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

Authors:
Takeshi Shinohara;Jianping Chen;Hiroki Ishizaka
Affiliations:
-;-;-
Venue:
DS '99 Proceedings of the Second International Conference on Discovery Science
Year:
1999

Citing 4
Cited 1

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DS '98 Proceedings of the First International Conference on Discovery Science

On Dimension Reduction Mappings for Approximate Retrieval of Multi-dimensional Data

Progress in Discovery Science, Final Report of the Japanese Discovery Science Project

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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 L1 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) transformation, 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.