Abstract

A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space | where k is logarithmic in n and independent of d | so that all pairwise distances are maintained within an arbitrarily small factor. All known constructions of such embeddings involve projecting the n points onto a random k-dimensional hyperplane. We give a novel construction of the embedding, suitable for database applications, which amounts to computing a simple aggregate over k random attribute partitions.

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