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Fuzzy C-Means in High Dimensional Spaces

Roland Winkler, Frank Klawonn, Rudolf Kruse

Source Title: International Journal of Fuzzy System Applications (IJFSA)1(1)

ISSN: 2156-177X|EISSN: 2156-1761|EISBN13: 9781613507056|DOI: 10.4018/ijfsa.2011010101

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MLA

Winkler, Roland, et al. "Fuzzy C-Means in High Dimensional Spaces." IJFSA vol.1, no.1 2011: pp.1-16. http://doi.org/10.4018/ijfsa.2011010101

APA

Winkler, R., Klawonn, F., & Kruse, R. (2011). Fuzzy C-Means in High Dimensional Spaces. International Journal of Fuzzy System Applications (IJFSA), 1(1), 1-16. http://doi.org/10.4018/ijfsa.2011010101

Chicago

Winkler, Roland, Frank Klawonn, and Rudolf Kruse. "Fuzzy C-Means in High Dimensional Spaces," International Journal of Fuzzy System Applications (IJFSA) 1, no.1: 1-16. http://doi.org/10.4018/ijfsa.2011010101

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Abstract

High dimensions have a devastating effect on the FCM algorithm and similar algorithms. One effect is that the prototypes run into the centre of gravity of the entire data set. The objective function must have a local minimum in the centre of gravity that causes FCM’s behaviour. In this paper, examine this problem. This paper answers the following questions: How many dimensions are necessary to cause an ill behaviour of FCM? How does the number of prototypes influence the 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 behaviour of the FCM algorithm and answer the above questions, the authors examine the values of the objective function and develop three test environments that consist of artificially generated data sets to provide a controlled environment. The paper concludes that FCM can only be applied successfully in high dimensions if the prototypes are initialized very close to the cluster centres.

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Fuzzy C-Means in High Dimensional Spaces

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