Cost-sensitive positive and unlabeled learning

Positive and Unlabeled learning (PU learning) aims to train a binary classifier solely based on positively labeled and unlabeled data when negatively labeled data are absent or distributed too diversely. However, none of the existing PU learning methods takes the class imbalance problem into account, which significantly neglects the minority class and is likely to generate a biased classifier. Therefore, this paper proposes a novel algorithm termed "Cost-Sensitive Positive and Unlabeled learning" (CSPU) which imposes different misclassification costs on different classes when conducting PU classification. Specifically, we assign distinct weights to the losses caused by false negative and false positive examples, and employ double hinge loss to build our CSPU algorithm under the framework of empirical risk minimization. Theoretically, we analyze the computational complexity, and also derive a generalization error bound of CSPU which guarantees the good performance of our algorithm on test data. Empirically, we compare CSPU with the state-of-the-art PU learning methods on synthetic dataset, OpenML benchmark datasets, and real-world datasets. The results clearly demonstrate the superiority of the proposed CSPU to other comparators in dealing with class imbalanced tasks. (C) 2021 Elsevier Inc. All rights reserved.