Vector search with small radiuses

• URL: http://arxiv.org/abs/2403.10746v1
• Date: Sat, 16 Mar 2024 00:34:25 GMT
• Title: Vector search with small radiuses
• Authors: Gergely Szilvasy, Pierre-Emmanuel Mazaré, Matthijs Douze,
• Abstract summary: This paper focuses on the common case where a hard decision needs to be taken depending on the vector retrieval results. We show that the value of a range search result can be modeled rigorously based on the query-to-vector distance. This yields a metric for range search, RSM, that is both principled and easy to compute without running an end-to-end evaluation.
• Score: 10.880913075221361
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In recent years, the dominant accuracy metric for vector search is the recall of a result list of fixed size (top-k retrieval), considering as ground truth the exact vector retrieval results. Although convenient to compute, this metric is distantly related to the end-to-end accuracy of a full system that integrates vector search. In this paper we focus on the common case where a hard decision needs to be taken depending on the vector retrieval results, for example, deciding whether a query image matches a database image or not. We solve this as a range search task, where all vectors within a certain radius from the query are returned. We show that the value of a range search result can be modeled rigorously based on the query-to-vector distance. This yields a metric for range search, RSM, that is both principled and easy to compute without running an end-to-end evaluation. We apply this metric to the case of image retrieval. We show that indexing methods that are adapted for top-k retrieval do not necessarily maximize the RSM. In particular, for inverted file based indexes, we show that visiting a limited set of clusters and encoding vectors compactly yields near optimal results.

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