The 2nu-SVM: A cost-sensitive extension of the nu-SVM

Standard classification algorithms aim to minimize the probability of making an incorrect classification. In many important applications, however, some kinds of errors are more important than others. In this report we review cost-sensitive extensions of standard support vector machines (SVMs). In particular, we describe cost-sensitive extensions of the C-SVM and the nu-SVM, which we denote the 2C-SVM and 2nu-SVM respectively. The C-SVM and the nu-SVM are known to be closely related, and we prove that the 2C-SVM and 2nu-SVM share a similar relationship. This demonstrates that the 2C-SVM and 2nu-SVM explore the same space of possible classifiers, and gives us a clear understanding of the parameter space for both versions.