# Instance-Dependent Label-Noise Learning with Manifold-Regularized Transition Matrix Estimation

arXiv: https://arxiv.org/abs/2206.02791 · HTML: https://mlsanity.com/paper/2206.02791/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 57 references that are in the map.
- First posted on arXiv 6 Jun 2022.

## Builds on (most cited first, 30 of 34)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Combating noisy labels by agreement: A joint training method with co-regularization](https://mlsanity.com/paper/2003.02752/) (2020)
- [Using Trusted Data to Train Deep Networks on Labels Corrupted by Severe Noise](https://mlsanity.com/paper/1802.05300/) (2018)
- [Are Anchor Points Really Indispensable in Label-Noise Learning?](https://mlsanity.com/paper/1906.00189/) (2019)
- [CleanNet: Transfer Learning for Scalable Image Classifier Training with Label Noise](https://mlsanity.com/paper/1711.07131/) (2017)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [Deep learning with noisy labels: exploring techniques and remedies in medical image analysis](https://mlsanity.com/paper/1912.02911/) (2019)
- [SELF: Learning to Filter Noisy Labels with Self-Ensembling](https://mlsanity.com/paper/1910.01842/) (2019)
- [Learning with Instance-Dependent Label Noise: A Sample Sieve Approach](https://mlsanity.com/paper/2010.02347/) (2020)
- [Peer Loss Functions: Learning from Noisy Labels without Knowing Noise Rates](https://mlsanity.com/paper/1910.03231/) (2019)
- [Dual T: Reducing Estimation Error for Transition Matrix in Label-noise Learning](https://mlsanity.com/paper/2006.07805/) (2020)
- [CurriculumNet: Weakly Supervised Learning from Large-Scale Web Images](https://mlsanity.com/paper/1808.01097/) (2018)
- [Deep Self-Learning From Noisy Labels](https://mlsanity.com/paper/1908.02160/) (2019)
- [Understanding and Improving Early Stopping for Learning with Noisy Labels](https://mlsanity.com/paper/2106.15853/) (2021)
- [Provably End-to-end Label-Noise Learning without Anchor Points](https://mlsanity.com/paper/2102.02400/) (2021)
- [Learning with Biased Complementary Labels](https://mlsanity.com/paper/1711.09535/) (2017)
- [Masking: A New Perspective of Noisy Supervision](https://mlsanity.com/paper/1805.08193/) (2018)
- [A Second-Order Approach to Learning with Instance-Dependent Label Noise](https://mlsanity.com/paper/2012.11854/) (2020)
- [Curriculum Loss: Robust Learning and Generalization against Label Corruption](https://mlsanity.com/paper/1905.10045/) (2019)
- [Classification with Asymmetric Label Noise: Consistency and Maximal Denoising](https://mlsanity.com/paper/1303.1208/) (2013)
- [Confidence Scores Make Instance-dependent Label-noise Learning Possible](https://mlsanity.com/paper/2001.03772/) (2020)

