Estimating the number of clusters using a windowing technique

Clustering is the process of partitioning a set of patterns into disjoint and homogeneous meaningful groups (clusters). A fundamental and unresolved issue in cluster analysis is to determine how many clusters are present in a given set of patterns. In this paper, we present the z-windows clustering algorithm, which aims to address this problem using a windowing technique. Extensive empirical tests that illustrate the efficiency and the accuracy of the propsoed method are presented. The text was submitted by the authors in English. Basilis Boutsinas. Received his diploma in Computer Engineering and Informatics in 1991 from the University of Patras, Greece. He also conducted studies in Electronics Engineering at the Technical Education Institute of Piraeus, Greece, and Pedagogics at the Pedagogical Academy of Lamia, Greece. He received his PhD on Knowledge Representation from the University of Patras in 1997. He has been an assistant professor in the Department of Business Administration at the University of Patras since 2001. His primary research interests include data mining, business intelligence, knowledge representation techniques, nonmonotonic reasoning, and parallel AI. Dimitris K. Tasoulis received his diploma in Mathematics from the University of Patras, Greece, in 2000. He attained his MSc degree in 2004 from the postgraduate course “Mathematics of Computers and Decision Making” from which he was awarded a postgraduate fellowship. Currently, he is a PhD candidate in the same course. His research activities focus on data mining, clustering, neural networks, parallel algorithms, and evolutionary computation. He is coauthor of more than ten publications. Michael N. Vrahatis is with the Department of Mathematics at the University of Patras, Greece. He received the diploma and PhD degree in Mathematics from the University of Patras in 1978 and 1982, respectively. He was a visiting research fellow at the Department of Mathematics, Cornell University (1987–1988) and a visiting professor to the INFN (Istituto Nazionale di Fisica Nucleare), Bologna, Italy (1992, 1994, and 1998); the Department of Computer Science, Katholieke Universiteit Leuven, Belgium (1999); the Department of Ocean Engineering, Design Laboratory, MIT, Cambridge, MA, USA (2000); and the Collaborative Research Center “Computational Intelligence” (SFB 531) at the Department of Computer Science, University of Dortmund, Germany (2001). He was a visiting researcher at CERN (European Organization of Nuclear Research), Geneva, Switzerland (1992) and at INRIA (Institut National de Recherche en Informatique et en Automatique), France (1998, 2003, and 2004). He is the author of more than 250 publications (more than 110 of which are published in international journals) in his research areas, including computational mathematics, optimization, neural networks, evolutionary algorithms, and artificial intelligence. His research publications have received more than 600 citations. He has been a principal investigator of several research grants from the European Union, the Hellenic Ministry of Education and Religious Affairs, and the Hellenic Ministry of Industry, Energy, and Technology. He is among the founders of the “University of Patras Artificial Intelligence Research Center” (UPAIRC), established in 1997, where currently he serves as director. He is the founder of the Computational Intelligence Laboratory (CI Lab), established in 2004 at the Department of Mathematics of University of Patras, where currently he serves as director.