Nearest Neighbor Search for Hyperbolic Embeddings

TL;DR

This paper introduces efficient algorithms for nearest neighbor search in hyperbolic space, leveraging Euclidean methods, with proven guarantees and demonstrated effectiveness on real datasets.

Contribution

It develops novel algorithms for hyperbolic nearest neighbor search based on Euclidean techniques, with theoretical guarantees and practical validation.

Findings

Algorithms outperform existing methods on real datasets.

Theoretical guarantees ensure reliable performance.

Effective integration with existing systems is demonstrated.

Abstract

Embedding into hyperbolic space is emerging as an effective representation technique for datasets that exhibit hierarchical structure. This development motivates the need for algorithms that are able to effectively extract knowledge and insights from datapoints embedded in negatively curved spaces. We focus on the problem of nearest neighbor search, a fundamental problem in data analysis. We present efficient algorithmic solutions that build upon established methods for nearest neighbor search in Euclidean space, allowing for easy adoption and integration with existing systems. We prove theoretical guarantees for our techniques and our experiments demonstrate the effectiveness of our approach on real datasets over competing algorithms.