Analytical and numerical evaluation of the suppressed fuzzy c-means algorithm: a study on the competition in c-means clustering models

  • Authors:

  • László Szilágyi;Sándor M. Szilágyi;Zoltán Benyó

  • Affiliations:

  • Sapientia Univ. of Transylvania, Fac. of Tech. and Human Sci., Corunca, Romania and Budapest Univ. of Technol. and Econ., Dept. of Cntrl. Eng. and Info. Technol., Budapest, Hungary;Sapientia University of Transylvania, Faculty of Technical and Human Sciences, Târgu Mureş, Şoseaua Sighişoarei 1/C, 547367, Corunca, Romania;Budapest University of Technology and Economics, Department of Control Engineering and Information Technology, Magyar tudósok krt. 2, 1117, Budapest, Hungary

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special Issue on Soft Computing in Decision Modeling; Guest Editors: Vicenc Torra, Yasuo Narukawa
  • Year:
  • 2009

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Abstract

Suppressed fuzzy c-means (s-FCM) clustering was introduced in Fan et al. (Pattern Recogn Lett 24:1607–1612, 2003) with the intention of combining the higher speed of hard c-means (HCM) clustering with the better classification properties of fuzzy c-means (FCM) algorithm. The authors modified the FCM iteration to create a competition among clusters: lower degrees of memberships were diminished according to a previously set suppression rate, while the largest fuzzy membership grew by swallowing all the suppressed parts of the small ones. Suppressing the FCM algorithm was found successful in the terms of accuracy and working time, but the authors failed to answer a series of important questions. In this paper, we clarify the view upon the optimality and the competitive behavior of s-FCM via analytical computations and numerical analysis. A quasi competitive learning rate (QLR) is introduced first, in order to quantify the effect of suppression. As the investigation of s-FCM’s optimality did not provide a precise result, an alternative, optimally suppressed FCM (Os-FCM) algorithm is proposed as a hybridization of FCM and HCM. Both the suppressed and optimally suppressed FCM algorithms underwent the same analytical and numerical evaluations, their properties were analyzed using the QLR. We found the newly introduced Os-FCM algorithm quicker than s-FCM at any nontrivial suppression level. Os-FCM should also be favored because of its guaranteed optimality.