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Fuzzy c-means in high dimensional spaces

Winkler, Roland and Klawonn, Frank and Kruse, Rudolf (2010) Fuzzy c-means in high dimensional spaces. International Journal of Fuzzy System Applications, 11. TAIWAN FUZZY SYSTEMS ASSOCIATION. ISSN 2156-177X.

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Official URL: http://www.ijfs.org.tw/

Abstract

High dimensions seem to have a devastating effect on the FCM algorithm and alike. One of these effects is that the prototypes tend to run into the centre of gravity of the entire data set. Obviously, the objective function must have a local minimum in the centre of gravity that causes FCM to its ill behaviour. In this paper, we concentrate on this problem rather than on new algorithms. We answer the following questions: How many dimensions are at least necessary to cause an ill behaviour of FCM? How does the number of prototypes influence the ill behaviour? Why has the objective function a local minimum in the centre of gravity? How must FCM be initialised to avoid the local minima in the centre of gravity? To understand the ill behaviour of the FCM algorithm and to answer the above questions, we take a closer look at the values of the objective function. We develop three test environments that consist of artificially generated data sets to provide a controlled environment. Finally, we conclude that FCM can only be applied successfully in high dimensions, if the prototypes are initialized very close to the cluster centres.

Document Type:Article
Title:Fuzzy c-means in high dimensional spaces
Authors:
AuthorsInstitution or Email of Authors
Winkler, Rolandroland.winkler@dlr.de
Klawonn, Frankf.klawonn@ostfalia.de
Kruse, Rudolfkruse@iws.cs.uni-magdeburg.de
Date:30 June 2010
Journal or Publication Title:International Journal of Fuzzy System Applications
Refereed publication:Yes
In SCOPUS:No
In ISI Web of Science:No
Volume:11
Publisher:TAIWAN FUZZY SYSTEMS ASSOCIATION
ISSN:2156-177X
Status:Published
Keywords:curse of dimensionality, fuzzy c-means, fuzzy clustering
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Aeronautics
HGF - Program Themes:ATM and Operation
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 Control > Air traffic systems
Deposited By: Roland Winkler
Deposited On:21 Jun 2010 09:11
Last Modified:07 Feb 2013 19:42

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