Approximate k-flat Nearest Neighbor Search
Wolfgang Mulzer, Huy L. Nguyen, Paul Seiferth, Yannik Stein

TL;DR
This paper introduces the first efficient data structure for approximate $k$-flat nearest neighbor search in high-dimensional spaces, generalizing previous results for points and lines, with improved space and query time performance.
Contribution
It presents a novel data structure for approximate $k$-flat nearest neighbor queries that leverages existing $0$-ANN solutions, applicable for any $k$, with tunable performance based on the base $0$-ANN parameters.
Findings
Achieves efficient query times for arbitrary $k$-flat NN problems.
Provides near-linear space solutions for 1-ANN, improving previous results.
Offers a flexible framework that depends on existing $0$-ANN data structures.
Abstract
Let be a nonnegative integer. In the approximate -flat nearest neighbor (-ANN) problem, we are given a set of points in -dimensional space and a fixed approximation factor . Our goal is to preprocess so that we can efficiently answer approximate -flat nearest neighbor queries: given a -flat , find a point in whose distance to is within a factor of the distance between and the closest point in . The case corresponds to the well-studied approximate nearest neighbor problem, for which a plethora of results are known, both in low and high dimensions. The case is called approximate line nearest neighbor. In this case, we are aware of only one provably efficient data structure, due to Andoni, Indyk, Krauthgamer, and Nguyen. For , we know of no previous results. We present the first…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Image and Video Retrieval Techniques · Algorithms and Data Compression
