Solving for multi-class: a survey and synthesis

We review common methods of solving for multi-class from binary and generalize them to a common framework. Since conditional probabilties are useful both for quantifying the accuracy of an estimate and for calibration purposes, these are a required part of the solution. There is some indication that the best solution for multi-class classification is dependent on the particular dataset. As such, we are particularly interested in data-driven solution design, whether based on a priori considerations or empirical examination of the data. Numerical results indicate that while a one-size-fits-all solution consisting of one-versus-one is appropriate for most datasets, a minority will benefit from a more customized approach. The techniques discussed in this paper allow for a large variety of multi-class configurations and solution methods to be explored so as to optimize classification accuracy, accuracy of conditional probabilities and speed.