Abstract
Approximate retrieval of multi-dimensional data, such as documents, digital images, and audio clips, is a method to get objects within some dissimilarity from a given object. We assume a metric space containing objects, where distance is used to measure dissimilarity. In Euclidean metric spaces, approximate retrieval is easily and efficiently realized by a spatial indexing/access method R-tree. First, we consider objects in discrete L 1 (or Manhattan distance) metric space, and present embedding method into Euclidean space for them. Then, 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 Lā metric space, as well as 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 Lā metric space, where a hyper-sphere is a hyper-cube in the usual sense. Finally we show that the distance function itself, which is simpler than H-Map, can be used as a dimension reduction mapping for any metric space.
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Shinohara, T., Ishizaka, H. (2002). On Dimension Reduction Mappings for Approximate Retrieval of Multi-dimensional Data. In: Arikawa, S., Shinohara, A. (eds) Progress in Discovery Science. Lecture Notes in Computer Science(), vol 2281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45884-0_14
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DOI: https://doi.org/10.1007/3-540-45884-0_14
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