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Survey of Filtered Approximate Nearest Neighbor Search over the Vector-Scalar Hybrid Data

Yanjun Lin, Kai Zhang, Zhenying He, Yinan Jing, X. Sean Wang

TL;DR

The paper addresses filtered approximate nearest neighbor search (FANNS) over vector-scalar hybrid data by formalizing hybrid datasets and queries, and by introducing a pruning-focused four-way framework (VSP, VJP, SSP, SJP) to classify FANNS algorithms. It comprehensively reviews 17 FANNS methods across vector- and scalar-pruning paradigms, mapping them to the framework and highlighting their design principles and trade-offs. The work also analyzes hybrid datasets and introduces the distribution factor as a new dimension of query difficulty, supported by qualitative visualizations and quantitative measures on real and synthetic data. Together, these contributions enable more meaningful comparisons, better benchmark design, and practical guidance for practitioners deploying FANNS in constrained retrieval tasks. The survey thereby lays a foundation for workload-aware indexing, hybrid-query benchmarks, and system-level algorithm selection in large-scale, real-world applications.

Abstract

Filtered approximate nearest neighbor search (FANNS), an extension of approximate nearest neighbor search (ANNS) that incorporates scalar filters, has been widely applied to constrained retrieval of vector data. Despite its growing importance, no dedicated survey on FANNS over the vector-scalar hybrid data currently exists, and the field has several problems, including inconsistent definitions of the search problem, insufficient framework for algorithm classification, and incomplete analysis of query difficulty. This survey paper formally defines the concepts of hybrid dataset and hybrid query, as well as the corresponding evaluation metrics. Based on these, a pruning-focused framework is proposed to classify and summarize existing algorithms, providing a broader and finer-grained classification framework compared to the existing ones. In addition, a review is conducted on representative hybrid datasets, followed by an analysis on the difficulty of hybrid queries from the perspective of distribution relationships between data and queries. This paper aims to establish a structured foundation for FANNS over the vector-scalar hybrid data, facilitate more meaningful comparisons between FANNS algorithms, and offer practical recommendations for practitioners. The code used for downloading hybrid datasets and analyzing query difficulty is available at https://github.com/lyj-fdu/FANNS

Survey of Filtered Approximate Nearest Neighbor Search over the Vector-Scalar Hybrid Data

TL;DR

The paper addresses filtered approximate nearest neighbor search (FANNS) over vector-scalar hybrid data by formalizing hybrid datasets and queries, and by introducing a pruning-focused four-way framework (VSP, VJP, SSP, SJP) to classify FANNS algorithms. It comprehensively reviews 17 FANNS methods across vector- and scalar-pruning paradigms, mapping them to the framework and highlighting their design principles and trade-offs. The work also analyzes hybrid datasets and introduces the distribution factor as a new dimension of query difficulty, supported by qualitative visualizations and quantitative measures on real and synthetic data. Together, these contributions enable more meaningful comparisons, better benchmark design, and practical guidance for practitioners deploying FANNS in constrained retrieval tasks. The survey thereby lays a foundation for workload-aware indexing, hybrid-query benchmarks, and system-level algorithm selection in large-scale, real-world applications.

Abstract

Filtered approximate nearest neighbor search (FANNS), an extension of approximate nearest neighbor search (ANNS) that incorporates scalar filters, has been widely applied to constrained retrieval of vector data. Despite its growing importance, no dedicated survey on FANNS over the vector-scalar hybrid data currently exists, and the field has several problems, including inconsistent definitions of the search problem, insufficient framework for algorithm classification, and incomplete analysis of query difficulty. This survey paper formally defines the concepts of hybrid dataset and hybrid query, as well as the corresponding evaluation metrics. Based on these, a pruning-focused framework is proposed to classify and summarize existing algorithms, providing a broader and finer-grained classification framework compared to the existing ones. In addition, a review is conducted on representative hybrid datasets, followed by an analysis on the difficulty of hybrid queries from the perspective of distribution relationships between data and queries. This paper aims to establish a structured foundation for FANNS over the vector-scalar hybrid data, facilitate more meaningful comparisons between FANNS algorithms, and offer practical recommendations for practitioners. The code used for downloading hybrid datasets and analyzing query difficulty is available at https://github.com/lyj-fdu/FANNS
Paper Structure (57 sections, 6 equations, 6 figures, 2 tables, 2 algorithms)

This paper contains 57 sections, 6 equations, 6 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. R1: Inconsistent definitions of the search problem.
  4. R2: Insufficient framework for algorithm classification.
  5. R3: Incomplete analysis of query difficulty.
  6. Our Contributions
  7. (1) More systematic definition of the search problem.
  8. (2) Finer-grained classification of FANNS algorithms.
  9. (3) Deeper analysis of query difficulty through a new factor.
  10. Preliminaries
  11. Definition of Hybrid Dataset
  12. Definition of Hybrid Query
  13. Definitions of Evaluation Metrics
  14. Background of ANNS Algorithms
  15. IVF index.
  16. ...and 42 more sections

Figures (6)

  • Figure 1: The proposed pruning-focused framework for classifying FANNS algorithms
  • Figure 2: Classification of FANNS algorithms under the pruning-focused framework and interrelationships among them.
  • Figure 3: Performance evaluations on hybrid queries with oracle partition indices. Each "x-y" is a set of hybrid queries, where the scalar value of base vectors is x and the scalar value of query vectors is y. Each set of base vectors is indexed using IVF and HNSW. The distribution relationship of each hybrid query set is ID, POD, or OOD, represented by circle, cross, or square.
  • Figure 4: UMAP visualizations of MNIST-8M (Left) and MTG (Right). Each filtered subset has a 2-dimensional distribution. In MNIST-8M, the distributions of each filtered subset are well-separated, exhibiting clustering behavior, while in MTG, the distributions of all filtered subsets are highly overlapping, sharing a similar overall distribution.
  • Figure 5: Mahalanobis Distance Histograms of MNIST-8M (Left) and MTG (Right). Each subgraph titled "x-y" shows the histograms of both "x-y" (in orange) and "x-x" (in blue), illustrating the distribution shift between query vectors and base vectors when sampled from different filtered subsets, compared to when they are sampled from the same filtered subset.
  • ...and 1 more figures

Theorems & Definitions (8)

  • definition thmcounterdefinition: Scalar Schema
  • definition thmcounterdefinition: Vector Space
  • definition thmcounterdefinition: Hybrid Dataset
  • definition thmcounterdefinition: Scalar Filter
  • definition thmcounterdefinition: Vector Similarity Function
  • definition thmcounterdefinition: Hybrid Query
  • definition thmcounterdefinition: Recall
  • definition thmcounterdefinition: Selectivity