# A Multilabel Classification Framework for Approximate Nearest Neighbor Search

arXiv: https://arxiv.org/abs/1910.08322 · HTML: https://mlsanity.com/paper/1910.08322/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [VIBE: Vector Index Benchmark for Embeddings](https://mlsanity.com/paper/2505.17810/) (2025)
- [LoRANN: Low-Rank Matrix Factorization for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/2410.18926/) (2024)
- [Fr'echet regression with implicit denoising and multicollinearity reduction](https://mlsanity.com/paper/2412.18247/) (2024)
- [GARLIC: GAussian Representation LearnIng for spaCe partitioning](https://mlsanity.com/paper/2505.24608/) (2025)

## Abstract (arXiv)

Both supervised and unsupervised machine learning algorithms have been used to learn partition-based index structures for approximate nearest neighbor (ANN) search. Existing supervised algorithms formulate the learning task as finding a partition in which the nearest neighbors of a training set point belong to the same partition element as the point itself, so that the nearest neighbor candidates can be retrieved by naive lookup or backtracking search. We formulate candidate set selection in ANN search directly as a multilabel classification problem where the labels correspond to the nearest neighbors of the query point, and interpret the partitions as partitioning classifiers for solving this task. Empirical results suggest that the natural classifier based on this interpretation leads to strictly improved performance when combined with any unsupervised or supervised partitioning strategy. We also prove a sufficient condition for consistency of a partitioning classifier for ANN search, and illustrate the result by verifying this condition for chronological k-d trees.