Exploiting Novel Properties of Space-Filling Curves for Data Analysis

Abstract

Abstract. 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.

A Framework for Interpolating Scattered Data Using Space-Filling Curves

“…The transformation is in fact a composite, comprising a translation, a rotation, a reflection (with probability 0.5) and a scaling. Details of the embedding can found in [16], the maximum scale factor in this study is 10. For reasons of computational simplicity the region of interest, i.e.…”

“…. , e η be identically and independently drawn legitimate transformations, further details for the sampling regime can be found in [16]. The aggregated interpolated value for the query site q j is simply the average interpolated value, i.e.f…”

“…This property was then used to construct novel shape descriptors for shape matching. The concern of this paper is to use the approach detailed in [16] for spatial interpolation. The essential idea is to transform the data-sites and query points using a shape preserving transformation and then map them onto a space-filling curve, where a simple interpolation scheme is used to impute the value at each query point.…”