Key points are not available for this paper at this time.
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.
Dimitris Achlioptas (Tue,) studied this question.