Fuzzy Subspace Clustering

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 [15] to attribute weighting fuzzy clustering [14]. In addition, by reformulating Gustafson–Kessel fuzzy clustering, a scheme for weighting and selecting principal axes can be obtained. While in [5] 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.