Fuzzy Subspace Clustering

Abstract

In clustering we often face the situation that only a subset of the available attributes is relevant for forming clusters, even though this may not be known beforehand. In such cases it is desirable to have a clustering algorithm that automatically weights attributes or even selects a proper subset. In this paper I study such an approach for fuzzy clustering, which is based on the idea to transfer an alternative to the fuzzifier (Klawonn and Hoppner, What is fuzzy about fuzzy clustering? Understanding and improving the concept of the fuzzifier, In: Proc. 5th Int. Symp. on Intelligent Data Analysis, 254–264, Springer, Berlin, 2003) to attribute weighting fuzzy clustering (Keller and Klawonn, Int J Uncertain Fuzziness Knowl Based Syst 8:735–746, 2000). In addition, by reformulating Gustafson–Kessel fuzzy clustering, a scheme for weighting and selecting principal axes can be obtained. While in Borgelt (Feature weighting and feature selection in fuzzy clustering, In: Proc. 17th IEEE Int. Conf. on Fuzzy Systems, IEEE Press, Piscataway, NJ, 2008) I already presented such an approach for a global selection of attributes and principal axes, this paper extends it to a cluster-specific selection, thus arriving at a fuzzy subspace clustering algorithm (Parsons, Haque, and Liu, 2004).