Learning Mixtures of Weighted Tree-Unions by Minimizing Description Length

This paper focuses on how to perform the unsupervised clustering of tree structures in an information theoretic setting. We pose the problem of clustering as that of locating a series of archetypes that can be used to represent the variations in tree structure present in the training sample. The archetypes are tree-unions that are formed by merging sets of sample trees, and are attributed with probabilities that measure the node frequency or weight in the training sample. The approach is designed to operate when the correspondences between nodes are unknown and must be inferred as part of the learning process. We show how the tree merging process can be posed as the minimisation of an information theoretic minimum descriptor length criterion. We illustrate the utility of the resulting algorithm on the problem of classifying 2D shapes using a shock graph representation.