Using the one-versus-rest strategy with samples balancing to improve pairwise coupling classification

The simplest classification task is to divide a set of objects into two classes, but most of the problems we find in real life applications are multi-class. There are many methods of decomposing such a task into a set of smaller classification problems involving two classes only. Among the methods, pairwise coupling proposed by Hastie and Tibshirani (1998) is one of the best known. Its principle is to separate each pair of classes ignoring the remaining ones. Then all objects are tested against these classifiers and a voting scheme is applied using pairwise class probability estimates in a joint probability estimate for all classes. A closer look at the pairwise strategy shows the problem which impacts the final result. Each binary classifier votes for each object even if it does not belong to one of the two classes which it is trained on. This problem is addressed in our strategy. We propose to use additional classifiers to select the objects which will be considered by the pairwise classifiers. A similar solution was proposed by Moreira and Mayoraz (1998), but they use classifiers which are biased according to imbalance in the number of samples representing classes.