Locality-sensitive Hashing In Function Spaces

Shand Will, Becker Stephen. Arxiv 2020

[Paper]    
ARXIV Independent LSH

We discuss the problem of performing similarity search over function spaces. To perform search over such spaces in a reasonable amount of time, we use {\it locality-sensitive hashing} (LSH). We present two methods that allow LSH functions on \(\mathbb{R}^N\) to be extended to \(L^p\) spaces: one using function approximation in an orthonormal basis, and another using (quasi-)Monte Carlo-style techniques. We use the presented hashing schemes to construct an LSH family for Wasserstein distance over one-dimensional, continuous probability distributions.

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