Abstract
The goal of this paper is to further investigate the extreme behaviour of the fuzzy clustering proportional membership model (FCPM) in contrast to the central tendency of fuzzy c-means (FCM). A data set from the field of psychiatry has been used for the experimental study, where the cluster prototypes are indeed extreme, expressing the concept of ‘ideal type’. While augmenting the original data set with patients bearing less severe syndromes, it is shown that the prototypes found by FCM are changed towards the more moderate characteristics of the data, in contrast with the almost unchanged prototypes found by FCPM, highlighting its suitability to model the concept of ‘ideal type’.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nascimento, S., Mirkin, B., Moura-Pires, F.: Multiple Prototypes Model for Fuzzy Clustering. In Kok, J., Hand, D. and Berthold, M., (eds.), Advances in Intelligent Data Analysis. Third International Symposium, (IDA’99), Lecture Notes in Computer Science, 1642, Springer-Verlag. (1999) 269–279
Nascimento, S., Mirkin, B., Moura-Pires, F.: A Fuzzy Clustering Model of Data with Proportional Membership. The 19th International Conference of the North American Fuzzy Information Processing Society (NAFIPS 2000). IEEE (2000) 261–266
Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)
Bezdek, J., Keller, J., Krishnapuram, R., Pal, T.: Fuzzy Models and Algorithms for Pattern Recognition and Image Processing. Kluwer Academic Publishers (1999)
Höppner, F., Klawonn, F., Kruse, R., Runkler, T.: Fuzzy Cluster Analysis. John Wiley and Sons (1999)
Mirkin, B.: Mathematical Classification and Clustering. Kluwer Academic Publishers (1996)
Mirkin, B.: Concept Learning and Feature Selection Based on Square-Error Clustering. In Machine Learning, 25(1) (1999) 25–40
Polyak, B.: Introduction to Optimization. Optimization Software, Inc., New York (1987)
Bertsekas, D.: Nonlinear Programming. Athena Scientific (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nascimento, S., Mirkin, B., Moura-Pires, F. (2001). Proportional Membership in Fuzzy Clustering as a Model of Ideal Types. In: Brazdil, P., Jorge, A. (eds) Progress in Artificial Intelligence. EPIA 2001. Lecture Notes in Computer Science(), vol 2258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45329-6_9
Download citation
DOI: https://doi.org/10.1007/3-540-45329-6_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43030-8
Online ISBN: 978-3-540-45329-1
eBook Packages: Springer Book Archive