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On Utilization of K-Means for Determination of q-Parameter for Tsallis-Entropy-Maximized-FCM
- Source :
- Journal of Software Engineering and Applications. 10:605-624
- Publication Year :
- 2017
- Publisher :
- Scientific Research Publishing, Inc., 2017.
-
Abstract
- In this paper, we consider a fuzzy c-means (FCM) clustering algorithm combined with the deterministic annealing method and the Tsallis entropy maximization. The Tsallis entropy is a q-parameter extension of the Shannon entropy. By maximizing the Tsallis entropy within the framework of FCM, membership functions similar to statistical mechanical distribution functions can be derived. One of the major considerations when using this method is how to determine appropriate q values and the highest annealing temperature, Thigh , for a given data set. Accordingly, in this paper, a method for determining these values simultaneously without introducing any additional parameters is presented. In our approach, the membership function is approximated by a series of expansion methods and the K-means clustering algorithm is utilized as a preprocessing step to estimate a radius of each data distribution. The results of experiments indicate that the proposed method is effective and both q and Thigh can be determined automatically and algebraically from a given data set.
- Subjects :
- 0209 industrial biotechnology
Mathematical optimization
Shannon's source coding theorem
Principle of maximum entropy
Tsallis entropy
02 engineering and technology
Joint entropy
Rényi entropy
020901 industrial engineering & automation
Maximum entropy probability distribution
0202 electrical engineering, electronic engineering, information engineering
Applied mathematics
020201 artificial intelligence & image processing
Entropy maximization
Entropy rate
Mathematics
Subjects
Details
- ISSN :
- 19453124 and 19453116
- Volume :
- 10
- Database :
- OpenAIRE
- Journal :
- Journal of Software Engineering and Applications
- Accession number :
- edsair.doi...........6d35f3771a81c2d32dca78ece07ef596