Extending the SVM element in PMML to allow for multiclass-classification using the one-against-one approach in ADAPA.

For multiclass-classification with k classes, k > 2, the R ksvm function uses the `one-against-one'-approach, in which k(k-1)/2 binary classifiers are trained; the appropriate class is found by a voting scheme.

In order to implement such a scheme in ADAPA, we needed to extend PMML 3.2. Basically, PMML asks for a single target category to be associated with each Support Vector Machine. In case of a binary classifier, PMML actually asks for the alternate binary target category.

So, in order to implement the one-against-one approach, we needed to give each machine an extra alternate target category given that all k(k-1)/2 machines are binary classifiers.

Note that ADAPA also supports one-against-all approach (also known as one-against-rest) for which the PMML extension is not necessary.

Voting schemes for multiclass-classification problems in SVM are described in:

C.-W. Hsu and C.-J. Lin
A comparison on methods for multi-class support vector machines
IEEE Transactions on Neural Networks, 13(2002) 415-425.
http://www.csie.ntu.edu.tw/~cjlin/papers/multisvm.ps.gz