Clustering in Fuzzy Subspaces

Abstract: Some data sets contain data clusters not in all dimension, but in subspaces. Known algo-rithms select attributes and identify clusters in subspaces. The paper presents a novel algorithm for subspace fuzzy clustering. Each data example has fuzzy membership to the cluster. Each cluster is defined in a certain subspace, but the the membership of the descriptors of the cluster to the subspace (called descriptor weight) is fuzzy (from interval [0, 1]) – the descriptors of the cluster can have partial membership to a subspace the cluster is defined in. Thus the clusters are fuzzy defined in their subspaces. The clusters are defined by their centre, fuzziness and weights of descriptors. The clustering algorithm is based on minimizing of criterion function. The paper is accompanied by the experimental results of clustering. This approach can be used for partition of input domain in extraction rule base for neuro-fuzzy systems