Abstract—In this paper we propose to combine two clustering approaches, namely fuzzy and possibilistic c-means. While fuzzy c-means algorithm finds suitable clusters for groups of data points, obtained memberships of data, however, encounters a major deficiency caused by misinterpretation of membership values of data points. Therefore, membership values cannot correctly interpret compatibility or degree to which data points belong to clusters. As a result, noisy data will be misinterpreted by incorrect memberships assigned, as sum of memberships of each noisy data to all clusters is constrained to be equal to 1. To overcome this, a possibilistic approach has been proposed which removes this constraint. It has, however, caused another shortcoming as cluster centers converge to an identical point. Therefore, possibilities cannot correctly interpret the degrees of compatibilities. To correct this problem, a number of works have been carried out which all try to change possibilistic objective function proposed by Krishnapuram and James M. Keller. In this work, a hierarchical approach has been proposed based on properties of both fuzzy and possibilistic approaches to overcome this deficiency. Sensitivities of both methods have been studied together with analyzing results obtained by both methods. Superiority of the proposed method as opposed to conventional possibilistic c-means is shown to be conspicuous.
Index Terms—Hierarchical clustering, possibilistic, fuzzy c-means, sensitivity analysis
Mehdi Salkhordeh Haghighi is with the Computer Department, Ferdowsi University of Mashhad, Iran, (haghighi@ieee.org)
Hadi Sadoghi Yazdi is with the Computer Department, Ferdowsi University of Mashhad, Iran, (sadoghi@sttu.ac.ir)
Abedin Vahedian is with the Computer Department, Ferdowsi University of Mashhad, Iran, (vahedian@um.ac.ir)
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Cite: Mehdi Salkhordeh Haghighi, Hadi Sadoghi Yazdi, Abedin Vahedian, "A Hierarchical Possibilistic Clustering,"
International Journal of Computer Theory and Engineering vol. 1, no. 4, pp. 465-472, 2009.
