# Dens-PU: PU Learning with Density-Based Positive Labeled Augmentation

arXiv: https://arxiv.org/abs/2303.11848 · HTML: https://mlsanity.com/paper/2303.11848/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 49 references that are in the map.
- First posted on arXiv 21 Mar 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels](https://mlsanity.com/paper/1705.01936/) (2017)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Classification from Positive, Unlabeled and Biased Negative Data](https://mlsanity.com/paper/1810.00846/) (2018)
- [Learning from Positive and Unlabeled Data with Arbitrary Positive Shift](https://mlsanity.com/paper/2002.10261/) (2020)
- [Functional Isolation Forest](https://mlsanity.com/paper/1904.04573/) (2019)

## Built on by (most cited first, 4 of 4)

- [ESA: Example Sieve Approach for Multi-Positive and Unlabeled Learning](https://mlsanity.com/paper/2412.02240/) (2024)
- [PUL-Inter-slice Defender: An Anomaly Detection Solution for Distributed Slice Mobility Attacks](https://mlsanity.com/paper/2510.02236/) (2025)
- [Angular Regularization for Positive-Unlabeled Learning on the Hypersphere](https://mlsanity.com/paper/2512.06785/) (2025)
- [Detecting Media Clones in Cultural Repositories Using a Positive Unlabeled Learning Approach](https://mlsanity.com/paper/2604.04071/) (2026)

## Abstract (arXiv)

This study proposes a novel approach for solving the PU learning problem based on an anomaly-detection strategy. Latent encodings extracted from positive-labeled data are linearly combined to acquire new samples. These new samples are used as embeddings to increase the density of positive-labeled data and, thus, define a boundary that approximates the positive class. The further a sample is from the boundary the more it is considered as a negative sample. Once a set of negative samples is obtained, the PU learning problem reduces to binary classification. The approach, named Dens-PU due to its reliance on the density of positive-labeled data, was evaluated using benchmark image datasets, and state-of-the-art results were attained.