Multi-positive and unlabeled learning

Abstract

The positive and unlabeled (PU) learning problem focuses on learning a classifier from positive and unlabeled data. Some methods have been developed to solve the PU learning problem. However, they are often limited in practical applications, since only binary classes are involved and cannot easily be adapted to multi-class data. Here we propose a one-step method that directly enables multi-class model to be trained using the given input multi-class data and that predicts the label based on the model decision. Specifically, we construct different convex loss functions for labeled and unlabeled data to learn a discriminant function F. The theoretical analysis on the generalization error bound shows that it is no worse than k√k times of the fully supervised multi-class classification methods when the size of the data in k classes is of the same order. Finally, our experimental results demonstrate the significance and effectiveness of the proposed algorithm in synthetic and real-world datasets.