Faster dual-tree traversal for nearest neighbor search

Abstract

Nearest neighbor search is a nearly ubiquitous problem in computer science. When nearest neighbors are desired for a query set instead of a single query point, dual-tree algorithms often provide the fastest solution, especially in low-to-medium dimensions (i.e. up to a hundred or so), and can give exact results or absolute approximation guarantees, unlike hashing techniques. Using a recent decomposition of dual-tree algorithms into modular pieces, we propose a new piece: an improved traversal strategy; it is applicable to any dual-tree algorithm. Applied to nearest neighbor search using both kd-trees and ball trees, the new strategy demonstrably outperforms the previous fastest approaches. Other problems the traversal may easily be applied to include kernel density estimation and max-kernel search.