Probability Estimates for Multi-class Classification by Pairwise Coupling

The two most well-known approaches for reducing a multiclass classification problem to a set of binary classification problems are known as oneper-class (OPC) and the pairwise coupling (PWC). In the one-per-class approach, we train a classifier for each of the classes using as positive examples the training examples that belong to that class, and as negatives all the other training examples. In the pairwise coupling approach, we train a classifier for each possible pair of classes ignoring the examples that do not belong to the classes in question. Given a decomposition method of the multiclass problem into a number of binary classification problems and a binary classification learning algorithm that outputs probability estimates, we would like to couple the estimates given by each binary classifier in order to obtain class probability membership estimates for the multiclass problem. Often the pairwise approach yields a more flexible class of models than a multiclass method. For example