Sampling a Near Neighbor in High Dimensions -- Who is the Fairest of Them All?

Given a set of points $S$ and a radius parameter $r>0$, the $r$-near neighbor ($r$-NN) problem asks for a data structure that, given any query point $q$, returns a point $p$ within distance at most $r$ from $q$.

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Near Neighbor: Who is the Fairest of Them All?

Namely, given a set of $n$ points $P$ and a parameter $r$, the goal is to preprocess the points, such that given a query point $q$, any point in the $r$-neighborhood of the query, i. e., $\ball(q, r)$, have the same probability of being reported as the near neighbor.

Sparse Approximation via Generating Point Sets

]{#1\left({#2}\right)} \newcommand{\npoints}{n} \newcommand{\ballD}{\mathsf{b}} \newcommand{\dataset}{{P}} $For a set$\dataset$of$\npoints$points in the unit ball$\ballD \subseteq \Re^d$, consider the problem of finding a small subset$\algset \subseteq \dataset$such that its convex-hull$\eps\$-approximates the convex-hull of the original set.

A Simple Algorithm for Maximum Margin Classification, Revisited

no code implementations6 Jul 2015

In this note, we revisit the algorithm of Har-Peled et.

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