Discriminative k-means clustering

The k-means algorithm is a partitional clustering method. Over 60 years old, it has been successfully used for a variety of problems. The popularity of k-means is in large part a consequence of its simplicity and efficiency. In this paper we are inspired by these appealing properties of k-means in the development of a clustering algorithm which accepts the notion of "positively" and "negatively" labelled data. The goal is to discover the cluster structure of both positive and negative data in a manner which allows for the discrimination between the two sets. The usefulness of this idea is demonstrated practically on the problem of face recognition, where the task of learning the scope of a person's appearance should be done in a manner which allows this face to be differentiated from others.