Support vector machines for classification of input vectors with different metrics

摘要

In this paper, a generalization of support vector machines is explored where it is considered that input vectors have different e_p norms for each class. It is proved that the optimization problem for binary classification by using the maximal margin principle with e_p and e_q norms only depends on the e_p norm if 1 ≤ p ≤ q. Furthermore, the selection of a different bias in the classifier function is a consequence of the e_q norm in this approach. Some commentaries on the most commonly used approaches of SVM are also given as particular cases.