One-Class Support Vector Machine with Relative Comparisons

One-class support vector machines （one-class SVMs） are powerful tools that are widely used in many applications. This paper describes a semi-supervised one-class SVM that uses supervision in terms of relative comparisons. The analysis uses a hypersphere version of one-class SVMs with a penalty term appended to the objective function. The method simultaneously finds the minimum sphere in the feature space that encloses most of the target points and considers the relative comparisons. The result is a standard convex quadratic programming problem, which can be solved by adapting standard methods for SVM training, i.e., sequential minimal optimization. This one-class SVM can be applied to semi-supervised clustering and multi-classification problems. Tests show that this method achieves higher accuracy and better generalization performance than previous SVMs.