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Fuzzy clustering with polynomial fuzzifier function in connection with m-estimators

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


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/
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
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Winkler, Rolandroland.winkler (at) dlr.deUNSPECIFIED
Klawonn, Frankf.klawonn (at) ostfalia.deUNSPECIFIED
Kruse, Rudolfkruse (at) iws.cs.uni-magdeburg.deUNSPECIFIED
Journal or Publication Title:Applied and Computational Mathematics
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In ISI Web of Science:Yes
Page Range:pp. 146-163
Publisher:Azerbaijan National Academy of Sciences
Series Name:International Journal of Applied and Computational Mathematics
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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