  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.
