H-Map: A Dimension Reduction Mapping for Approximate Retrieval of Multi-dimensional Data

Abstract

We propose a projection mapping H-Map to reduce dimensionality of multi-dimensional data, which can be applied to any metric space such as L ₁ or L _∞ metric space, as well as Euclidean space. We investigate properties of H-Map and show its usefulness for spatial indexing, by comparison with a traditional Karhunen-Loéve (K-L) trans-formation, which can be applied only to Euclidean space. H-Map does not require coordinates of data unlike K-L transformation. H-Map has an advantage in using spatial indexing such as R-tree because it is a continuous mapping from a metric space to an L _∞ metric space, where a hyper-sphere is a hyper-cube in the usual sense.