Support vector machines for classification of input vectors with different metrics

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