The range of the value for the fuzzifier of the fuzzy c-means algorithm

  • Authors:

  • Ming Huang;Zhixun Xia;Hongbo Wang;Qinghua Zeng;Qian Wang

  • Affiliations:

  • Science and Technology on Scramjet Laboratory, National University of Defense Technology, Hunan, Changsha 410073, China and Xi'an Satellite Control Center, Shaanxi, Xi'an 710043, China;Science and Technology on Scramjet Laboratory, National University of Defense Technology, Hunan, Changsha 410073, China;Science and Technology on Scramjet Laboratory, National University of Defense Technology, Hunan, Changsha 410073, China;Science and Technology on Scramjet Laboratory, National University of Defense Technology, Hunan, Changsha 410073, China;Northwest Institute of Nuclear Technology, Shaanxi, Xi'an 710024, China

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2012

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Abstract

The fuzzy c-means algorithm (FCM) is a widely used clustering algorithm. It is well known that the fuzzifier, m, which is also called fuzzy weighting exponent, has a significant impact on the performance of the FCM. Most of the researches have shown that there exists an effective range of the value for m. However, since the method adopted by researchers is mainly experimental or empirical, it is still an open problem how to select an appropriate fuzzifier m in theory when implementing the FCM. In this paper, we propose a theoretical approach to determine the range of the value of m. This approach utilizes the behavior of membership function on two data points, based on which we reveal the partial relationship between the fuzzifier m and the dataset structure.