Fractals for secondary key retrieval
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The R*-tree: an efficient and robust access method for points and rectangles
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
CIKM '93 Proceedings of the second international conference on Information and knowledge management
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
H-Map: A Dimension Reduction Mapping for Approximate Retrieval of Multi-dimensional Data
DS '99 Proceedings of the Second International Conference on Discovery Science
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High-dimensional data, such as documents, digital images, and audio clips, can be considered as spatial objects, which induce a metric space where the metric can be used to measure dissimilarities between objects. We propose a method for retrieving objects within some distance from a given object by utilizing a spatial indexing/access method R-tree. Since R-tree usually assumes a Euclidean metric, we have to embed objects into a Euclidean space. However, some of naturally defined distance measures, such as L1 distance (or Manhattan distance), cannot be embedded into any Euclidean space. First, we prove that objects in discrete L1 metric space can be embedded into vertices of a unit hypercube when the square root of L1 distance is used as the distance. To take fully advantage of R-tree spatial indexing, we have to project objects into space of relatively lower dimension. We adopt FastMap by Faloutsos and Lin to reduce the dimension of object space. The range corresponding to a query (Q, h) for retrieving objects within distance h from a object Q is naturally considered as a hyper-sphere even after FastMap projection, which is an orthogonal projection in Euclidean space. However, it is turned out that the query range is contracted into a smaller hyper-box than the hyper-sphere by applying FastMap to objects embedded in the above mentioned way. Finally, we give a brief summary of experiments in applying our method to Japanese chess boards.