Generalized fuzzy c-means algorithms

  • Authors:
  • Nicolaos B. Karayiannis

  • Affiliations:
  • Department of Electrical and Computer Engineering, University of Houston, Houston, TX 77204-4793, USA

  • Venue:
  • Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
  • Year:
  • 2000

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper presents the development, testing and evaluation ofgeneralized fuzzy c-means (FCM) algorithms. The proposed algorithmsare developed by relaxing the constraints imposed on the membershipfunctions by the axiomatic requirements associated with fuzzyc-partitions. Clustering is formulated as a constrainedminimization problem, whose solution depends on the constraintsimposed on the membership functions. This minimization problemresults in a broad family of Generalized FCM algorithms, whichinclude the FCM algorithm as a special case. The Minimum FCM andGeometric FCM algorithms are also obtained as limiting cases ofGeneralized FCM algorithms. The proposed formulation assigns toeach feature vector a parameter that can be used to measure thecertainty of its assignment to various clusters. These parameterscan be used to identify outliers in the feature set. TheGeneralized FCM algorithms are evaluated and tested by experimentsinvolving the IRIS data set and a two-dimensional vowel dataset.