Title: Probabilistic Kernel Function for Fast Angle Testing
Primary area: other topics in machine learning (i.e., none of the above)
Keywords: Randomized algorithm, Locality Sensitive Hashing, Directional statistics

Abstract: In this paper, we study the angle testing problem 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 employs 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 both theoretically and experimentally shown to outperform Gaussian-distribution-based kernel functions. We further 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 state-of-the-art graph-based search algorithm HNSW.

TL;DR: We propose two probabilistic kernel functions for angle testing, which can be used to accelerate vector-based similarity search.