# Probability-density-aware Semi-supervised Learning

arXiv: https://arxiv.org/abs/2412.17547 · HTML: https://mlsanity.com/paper/2412.17547/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 22 references that are in the map.
- First posted on arXiv 23 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [CoMatch: Semi-supervised Learning with Contrastive Graph Regularization](https://mlsanity.com/paper/2011.11183/) (2020)
- [SimMatch: Semi-supervised Learning with Similarity Matching](https://mlsanity.com/paper/2203.06915/) (2022)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Low-shot learning with large-scale diffusion](https://mlsanity.com/paper/1706.02332/) (2017)
- [One Positive Label is Sufficient: Single-Positive Multi-Label Learning with Label Enhancement](https://mlsanity.com/paper/2206.00517/) (2022)
- [Density-Aware Graph for Deep Semi-Supervised Visual Recognition](https://mlsanity.com/paper/2003.13194/) (2020)
- [Transductive Label Augmentation for Improved Deep Network Learning](https://mlsanity.com/paper/1805.10546/) (2018)

## Abstract (arXiv)

Semi-supervised learning (SSL) assumes that neighbor points lie in the same category (neighbor assumption), and points in different clusters belong to various categories (cluster assumption). Existing methods usually rely on similarity measures to retrieve the similar neighbor points, ignoring cluster assumption, which may not utilize unlabeled information sufficiently and effectively. This paper first provides a systematical investigation into the significant role of probability density in SSL and lays a solid theoretical foundation for cluster assumption. To this end, we introduce a Probability-Density-Aware Measure (PM) to discern the similarity between neighbor points. To further improve Label Propagation, we also design a Probability-Density-Aware Measure Label Propagation (PMLP) algorithm to fully consider the cluster assumption in label propagation. Last but not least, we prove that traditional pseudo-labeling could be viewed as a particular case of PMLP, which provides a comprehensive theoretical understanding of PMLP's superior performance. Extensive experiments demonstrate that PMLP achieves outstanding performance compared with other recent methods.