Objective Functions for Fuzzy Clustering

Conference paper

DOI: 10.1007/978-3-642-32378-2_1

Part of the Studies in Computational Intelligence book series (SCI, volume 445)
Cite this paper as:
Borgelt C. (2013) Objective Functions for Fuzzy Clustering. In: Moewes C., Nürnberger A. (eds) Computational Intelligence in Intelligent Data Analysis. Studies in Computational Intelligence, vol 445. Springer, Berlin, Heidelberg


Fuzzy clustering comprises a family of prototype-based clustering methods that can be formulated as the problem of minimizing an objective function. These methods can be seen as “fuzzifications” of, for example, the classical c-means algorithm, which strives to minimize the sum of the (squared) distances between the data points and the cluster centers to which they are assigned. However, it is well known that in order to “fuzzify” such a crisp clustering approach, it is not enough to merely allow values from the unit interval for the variables encoding the assignments of the data points to the clusters (that is, for the elements of the partition matrix): the minimum is still obtained for a crisp data point assignment. As a consequence, additional means have to be employed in the objective function in order to obtain actual degrees of membership. This paper surveys the most common fuzzification means and examines and compares their properties.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Edificio de InvestigaciónEuropean Centre for Soft ComputingMieresSpain

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