提出几何矫正方法，更好处理数据不平衡问题。
Geometric Manifold Rectification for Imbalanced Learning
- 基于局部几何先验，用自适应距离加权投票估计置信度。
- 采用非对称清洗策略，保护少数类样本不被误删。
- 在多个基准数据集上表现优于传统采样方法。
数据不平衡在机器学习中构成重大挑战，尤其当表格数据存在噪声和类别边界重叠时。从几何角度看，核心困难在于多数类拓扑侵入少数类流形，掩盖真实决策边界。传统欠采样方法（如编辑最近邻，ENN）通常采用对称清洗规则和统一投票机制，无法捕捉局部流形结构，常误删有信息的少数类样本。本文提出GMR（几何流形矫正）框架，通过利用局部几何先验，稳健处理结构化不平衡数据。主要贡献包括：(1) 几何置信度估计，使用逆距离加权kNN投票与自适应距离度量捕捉局部可靠性；(2) 非对称清洗策略，对多数类严格清洗，对少数类保守保护，设置安全阈值限制少数类移除。在多个基准数据集上的大量实验表明，GMR性能可媲美强采样基线。
原文摘要 · Abstract (English)
Imbalanced classification presents a formidable challenge in machine learning, particularly when tabular datasets are plagued by noise and overlapping class boundaries. From a geometric perspective, the core difficulty lies in the topological intrusion of the majority class into the minority manifold, which obscures the true decision boundary. Traditional undersampling techniques, such as Edited Nearest Neighbours (ENN), typically employ symmetric cleaning rules and uniform voting, failing to capture the local manifold structure and often inadvertently removing informative minority samples. In this paper, we propose GMR (Geometric Manifold Rectification), a novel framework designed to robustly handle imbalanced structured data by exploiting local geometric priors. GMR makes two contributions: (1) Geometric confidence estimation that uses inverse-distance weighted kNN voting with an adaptive distance metric to capture local reliability; and (2) asymmetric cleaning that is strict on majority samples while conservatively protecting minority samples via a safe-guarding cap on minority removal. Extensive experiments on multiple benchmark datasets show that GMR is competitive with strong sampling baselines.
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