通过粒球计算自适应调整KNN的邻域大小，提升分类精度与稳定性。
Adaptive $k$ Nearest Neighbors Classifier via Granular Ball Computing
- 用粒球分层划分数据，基于Fisher准则动态生成多粒度表示。
- 预测时根据最近粒球内实际样本数动态确定有效k值。
- 对噪声和局部扰动更鲁棒，适合高维或分布复杂的数据集。
K近邻（KNN）算法在各类任务中广泛应用，k值的选择是影响性能的关键问题。本文提出一种基于粒球计算的自适应高效KNN方法，包含两个阶段：训练阶段首先粗略划分数据以降低粒球内数据分布复杂度，再引入Fisher准则控制粒球分裂与停止，生成多粒度粒球表示；预测阶段先通过加权距离机制定位最近粒球，再围绕测试样本构建自适应邻域，有效k值由该邻域内实际样本数动态决定。最近粒球诱导的邻域提供更稳定的局部群体信息，从而增强对噪声和局部扰动的鲁棒性。实验表明，所提方法在多个数据集上均优于现有KNN变体，在准确率与效率方面表现更优。代码已开源：https://github.com/lianxiaoyu724/Adaptive-GBKNN。
原文摘要 · Abstract (English)
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.
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