Adaptive Estimation for Approximate k-Nearest-Neighbor Computations
This addresses inefficiencies in nearest-neighbor algorithms for data analysis and machine learning applications, though it is incremental as it builds on existing adaptive estimation frameworks.
The paper tackles the problem of varying computational difficulty in approximate k-nearest-neighbor searches by proposing an algorithm that adaptively estimates distances, showing it is essentially optimal for such methods and achieves significant speedups over naive approaches in theory and experiments.
Algorithms often carry out equally many computations for "easy" and "hard" problem instances. In particular, algorithms for finding nearest neighbors typically have the same running time regardless of the particular problem instance. In this paper, we consider the approximate k-nearest-neighbor problem, which is the problem of finding a subset of O(k) points in a given set of points that contains the set of k nearest neighbors of a given query point. We propose an algorithm based on adaptively estimating the distances, and show that it is essentially optimal out of algorithms that are only allowed to adaptively estimate distances. We then demonstrate both theoretically and experimentally that the algorithm can achieve significant speedups relative to the naive method.