Learning Mixtures of Tree-Unions by Minimizing Description Length

This paper focuses on how to perform the unsupervised learning of tree structures in an information theoretic setting. The approach is a purely structural one and is designed to work with representations where the correspondences between nodes are not given, but must be inferred from the structure. This is in contrast with other structural learning algorithms where the node-correspondences are assumed to be known. The learning process fits a mixture of structural models to a set of samples using a minimum description length formulation. The method extracts both a structural archetype that desribes the observed structural variation, and the node-correspondences that map nodes from trees in the sample set to nodes in the structural model. We use the algorithm to classify a set of shapes based on their shock graphs.