Open-Set Support Vector Machines

Often, when dealing with real-world recognition problems, we do not need, and often cannot have, knowledge of the entire set of possible classes that might appear during operational testing. In such cases, we need to think of robust classification methods able to deal with the "unknown" and properly reject samples belonging to classes never seen during training. Notwithstanding, existing classifiers to date were mostly developed for the closed-set scenario, i.e., the classification setup in which it is assumed that all test samples belong to one of the classes with which the classifier was trained. In the open-set scenario, however, a test sample can belong to none of the known classes and the classifier must properly reject it by classifying it as unknown. In this work, we extend upon the well-known Support Vector Machines (SVM) classifier and introduce the Open-Set Support Vector Machines (OSSVM), which is suitable for recognition in open-set setups. OSSVM balances the empirical risk and the risk of the unknown and ensures that the region of the feature space in which a test sample would be classified as known (one of the known classes) is always bounded, ensuring a finite risk of the unknown. In this work, we also highlight the properties of the SVM classifier related to the open-set scenario, and provide necessary and sufficient conditions for an RBF SVM to have bounded open-space risk.