# PUAL: A Classifier on Trifurcate Positive-Unlabeled Data

arXiv: https://arxiv.org/abs/2405.20970 · HTML: https://mlsanity.com/paper/2405.20970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 6 of 6)

- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Instance-Dependent PU Learning by Bayesian Optimal Relabeling](https://mlsanity.com/paper/1808.02180/) (2018)
- [Nonparametric semi-supervised learning of class proportions](https://mlsanity.com/paper/1601.01944/) (2016)
- [Split-PU: Hardness-aware Training Strategy for Positive-Unlabeled Learning](https://mlsanity.com/paper/2211.16756/) (2022)

## Abstract (arXiv)

Positive-unlabeled (PU) learning aims to train a classifier using the data containing only labeled-positive instances and unlabeled instances. However, existing PU learning methods are generally hard to achieve satisfactory performance on trifurcate data, where the positive instances distribute on both sides of the negative instances. To address this issue, firstly we propose a PU classifier with asymmetric loss (PUAL), by introducing a structure of asymmetric loss on positive instances into the objective function of the global and local learning classifier. Then we develop a kernel-based algorithm to enable PUAL to obtain non-linear decision boundary. We show that, through experiments on both simulated and real-world datasets, PUAL can achieve satisfactory classification on trifurcate data.