# Locality-sensitive hashing in function spaces

@article{Shand2020LocalitysensitiveHI, title={Locality-sensitive hashing in function spaces}, author={Will Shand and Stephen Becker}, journal={ArXiv}, year={2020}, volume={abs/2002.03909} }

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…

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