False clustering rate control in mixture models

The clustering task consists in delivering labels to the members of a sample. For most data sets, some individuals are ambiguous and intrinsically difficult to attribute to one or another cluster. However, in practical applications, misclassifying individuals is potentially disastrous. To overcome this difficulty, the idea followed here is to classify only a part of the sample in order to obtain a small misclassification rate. This approach is well known in the supervised setting, and referred to as classification with an abstention option. The purpose of this paper is to revisit this approach in an unsupervised mixture-model framework. The problem is formalized in terms of controlling the false clustering rate (FCR) below a prescribed level {\alpha}, while maximizing the number of classified items. New procedures are introduced and their behavior is shown to be close to the optimal one by establishing theoretical results and conducting numerical experiments. An application to breast cancer data illustrates the benefits of the new approach from a practical viewpoint.