Solving for multi-class: a survey and synthesis

Many of the best statistical classification algorithms are binary classifiers that can only distinguish between one of two classes. The number of possible ways of generalizing binary classification to multi-class increases exponentially with the number of classes. There is some indication that the best method will depend on the dataset. Hence, we are particularly interested in data-driven solution design, whether based on prior considerations or on empirical examination of the data. Here we demonstrate how a recursive control language can be used to describe a multitude of different partitioning strategies in multi-class classification, including those in most common use. We use it both to manually construct new partitioning configurations as well as to examine those that have been automatically designed. Eight different strategies were tested on eight different datasets using a support vector machine (SVM) as the base binary classifier. Numerical results suggest that a one-size-fits-all solution consisting of one-versus-one is appropriate for most datasets. Three datasets showed better accuracy using different methods. The best solution for the most improved dataset exploited a property of the data to produce an uncertainty coefficient 36\% higher (0.016 absolute gain) than one-vs.-one. For the same dataset, an adaptive solution that empirically examined the data was also more accurate than one-vs.-one while being faster.