Support vector machines for classification of input vectors with different metrics

Authors:
L. Gonzalez-Abril;F. Velasco;J. A. Ortega;L. Franco
Affiliations:
Applied Economics I Department, Seville University, 41018 Seville, Spain;Applied Economics I Department, Seville University, 41018 Seville, Spain;Computer Languages and Systems Department, Seville University, 41012 Seville, Spain;Applied Economics I Department, Seville University, 41018 Seville, Spain
Venue:
Computers & Mathematics with Applications
Year:
2011

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Abstract

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