Winkler, Roland and Klawonn, Frank and Kruse, Rudolf (2011) Fuzzy clustering with polynomial fuzzifier function in connection with m-estimators. Applied and Computational Mathematics, 10 (1), pp. 146-163. Azerbaijan National Academy of Sciences. ISSN 1683-3511.
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Official URL: http://www.science.az/acm/absV10N1/titul_10_1_2010_son.htm
Abstract
Fuzzy clustering approaches use membership values or weights to assign data to clusters. In standard fuzzy clustering, a parameter called fuzzifier is introduced which leads to certain disadvantages. That can be overcome by a more general approach replacing the usual fuzzifier by more general functions such as polynomial functions. Very similar to various forms of fuzzy clustering algorithms with just one prototype are M-estimators. The fuzzy clustering algorithm with polynomial fuzzifier function is used to define a new M-estimator. It is demonstrated that polynomial fuzzifier functions for M-estimators have better robustness properties than the usual fuzzifier. The special case of one prototype of fuzzy clustering algorithms can be reformulated as M-estimator. In this extend, some M-estimators can be considered to be special cases of fuzzy clustering algorithms. This is not the case for M-estimators that can not be applied with multiple prototypes. However, it is possible to extend an M-estimator in such a way that it provides an update mechanism similar to fuzzy clustering for multiple prototypes.
Item URL in elib: | https://elib.dlr.de/63936/ | ||||||||||||
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Document Type: | Article | ||||||||||||
Additional Information: | Scopus referiert: Begutachtungsstatus auf referiert in Journal gesetzt. | ||||||||||||
Title: | Fuzzy clustering with polynomial fuzzifier function in connection with m-estimators | ||||||||||||
Authors: |
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Date: | 2011 | ||||||||||||
Journal or Publication Title: | Applied and Computational Mathematics | ||||||||||||
Refereed publication: | Yes | ||||||||||||
Open Access: | No | ||||||||||||
Gold Open Access: | No | ||||||||||||
In SCOPUS: | Yes | ||||||||||||
In ISI Web of Science: | Yes | ||||||||||||
Volume: | 10 | ||||||||||||
Page Range: | pp. 146-163 | ||||||||||||
Publisher: | Azerbaijan National Academy of Sciences | ||||||||||||
Series Name: | International Journal of Applied and Computational Mathematics | ||||||||||||
ISSN: | 1683-3511 | ||||||||||||
Status: | Published | ||||||||||||
Keywords: | fuzzy c-means, M-estimators, polynomial fuzzifier function, robust statistics, noise clustering, multiple prototypes, robust statistics | ||||||||||||
HGF - Research field: | Aeronautics, Space and Transport | ||||||||||||
HGF - Program: | Aeronautics | ||||||||||||
HGF - Program Themes: | ATM and Operation (old) | ||||||||||||
DLR - Research area: | Aeronautics | ||||||||||||
DLR - Program: | L AO - Air Traffic Management and Operation | ||||||||||||
DLR - Research theme (Project): | L - Effiziente Flugführung und Flugbetrieb (old) | ||||||||||||
Location: | Braunschweig | ||||||||||||
Institutes and Institutions: | Institute of Flight Guidance > Air traffic systems | ||||||||||||
Deposited By: | Winkler, Roland | ||||||||||||
Deposited On: | 19 Apr 2010 15:24 | ||||||||||||
Last Modified: | 06 Sep 2019 15:21 |
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