Adaptive $k$ Nearest Neighbors Classifier via Granular Ball Computing

2026-08-13

AI Summary

This study addresses the limitation of traditional k-nearest neighbors (KNN) algorithms, which employ a fixed k value and thus fail to adapt to local data characteristics, compromising classification performance. To overcome this, the authors propose an adaptive KNN method grounded in granular ball computing. During training, multi-granularity granular balls are constructed using Fisher’s criterion; at prediction time, the nearest granular ball is identified via a weighted distance metric, enabling dynamic determination of the optimal k value. This approach facilitates data-driven, adaptive neighborhood partitioning, substantially enhancing robustness against noise and local perturbations. Experimental results demonstrate that the proposed method consistently achieves higher classification accuracy and improved computational efficiency across multiple datasets compared to existing KNN variants.

Abstract

The $k$-Nearest Neighbor~(KNN) algorithm is widely used across various tasks. The selection of the $k$ value is a key issue because it significantly impacts performance. In this paper, an adaptive and efficient KNN approach via granular-ball computing is proposed. The method consists of two stages. \textcolor{black}{In the training stage, the dataset is first coarsely partitioned to reduce the complexity of data distributions within a granular ball, and then the Fisher criterion is introduced to control ball splitting and stopping, yielding a multi-granularity granular ball representation. In the prediction stage, the nearest granular ball is first located through a weighted distance mechanism, and an adaptive neighborhood is then constructed around the test sample. The effective $k$ value is dynamically determined by the actual number of samples contained in this neighborhood. The neighborhood induced by the nearest granular ball provides more stable local group information, thereby improving robustness against noise and local perturbations.} Experimental results demonstrate that the proposed method outperforms existing KNN variants across multiple datasets in terms of both accuracy and efficiency. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/Adaptive-GBKNN.

Problem

• k-Nearest Neighbor
• k value selection
• classification
• adaptive neighborhood

Innovation

• Granular Ball Computing
• Adaptive k-Nearest Neighbors
• Fisher Criterion
• Multi-granularity Representation
• Weighted Distance Mechanism