## Built on by (most cited first, 30 of 49)

- [Label-Retrieval-Augmented Diffusion Models for Learning from Noisy Labels](https://mlsanity.com/paper/2305.19518/) (2023)
- [Instance-Dependent Noisy Label Learning via Graphical Modelling](https://mlsanity.com/paper/2209.00906/) (2022)
- [FedDiv: Collaborative Noise Filtering for Federated Learning with Noisy Labels](https://mlsanity.com/paper/2312.12263/) (2023)
- [Instance-dependent Label Distribution Estimation for Learning with Label Noise](https://mlsanity.com/paper/2212.08380/) (2022)
- [SAP: Corrective Machine Unlearning with Scaled Activation Projection for Label Noise Robustness](https://mlsanity.com/paper/2403.08618/) (2024)
- [Federated Learning with Instance-Dependent Noisy Label](https://mlsanity.com/paper/2312.10324/) (2023)
- [Diversified and Personalized Multi-rater Medical Image Segmentation](https://mlsanity.com/paper/2403.13417/) (2024)
- [Foster Adaptivity and Balance in Learning with Noisy Labels](https://mlsanity.com/paper/2407.02778/) (2024)
- [Trusted Multi-view Learning under Noisy Supervision](https://mlsanity.com/paper/2404.11944/) (2024)
- [Generalizable Person Re-identification via Balancing Alignment and Uniformity](https://mlsanity.com/paper/2411.11471/) (2024)
- [Quantifying and mitigating the impact of label errors on model disparity metrics](https://mlsanity.com/paper/2310.02533/) (2023)
- [Estimating Noisy Class Posterior with Part-level Labels for Noisy Label Learning](https://mlsanity.com/paper/2405.05714/) (2024)
- [A Survey of Computer Vision Technologies In Urban and Controlled-environment Agriculture](https://mlsanity.com/paper/2210.11318/) (2022)
- [Combating Label Noise With A General Surrogate Model For Sample Selection](https://mlsanity.com/paper/2310.10463/) (2023)
- [Learning with Imbalanced Noisy Data by Preventing Bias in Sample Selection](https://mlsanity.com/paper/2402.11242/) (2024)
- [ProSelfLC: Progressive Self Label Correction Towards A Low-Temperature Entropy State](https://mlsanity.com/paper/2207.00118/) (2022)
- [QMix: Quality-aware Learning with Mixed Noise for Robust Retinal Disease Diagnosis](https://mlsanity.com/paper/2404.05169/) (2024)
- [Instance-dependent Noisy-label Learning with Graphical Model Based Noise-rate Estimation](https://mlsanity.com/paper/2305.19486/) (2023)
- [PNT-Edge: Towards Robust Edge Detection with Noisy Labels by Learning Pixel-level Noise Transitions](https://mlsanity.com/paper/2307.14070/) (2023)
- [Learning with Noisy Labels: Interconnection of Two Expectation-Maximizations](https://mlsanity.com/paper/2401.04390/) (2024)
- [Camera-aware Label Refinement for Unsupervised Person Re-identification](https://mlsanity.com/paper/2403.16450/) (2024)
- [Extracting Clean and Balanced Subset for Noisy Long-tailed Classification](https://mlsanity.com/paper/2404.06795/) (2024)
- [D2SP: Dynamic Dual-Stage Purification Framework for Dual Noise Mitigation in Vision-based Affective Recognition](https://mlsanity.com/paper/2406.16473/) (2024)
- [ANNE: Adaptive Nearest Neighbors and Eigenvector-based Sample Selection for Robust Learning with Noisy Labels](https://mlsanity.com/paper/2411.01613/) (2024)
- [Enhanced Sample Selection with Confidence Tracking: Identifying Correctly Labeled yet Hard-to-Learn Samples in Noisy Data](https://mlsanity.com/paper/2504.17474/) (2025)
- [Optimal Transport for LLM Reward Modeling from Noisy Preference](https://mlsanity.com/paper/2605.06036/) (2026)
- [LNL+K: Enhancing Learning with Noisy Labels Through Noise Source Knowledge Integration](https://mlsanity.com/paper/2306.11911/) (2023)
- [GeoT: Geometry-guided Instance-dependent Transition Matrix for Semi-supervised Tooth Point Cloud Segmentation](https://mlsanity.com/paper/2503.16976/) (2025)
- [Noise-Aware Generalization: Robustness to In-Domain Noise and Out-of-Domain Generalization](https://mlsanity.com/paper/2504.02996/) (2025)
- [Neighbour Consistency Guided Pseudo-Label Refinement for Unsupervised Person Re-Identification](https://mlsanity.com/paper/2211.16847/) (2022)

## Abstract (arXiv)

In label-noise learning, estimating the transition matrix has attracted more and more attention as the matrix plays an important role in building statistically consistent classifiers. However, it is very challenging to estimate the transition matrix T(x), where x denotes the instance, because it is unidentifiable under the instance-dependent noise(IDN). To address this problem, we have noticed that, there are psychological and physiological evidences showing that we humans are more likely to annotate instances of similar appearances to the same classes, and thus poor-quality or ambiguous instances of similar appearances are easier to be mislabeled to the correlated or same noisy classes. Therefore, we propose assumption on the geometry of T(x) that "the closer two instances are, the more similar their corresponding transition matrices should be". More specifically, we formulate above assumption into the manifold embedding, to effectively reduce the degree of freedom of T(x) and make it stably estimable in practice. The proposed manifold-regularized technique works by directly reducing the estimation error without hurting the approximation error about the estimation problem of T(x). Experimental evaluations on four synthetic and two real-world datasets demonstrate that our method is superior to state-of-the-art approaches for label-noise learning under the challenging IDN.