  Classification is a fundamental task in machine learning and data mining.
Existing classification methods are designed to classify unknown instances
within a set of previously known training classes. Such a classification takes
the form of a prediction within a closed-set of classes. However, a more
realistic scenario that fits real-world applications is to consider the
possibility of encountering instances that do not belong to any of the training
classes, $i.e.$, an open-set classification. In such situation, existing
closed-set classifiers will assign a training label to these instances
resulting in a misclassification. In this paper, we introduce Galaxy-X, a novel
multi-class classification approach for open-set recognition problems. For each
class of the training set, Galaxy-X creates a minimum bounding hyper-sphere
that encompasses the distribution of the class by enclosing all of its
instances. In such manner, our method is able to distinguish instances
resembling previously seen classes from those that are of unknown ones. To
adequately evaluate open-set classification, we introduce a novel evaluation
procedure. Experimental results on benchmark datasets show the efficiency of
our approach in classifying novel instances from known as well as unknown
classes.
