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Geometric Manifold Rectification for Imbalanced Learning

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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