kNN-Graph: An adaptive graph model for $k$-nearest neighbors

TL;DR

This paper introduces an adaptive graph model for k-nearest neighbors that decouples inference speed from computational complexity, enabling real-time classification without accuracy loss by leveraging a hierarchical graph structure and pre-computed voting.

Contribution

The authors propose a novel hierarchical graph framework that shifts neighbor selection to training, significantly improving inference speed while maintaining accuracy in kNN classification.

Findings

Achieves real-time inference speeds on large datasets

Maintains high classification accuracy comparable to exact kNN

Outperforms state-of-the-art approximate methods in speed and accuracy

Abstract

The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between inference speed and accuracy. Existing approximate nearest neighbor solutions accelerate retrieval but often degrade classification precision and lack adaptability in selecting the optimal neighborhood size (k). Here, we present an adaptive graph model that decouples inference latency from computational complexity. By integrating a Hierarchical Navigable Small World (HNSW) graph with a pre-computed voting mechanism, our framework completely transfers the computational burden of neighbor selection and weighting to the training phase. Within this topological structure, higher graph layers enable rapid navigation, while lower layers encode precise, node-specific decision boundaries with adaptive neighbor counts. Benchmarking against eight state-of-the-art baselines across six diverse datasets, we demonstrate that this architecture significantly accelerates inference speeds, achieving real-time performance, without compromising classification accuracy. These findings offer a scalable, robust solution to the long-standing inference bottleneck of kNN, establishing a new structural paradigm for graph-based nonparametric learning.