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.

通过引入正类样本上的非对称损失结构，构建了一个 PU 分类器，并开发了基于核的算法，使得 PUAL 能够获得非线性的决策边界，实验证明 PUAL 在三分数据上可以实现令人满意的分类效果。

PUAL：一种用于三分正负样本数据的分类器

PUAL: A Classifier on Trifurcate Positive-Unlabeled Data

Positive-Unlabeled (PU) Learning is a challenge presented by binary
classification problems where there is an abundance of unlabeled data along
with a small number of positive data instances, which can be used to address
chronic disease screening problem. State-of-the-art PU learning methods have
resulted in the development of various risk estimators, yet they neglect the
differences among distinct populations. To address this issue, we present a
novel Positive-Unlabeled Learning Tree (PUtree) algorithm. PUtree is designed
to take into account communities such as different age or income brackets, in
tasks of chronic disease prediction. We propose a novel approach for binary
decision-making, which hierarchically builds community-based PU models and then
aggregates their deliverables. Our method can explicate each PU model on the
tree for the optimized non-leaf PU node splitting. Furthermore, a mask-recovery
data augmentation strategy enables sufficient training of the model in
individual communities. Additionally, the proposed approach includes an
adversarial PU risk estimator to capture hierarchical PU-relationships, and a
model fusion network that integrates data from each tree path, resulting in
robust binary classification results. We demonstrate the superior performance
of PUtree as well as its variants on two benchmarks and a new
diabetes-prediction dataset.

提出了一种新颖的 Positive-Unlabeled Learning Tree (PUtree) 算法，该算法通过考虑不同群体（如年龄或收入段）来解决慢性疾病预测任务中的正无标记学习问题，包括建立基于群体的 PU 模型、采用掩蔽恢复数据增强策略进行模型训练、使用对抗 PU 风险评估器捕捉层次化的 PU 关系，并通过模型融合网络对每条路径的数据进行整合，实现稳健的二元分类结果。在两个基准数据集和一个新的糖尿病预测数据集上验证了 PUtree 及其变体的卓越性能。