Generalized Relative Neighborhood Graph (GRNG) for Similarity Search

TL;DR

This paper introduces the Generalized Relative Neighborhood Graph (GRNG), a new graph structure that enables efficient, exact similarity search by capturing higher-order relationships, outperforming existing approximate methods.

Contribution

The paper proposes GRNG, a novel graph that guides exact RNG construction and extends to a multi-layer hierarchy, improving scalability and accuracy over prior approximate algorithms.

Findings

GRNG enables efficient exact similarity search.

Multi-layer hierarchy significantly improves construction speed.

Outperforms state-of-the-art approximate RNG methods.

Abstract

Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often organized as a manifold with low intrinsic dimension, the notion of a neighbor must recognize higher-order relationship, to capture neighbors in all directions. Proximity graphs, such as the Relative Neighbor Graphs (RNG), use trinary relationships which capture the notion of direction and have been successfully used in a number of applications. However, the current algorithms for computing the RNG, despite widespread use, are approximate and not scalable. This paper proposes a novel type of graph, the Generalized Relative Neighborhood Graph (GRNG) for use in a pivot layer that then guides the efficient and exact construction of the RNG of a set of exemplars. It also shows how to extend this to a multi-layer hierarchy which significantly improves over the state-of-the-art methods which can only construct an approximate RNG.