# Geometric Manifold Rectification for Imbalanced Learning

arXiv: https://arxiv.org/abs/2602.13045 · HTML: https://mlsanity.com/paper/2602.13045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 13 Feb 2026.

## Builds on (most cited first, 12 of 12)

- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Generative Adversarial Minority Oversampling](https://mlsanity.com/paper/1903.09730/) (2019)
- [LoRAS: An oversampling approach for imbalanced datasets](https://mlsanity.com/paper/1908.08346/) (2019)
- [MEL: Efficient Multi-Task Evolutionary Learning for High-Dimensional Feature Selection](https://mlsanity.com/paper/2402.08982/) (2024)
- [A Self-adaptive Weighted Differential Evolution Approach for Large-scale Feature Selection](https://mlsanity.com/paper/2110.14166/) (2021)

## Abstract (arXiv)

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.