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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
computer science
Fuzzy c-means: Optimality of solutions and effective termination of the algorithm
Pattern Recognition, Volume 19, No. 6, Year 1986
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Description
In this paper, the solutions produced by the fuzzy c-means algorithm for a general class of problems are examined and a method to test for the local optimality of such solutions is established. An equivalent mathematical program is defined for the c-means problem utilizing a generalized norm, then the properties of the resulting optimization problem are investigated. It is shown that the gradient of the resulting objective function at the solution produced by the c-means algorithm in this case takes a special structure which can be used in terminating the algorithm. Moreover, the local optimality of the solution obtained is checked utilizing the Hessian of the criterion function. The solution is a local minimum point if the Hessian matrix at this point is positive semidefinite. Simple rules are proposed to help in checking the definiteness of the matrix. © 1986.
Authors & Co-Authors
Ismail, Mohamed A.
Canada, Windsor
University of Windsor
Selim, Shokri Z.
Saudi Arabia, Dhahran
King Fahd University of Petroleum and Minerals
Statistics
Citations: 65
Authors: 2
Affiliations: 2
Identifiers
Doi:
10.1016/0031-3203(86)90048-8
ISSN:
00313203