  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.
