From Average Embeddings To Nearest Neighbor Search

05/12/2021

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by   Alexandr Andoni, et al.

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In this note, we show that one can use average embeddings, introduced recently in [Naor'20, arXiv:1905.01280], to obtain efficient algorithms for approximate nearest neighbor search. In particular, a metric X embeds into ℓ_2 on average, with distortion D, if, for any distribution μ on X, the embedding is D Lipschitz and the (square of) distance does not decrease on average (wrt μ). In particular existence of such an embedding (assuming it is efficient) implies a O(D^3) approximate nearest neighbor search under X. This can be seen as a strengthening of the classic (bi-Lipschitz) embedding approach to nearest neighbor search, and is another application of data-dependent hashing paradigm.