Exploiting Novel Properties of Space-Filling Curves for Data Analysis

Using space-filling curves to order multidimensional data has been found to be useful in a variety of application domains. This paper examines the space-filling curve induced ordering of multidimensional data that has been transformed using shape preserving transformations. It is demonstrated that, although the orderings are not invariant under these transformations, the probability of an ordering is dependent on the geometrical configuration of the multidimensional data. This novel property extends the potential applicability of space-filling curves and is demonstrated by constructing novel features for shape matching.