Hierarchical semi-supervised clustering using KSC based model

This paper introduces a methodology to incorporate the label information in discovering the underlying clusters in a hierarchical setting using multi-class semi-supervised clustering algorithm. The method aims at revealing the relationship between clusters given few labels associated to some of the clusters. The problem is formulated as a regularized kernel spectral clustering algorithm in the primal-dual setting. The available labels are incorporated in different levels of hierarchy from top to bottom. As we advance towards the lowers levels in the tree all the previously added labels are used in the generation of the new levels of hierarchy. The model is trained on a subset of the data and then applied to the rest of the data in a learning framework. Thanks to the previously learned model, the out-of-sample extension property of the model allows then to predict the memberships of a new point. A combination of an internal clustering quality index and classification accuracy is used for model selection. Experiments are conducted on synthetic data and real image segmentation problems to show the applicability of the proposed approach.