A Tour of Locality Sensitive Filtering on the Sphere
Luca Becchetti, Andrea Clementi, Luciano Gual\`a, Emanuele Natale, Luca Pep\`e Sciarria, Alessandro Straziota

TL;DR
This paper provides a unified overview and analysis of Locality Sensitive Filtering techniques for the Angular Approximate Near Neighbor problem, highlighting their connections, optimality, and core mechanisms.
Contribution
It introduces a new LSF-based data structure for Angular ANN and offers a streamlined, optimal analysis connecting existing techniques and results.
Findings
Designed and analyzed an LSF-based data structure for Angular ANN
Proved the optimality of the proposed data structure
Revisited and strengthened a key technical lemma
Abstract
The Approximate Near Neighbor (ANN) problem is a cornerstone in high-dimensional data analysis, with applications ranging from information retrieval to data mining. Among the most successful paradigms for solving ANN in high-dimensional metric spaces is Locality Sensitive Hashing (LSH), alongside the more recent Locality Sensitive Filtering (LSF). Since the seminal work of Indyk and Motwani, literature has expanded into a complex landscape of variants, often presented under different perspectives and adopting different notation. In this work, we address the technical challenge of navigating this landscape, by providing a self-contained, unified view of the essential algorithmic ingredients governing LSH-based and LSF-based solutions for angular distance -- a case of particular relevance in modern applications. In doing so, we touch on deep connections between LSF and LSH strategies.…
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