HD-Index: Pushing the Scalability-Accuracy Boundary for Approximate kNN Search in High-Dimensional Spaces

TL;DR

HD-Index is a new hierarchical indexing method that improves approximate kNN search in massive high-dimensional datasets by combining RDB-trees with Hilbert keys and advanced pruning techniques.

Contribution

The paper introduces HD-Index, a scalable indexing scheme that enhances approximate kNN search efficiency and accuracy in high-dimensional spaces using novel hierarchical structures and inequalities.

Findings

Effective on billion-scale datasets

Outperforms existing methods in speed and accuracy

Scalable to high dimensions (up to 1000+)

Abstract

Nearest neighbor searching of large databases in high-dimensional spaces is inherently difficult due to the curse of dimensionality. A flavor of approximation is, therefore, necessary to practically solve the problem of nearest neighbor search. In this paper, we propose a novel yet simple indexing scheme, HD-Index, to solve the problem of approximate k-nearest neighbor queries in massive high-dimensional databases. HD-Index consists of a set of novel hierarchical structures called RDB-trees built on Hilbert keys of database objects. The leaves of the RDB-trees store distances of database objects to reference objects, thereby allowing efficient pruning using distance filters. In addition to triangular inequality, we also use Ptolemaic inequality to produce better lower bounds. Experiments on massive (up to billion scale) high-dimensional (up to 1000+) datasets show that HD-Index is effective, efficient, and scalable.