Large-Margin Label-Calibrated Support Vector Machines for Positive and Unlabeled Learning

Positive and unlabeled learning (PU learning) aims to train a binary classifier based on only PU data. Existing methods usually cast PU learning as a label noise learning problem or a cost-sensitive learning problem. However, none of them fully take the data distribution information into consideration when designing the model, which hinders them from acquiring more encouraging performance. In this paper, we argue that the clusters formed by positive examples and potential negative examples in the feature space should be critically utilized to establish the PU learning model, especially when the negative data are not explicitly available. To this end, we introduce a hat loss to discover the margin between data clusters, a label calibration regularizer to amend the biased decision boundary to the potentially correct one, and propose a novel discriminative PU classifier termed "Large-margin Label-calibrated Support Vector Machines" (LLSVM). Our LLSVM classifier can work properly in the absence of negative training examples and effectively achieve the max-margin effect between positive and negative classes. Theoretically, we derived the generalization error bound of LLSVM which reveals that the introduction of PU data does help to enhance the algorithm performance. Empirically, we compared LLSVM with state-of-the-art PU methods on various synthetic and practical data sets, and the results confirm that the proposed LLSVM is more effective than other compared methods on dealing with PU learning tasks.