Fuzzy Entropy Based Fuzzy c-Means Clustering with Deterministic and Simulated Annealing Methods
Summary :
This article explains how to apply the deterministic annealing (DA) and simulated annealing (SA) methods to fuzzy entropy based fuzzy c-means clustering. By regularizing the fuzzy c-means method with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained, and, while optimizing its parameters by SA, the minimum of the Helmholtz free energy for fuzzy c-means clustering is searched by DA. Numerical experiments are performed and the obtained results indicate that this combinatorial algorithm of SA and DA can represent various cluster shapes and divide data more properly and stably than the standard single DA algorithm.
- Publication
- IEICE TRANSACTIONS on Information Vol.E92-D No.6 pp.1232-1239
- Publication Date
- 2009/06/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E92.D.1232
- Type of Manuscript
- PAPER
- Category
- Computation and Computational Models
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Makoto YASUDA, Takeshi FURUHASHI, "Fuzzy Entropy Based Fuzzy c-Means Clustering with Deterministic and Simulated Annealing Methods" in IEICE TRANSACTIONS on Information,
vol. E92-D, no. 6, pp. 1232-1239, June 2009, doi: 10.1587/transinf.E92.D.1232.
Abstract: This article explains how to apply the deterministic annealing (DA) and simulated annealing (SA) methods to fuzzy entropy based fuzzy c-means clustering. By regularizing the fuzzy c-means method with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained, and, while optimizing its parameters by SA, the minimum of the Helmholtz free energy for fuzzy c-means clustering is searched by DA. Numerical experiments are performed and the obtained results indicate that this combinatorial algorithm of SA and DA can represent various cluster shapes and divide data more properly and stably than the standard single DA algorithm.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E92.D.1232/_p
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@ARTICLE{e92-d_6_1232,
author={Makoto YASUDA, Takeshi FURUHASHI, },
journal={IEICE TRANSACTIONS on Information},
title={Fuzzy Entropy Based Fuzzy c-Means Clustering with Deterministic and Simulated Annealing Methods},
year={2009},
volume={E92-D},
number={6},
pages={1232-1239},
abstract={This article explains how to apply the deterministic annealing (DA) and simulated annealing (SA) methods to fuzzy entropy based fuzzy c-means clustering. By regularizing the fuzzy c-means method with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained, and, while optimizing its parameters by SA, the minimum of the Helmholtz free energy for fuzzy c-means clustering is searched by DA. Numerical experiments are performed and the obtained results indicate that this combinatorial algorithm of SA and DA can represent various cluster shapes and divide data more properly and stably than the standard single DA algorithm.},
keywords={},
doi={10.1587/transinf.E92.D.1232},
ISSN={1745-1361},
month={June},}
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TY - JOUR
TI - Fuzzy Entropy Based Fuzzy c-Means Clustering with Deterministic and Simulated Annealing Methods
T2 - IEICE TRANSACTIONS on Information
SP - 1232
EP - 1239
AU - Makoto YASUDA
AU - Takeshi FURUHASHI
PY - 2009
DO - 10.1587/transinf.E92.D.1232
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E92-D
IS - 6
JA - IEICE TRANSACTIONS on Information
Y1 - June 2009
AB - This article explains how to apply the deterministic annealing (DA) and simulated annealing (SA) methods to fuzzy entropy based fuzzy c-means clustering. By regularizing the fuzzy c-means method with fuzzy entropy, a membership function similar to the Fermi-Dirac distribution function, well known in statistical mechanics, is obtained, and, while optimizing its parameters by SA, the minimum of the Helmholtz free energy for fuzzy c-means clustering is searched by DA. Numerical experiments are performed and the obtained results indicate that this combinatorial algorithm of SA and DA can represent various cluster shapes and divide data more properly and stably than the standard single DA algorithm.
ER -
English
