Generalizing from Example Clusters

We consider the following problem: Given a set of data and one or more examples of clusters, find a clustering of the whole data set that is consistent with the given clusters. This is essentially a semi-supervised clustering problem, but it differs from previously studied semi-supervised clustering settings in significant ways. Earlier work has shown that none of the existing methods for semi-supervised clustering handle this problem well. We identify two reasons for this, which are related to the default metric learning methods not working well in this situation, and to overfitting behavior. We investigate the latter in more detail and propose a new method that explicitly guards against overfitting. Experimental results confirm that the new method generalizes much better. Several other problems identified here remain open.