Clustering in the membership embedding space

In several applications of data mining to high-dimensional data, clustering techniques developed for low-to-moderate sized problems obtain unsatisfactory results. This is an aspect of the curse of dimensionality issue. A traditional approach is based on representing the data in a suitable similarity space instead of the original high-dimensional attribute space. In this paper, we propose a solution to this problem using the projection of data onto a so-called membership embedding space obtained by using the memberships of data points on fuzzy sets centred on some prototypes. This approach can increase the efficiency of the popular fuzzy C-means method in the presence of high-dimensional datasets, as we show in an experimental comparison. We also present a constructive method for prototypes selection based on simulated annealing that is viable for semi-supervised clustering problems.