Abstract
Label propagation is a well-explored family of methods for training a semi-supervised classifier where input data points (both labeled and unlabeled) are connected in the form of a weighted graph. For binary classification, the performance of these methods starts degrading considerably whenever input dataset exhibits following characteristics - (i) one of the class label is rare label or equivalently, class imbalance (CI) is very high, and (ii) degree of supervision (DoS) is very low - defined as fraction of labeled points. These characteristics are common in many real-world datasets relating to network fraud detection. Moreover, in such applications, the amount of class imbalance is not known a priori. In this paper, we have proposed and justified the use of an alternative formulation for graph label propagation under such extreme behavior of the datasets. In our formulation, objective function is the difference of two convex quadratic functions and the constraints are box constraints. We solve this program using Concave-Convex Procedure (CCCP). Whenever the problem size becomes too large, we suggest to work with a k-NN subgraph of the given graph which can be sampled by using Locality Sensitive Hashing (LSH) technique. We have also discussed various issues that one typically faces while sampling such a k-NN subgraph in practice. Further, we have proposed a novel label flipping method on top of the CCCP solution, which improves the result of CCCP further whenever class imbalance information is made available a priori. Our method can be easily adopted for a MapReduce platform, such as Hadoop. We have conducted experiments on 11 datasets comprising a graph size of up to 20K nodes, CI as high as 99.6%, and DoS as low as 0.5%. Our method has resulted up to 19.5-times improvement in F-measure and up to 17.5-times improvement in AUC-PR measure against baseline methods.