One-Class Classification by Norm Ball Covering

Abstract

One-class classification (OCC) is a supervised learning technique for classification, where the classifier is constructed only by training the objects in the target class and determines whether new ones belong to the class or not. There have been attempts to solve OCC problem such as Support Vector Machines (SVM), Parzen Density Estimation (PDE) and other methods commonly used in multi-class classification.

In this paper, a new approach to OCC was proposed. The classifier consists of norm balls covering the objects in the target class: an object is classified in the target class if at least one of the norm balls covers it, otherwise it is rejected. We presented an algorithm of generating finite norm ball candidates. Then, by applying two conditions for 'good' norm ball the final candidates were chosen out of the candidates. An integer programming model for the selection of the optimal norm balls was solved so that the norm balls with the minimum number effectively detect the target objects with the good predictive power.

The experiments were carried out to test the overall performance of our classifier using some artificial and real data from UCI Repository. The results showed that proposed model was comparable to OCC methods in the comparison group. Also, it had high sparsity leading to low testing burden compared to the other classifiers. In the noise experiment, maximum norm ball classifier was robust to noises.