Learning via linear operators: Maximum margin regression; multiclass and multiview learning at one-class complexity

We introduce a maximum margin framework realizing a regression type learning in an arbitrary Hilbert space whilst the corresponding dual problem preserving the structure and, therefore, the complexity that of the binary Support Vector Machine (SVM). We demonstrate via some examples this learning framework is broadly applicable in several seemingly different problems. One example is the multiclass classification problem which, in this way, can be implemented with the complexity of a binary SVM. The reduction of the complexity does not involve diminishing performance but, in some cases this approach can improve the classification accuracy. The multiclass classification is realized where the output labels are vector valued. Other examples implement multiview learning problems.