Analysis of approximate nearest neighbor searching with clustered point sets

TL;DR

This paper empirically compares different data structures for approximate nearest neighbor searching, showing that alternative methods outperform kd-trees on clustered data and queries.

Contribution

It introduces and evaluates two novel splitting methods, sliding-midpoint and minimum-ambiguity, demonstrating their effectiveness on clustered datasets.

Findings

Alternative methods outperform kd-trees on clustered data.

Minimum-ambiguity method reduces query ambiguity.

Sliding-midpoint balances cell aspect ratio and emptiness.

Abstract

We present an empirical analysis of data structures for approximate nearest neighbor searching. We compare the well-known optimized kd-tree splitting method against two alternative splitting methods. The first, called the sliding-midpoint method, which attempts to balance the goals of producing subdivision cells of bounded aspect ratio, while not producing any empty cells. The second, called the minimum-ambiguity method is a query-based approach. In addition to the data points, it is also given a training set of query points for preprocessing. It employs a simple greedy algorithm to select the splitting plane that minimizes the average amount of ambiguity in the choice of the nearest neighbor for the training points. We provide an empirical analysis comparing these two methods against the optimized kd-tree construction for a number of synthetically generated data and query sets. We demonstrate that for clustered data and query sets, these algorithms can provide significant improvements over the standard kd-tree construction for approximate nearest neighbor searching.