widely in pattern recognition, image processing, and data analysis. It aims to organize a collection of data items into c clusters, such that items within a cluster are more similar to each other than they are items in the other clusters. The number of clusters c is the most important parameter, in the sense that the remaining parameters have less influence on the resulting partition. To determine the best number of classes several methods were made, and are called validity index. This paper presents a new validity index for fuzzy clustering called a Modified Partition Coefficient And Exponential Separation (MPCAES) index. The efficiency of the proposed MPCAES index is compared with several popular validity indexes. More information about these indexes is acquired in series of numerical comparisons and also real data Iris.
Keywords: Fuzzy clustering, Fuzzy c-means, Validity index
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ABOUT THE AUTHORS
Mohamed Fadhel Saad
Mohamed Fadhel SAAD is currently a research staff member at Research Group on Intelligent Machines (REGIM). He is a Master Technologist to Higher Institute of Technological Studies of Gafsa. He received the Aggregation Specialty: Applied data processing to the management September 2000. In 2003 he started his Ph.D. studies at ENIS, University of Sfax, Tunisia. His main research interests are clustering, pattern recognition and fuzzy logics. He is a student member of the Institute of Electrical and Electronics Engineers (IEEE).
Adel M. Alimi
Adel M. Alimi received his Ph.D. degree in Electrical Engineering from Polytechnic school of Montréal, Canada, September 1995. He received this Habilitation To manage research (hdr) in Electric Engineering, option industrial computing, ENIS, University of Sfax, Tunisia. He is currently a Professor of industrial data processing at ENIS, University of Sfax, Tunisia since December 2006. His research interests include intelligent techniques, intelligent recognition of shapes and the manuscript, intelligent systems architecture and intelligent analysis of data. He has published prolifically in refereed journals, conferences, and workshops. He has served regularly in the organization committees and the program committees of many international conferences and workshops, and has also been a reviewer for the leading academic journals in his fields. He is a senior member of the Institute of Electrical and Electronics Engineers (IEEE), president of Tunisia Chapter of the IEEE Computer Society since 2010, advisor of the National Engineering School of Sfax Student Branch Chapter of the IEEE Robotics and Automation Society since 2010, advisor of the National Engineering School of Sfax Student Branch Chapter of the IEEE Computational Intelligence Society since 2010.
Mohamed Fadhel Saad
Mohamed Fadhel SAAD is currently a research staff member at Research Group on Intelligent Machines (REGIM). He is a Master Technologist to Higher Institute of Technological Studies of Gafsa. He received the Aggregation Specialty: Applied data processing to the management September 2000. In 2003 he started his Ph.D. studies at ENIS, University of Sfax, Tunisia. His main research interests are clustering, pattern recognition and fuzzy logics. He is a student member of the Institute of Electrical and Electronics Engineers (IEEE).
Adel M. Alimi
Adel M. Alimi received his Ph.D. degree in Electrical Engineering from Polytechnic school of Montréal, Canada, September 1995. He received this Habilitation To manage research (hdr) in Electric Engineering, option industrial computing, ENIS, University of Sfax, Tunisia. He is currently a Professor of industrial data processing at ENIS, University of Sfax, Tunisia since December 2006. His research interests include intelligent techniques, intelligent recognition of shapes and the manuscript, intelligent systems architecture and intelligent analysis of data. He has published prolifically in refereed journals, conferences, and workshops. He has served regularly in the organization committees and the program committees of many international conferences and workshops, and has also been a reviewer for the leading academic journals in his fields. He is a senior member of the Institute of Electrical and Electronics Engineers (IEEE), president of Tunisia Chapter of the IEEE Computer Society since 2010, advisor of the National Engineering School of Sfax Student Branch Chapter of the IEEE Robotics and Automation Society since 2010, advisor of the National Engineering School of Sfax Student Branch Chapter of the IEEE Computational Intelligence Society since 2010.
