A new method for positive and unlabeled learning with privileged information

Positive and unlabeled learning (PU learning) has been studied to address the situation in which only positive and unlabeled examples are available. Most of the previous work has been devoted to identifying negative examples from the unlabeled data, so that the supervised learning approaches can be applied to build a classifier. However, for the remaining unlabeled data, they either exclude them from the learning phase or force them to belong to a class, and this always limits the performance of PU learning. In addition, previous PU methods assume the training data and the testing data have the same features representations. However, we can always collect the features that the training data have while the test data do not have, these kinds of features are called privileged information. In this paper, we propose a new method, which is based on similarity approach for the problem of positive and unlabeled learning with privileged information (SPUPIL), which consists of two steps. The proposed SPUPIL method first conducts KNN method to generate the similarity weights and then the similarity weights and privileged information are incorporated to the learning model based on Ranking SVM to build a more accurate classifier. We also use the Lagrangian method to transform the original model into its dual problem, and solve it to obtain the classifier. Extensive experiments on the real data sets show that the performance of the SPUPIL is better than the state-of-the-art PU learning methods.