A pairwise ranking based approach to learning with positive and unlabeled examples

A large fraction of binary classification problems arising in web applications are of the type where the positive class is well defined and compact while the negative class comprises everything else in the distribution for which the classifier is developed; it is hard to represent and sample from such a broad negative class. Classifiers based only on positive and unlabeled examples reduce human annotation effort significantly by removing the burden of choosing a representative set of negative examples. Various methods have been proposed in the literature for building such classifiers. Of these, the state of the art methods are Biased SVM and Elkan & Noto's methods. While these methods often work well in practice, they are computationally expensive since hyperparameter tuning is very important, particularly when the size of labeled positive examples set is small and class imbalance is high. In this paper we propose a pairwise ranking based approach to learn from positive and unlabeled examples (LPU) and we give a theoretical justification for it. We present a pairwise RankSVM (RSVM) based method for our approach. The method is simple, efficient, and its hyperparameters are easy to tune. A detailed experimental study using several benchmark datasets shows that the proposed method gives competitive classification performance compared to the mentioned state of the art methods, while training 3-10 times faster. We also propose an efficient AUC based feature selection technique in the LPU setting and demonstrate its usefulness on the datasets. To get an idea of the goodness of the LPU methods we compare them against supervised learning (SL) methods that also make use of negative examples in training. SL methods give a slightly better performance than LPU methods when there is a rich set of negative examples; however, they are inferior when the number of negative training examples is not large enough.