Learning shape-classes using a mixture of tree-unions

Abstract

Abstract-This paper poses the problem of tree-clustering as that of fitting a mixture of tree unions to a set of sample trees. The treeunions are structures from which the individual data samples belonging to a cluster can be obtained by edit operations. The distribution of observed tree nodes in each cluster sample is assumed to be governed by a Bernoulli distribution. The clustering method is designed to operate when the correspondences between nodes are unknown and must be inferred as part of the learning process. We adopt a minimum description length approach to the problem of fitting the mixture model to data. We make maximum-likelihood estimates of the Bernoulli parameters. The tree-unions and the mixing proportions are sought so as to minimize the description length criterion. This is the sum of the negative logarithm of the Bernoulli distribution, and a message-length criterion that encodes both the complexity of the uniontrees and the number of mixture components. We locate node correspondences by minimizing the edit distance with the current tree unions, and show that the edit distance is linked to the description length criterion. The method can be applied to both unweighted and weighted trees. We illustrate the utility of the resulting algorithm on the problem of classifying 2D shapes using a shock graph representation.

Learning spatiotemporal graphs of human activities

“…These correspondences must be estimated by graph matching. The most related to ours is recent work on 2D shape recognition based on learning structural archetypes of graphs -such as, e.g., super-graph [4], mixture of trees [23], and generative Delaunay graph [22]. These approaches typically make restrictive assumptions (e.g., model edges are independent and have Bernoulli distribution [22]), and cannot handle weights associated with both nodes and edges.…”

“…The most related to ours is recent work on 2D shape recognition based on learning structural archetypes of graphs -such as, e.g., super-graph [4], mixture of trees [23], and generative Delaunay graph [22]. These approaches typically make restrictive assumptions (e.g., model edges are independent and have Bernoulli distribution [22]), and cannot handle weights associated with both nodes and edges. We also extend the tree-union models for object recognition and texture analysis, presented in [21,2], by accommodating arbitrary permutations of nodes in our spatiotemporal graphs.…”

Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering

“…The learning of explicit cluster prototypes is a difficult task. For instance, in related work we have developed a greedy algorithm that minimizes a description length criterion (Torsello and Hancock, 2006). Lozano and Escolano (2003) use the EM algorithm to learn the prototype.…”

Learning a Generative Model for Structural Representations

“…These techniques provide a structural model of the samples -however, the way in which the supergraph is learned or estimated is largely heuristic in nature and is not rooted in a statistical learning framework. Torsello and Hancock [16] proposed an approach to learn trees by defining a superstructure called tree-union that captures the relations and observation probabilities of all nodes of all the trees in the training set. The structure is obtained by merging the corresponding nodes of the structures and is critically dependent on both the extracted correspondence and the order in which trees are merged.…”