Fuzzy Classification Function of Standard Fuzzy c-Means Algorithm for Data with Tolerance Using Kernel Function

  • Authors:

  • Yuchi Kanzawa;Yasunori Endo;Sadaaki Miyamoto

  • Affiliations:

  • Shibaura Institute of Technology, Tokyo, Japan 135-8548;University of Tsukuba, Tsukuba, Japan 305-8573;University of Tsukuba, Tsukuba, Japan 305-8573

  • Venue:
  • MDAI '08 Sabadell Proceedings of the 5th International Conference on Modeling Decisions for Artificial Intelligence
  • Year:
  • 2008

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this paper, the fuzzy classification functions of the standard fuzzy c-means for data with tolerance using kernel functions are proposed.First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the standard fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.