Probabilistic Kernel Function for Fast Angle Testing

TL;DR

This paper introduces two deterministic, probabilistic kernel functions for angle testing in high-dimensional similarity search, outperforming Gaussian-based methods without requiring asymptotic assumptions.

Contribution

The paper proposes novel projection-based kernel functions for angle comparison and thresholding that are deterministic and outperform traditional Gaussian-based kernels.

Findings

Achieves 2.5x--3x higher QPS compared to HNSW

Does not rely on asymptotic assumptions

Outperforms Gaussian-distribution-based kernels

Abstract

In this paper, we study the angle testing problem in the context of similarity search in high-dimensional Euclidean spaces and propose two projection-based probabilistic kernel functions, one designed for angle comparison and the other for angle thresholding. Unlike existing approaches that rely on random projection vectors drawn from Gaussian distributions, our approach leverages reference angles and adopts a deterministic structure for the projection vectors. Notably, our kernel functions do not require asymptotic assumptions, such as the number of projection vectors tending to infinity, and can be theoretically and experimentally shown to outperform Gaussian-distribution-based kernel functions. We apply the proposed kernel function to Approximate Nearest Neighbor Search (ANNS) and demonstrate that our approach achieves a 2.5x--3x higher query-per-second (QPS) throughput compared to the widely-used graph-based search algorithm HNSW.