A family of measures for best top-n class-selective decision rules

When classes strongly overlap in the feature space, or when some classes are not known in advance, the performance of a classifier heavily decreases. To overcome this problem, the reject option has been introduced. It simply consists in withdrawing the decision, and let another classifier, or an expert, take the decision whenever exclusively classifying is not reliable enough. The classification problem is then a matter of class-selection, from none to all classes. In this paper, we propose a family of measures suitable to define such decision rules. It is based on a new family of operators that are able to detect blocks of similar values within a set of numbers in the unit interval, the soft labels of an incoming pattern to be classified, using a single threshold. Experiments on synthetic and real datasets available in the public domain show the efficiency of our approach.