Exact and/or Fast Nearest Neighbors

TL;DR

This paper introduces Certified Cosine, a novel method for high-dimensional nearest neighbor search that provides certificates guaranteeing correctness, often avoiding exhaustive search and outperforming previous exact methods.

Contribution

The paper presents Certified Cosine, a new approach leveraging cosine similarity structure to certify nearest neighbors, improving efficiency and accuracy in high-dimensional data retrieval.

Findings

Certificates guarantee correct nearest neighbors in high dimensions.

Certified Cosine outperforms previous exact methods.

Avoids exhaustive search in many cases.

Abstract

Prior methods for retrieval of nearest neighbors in high dimensions are fast and approximate--providing probabilistic guarantees of returning the correct answer--or slow and exact performing an exhaustive search. We present Certified Cosine, a novel approach to nearest-neighbors which takes advantage of structure present in the cosine similarity distance metric to offer certificates. When a certificate is constructed, it guarantees that the nearest neighbor set is correct, possibly avoiding an exhaustive search. Certified Cosine's certificates work with high dimensional data and outperform previous exact nearest neighbor methods on these datasets.