Locality-sensitive hashing in function spaces
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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 locality-sensitive hashing (LSH). We present two methods that allow LSH functions on 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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