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  • title: Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss
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            Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss
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            Approximate Euclidean lengths and distances beyond Johnson-Lindenstrauss

            Nov 28, 2022

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            Aleksandros Sobczyk

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            Mathieu Luisier

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            A classical result of Johnson and Lindenstrauss states that a set of n high dimensional data points can be projected down to O(log n/ϵ^2) dimensions such that the square of their pairwise distances is preserved up to a small distortion ϵ∈(0,1). It has been proved that the JL lemma is optimal for the general case, therefore, improvements can only be explored for special cases. This work aims to improve the ϵ^-2 dependency based on techniques inspired by the Hutch++ Algorithm <cit.>, which …

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