Density of closed balls in real-valued and autometrized boolean spaces for clustering applications

Abstract

The use of real-valued distances between bit vectors is customary in clustering applications. However, there is another, rarely used, kind of distances on bit vector spaces: the autometrized Boolean-valued distances, taking values in the same Boolean algebra, instead of. In this paper we use the topological concept of closed ball to define density in regions of the bit vector space and then introduce two algorithms to compare these different sorts of distances. A few, initial experiments using public databases, are consistent with the hypothesis that Boolean distances can yield a better classification, but more experiments are necessary to confirm it. © 2008 Springer Berlin Heidelberg.