Learning a Generative Model for Structural Representations

Abstract

Abstract. Graph-based representations have been used with considerable success in computer vision in the abstraction and recognition of object shape and scene structure. Despite this, the methodology available for learning structural representations from sets of training examples is relatively limited. This paper addresses the problem of learning archetypal structural models from examples. To this end we define a generative model for graphs where the distribution of observed nodes and edges is governed by a set of independent Bernoulli trials with parameters to be estimated from data in a situation where the correspondences between the nodes in the data graphs and the nodes in the model are not known ab initio and must be estimated from local structure. This results in an EM-like approach where we alternate the estimation of the node correspondences with the estimation of the model parameters. The former estimation is cast as an instance of graph matching, while the latter estimation, together with model order selection, is addressed within a Minimum Message Length (MML) framework. Experiments on a shape recognition task show the effectiveness of the proposed learning approach.

Supervised Learning of Graph Structure

“…To solve this problem we follow [16] in adopting a minimum message length approach to model selection, but we deviate from it in that we use the message length to prune an initially oversized model.…”

“…Further, the issue of model order selection was not addressed. Torsello and Dowe [16] addressed the generalization capabilities of the approach by adding to the generative model the ability to add nodes, thus not requiring to model explicitly isotropic random noise, however correspondence estimation in this approach was cumbersome and while it used a minimum message length principle for selecting model-complexity, that could be only used to choose from different learned structures since it had no way to change the complexity while learning the model.…”

Generative Models for Chemical Structures

“…There have been several proposed solutions − to this problem for generic graphs. One approach is to construct a canonical representation of each graph using a graph alignment algorithm and then embed − each ordered graph in a vector space.…”

“…However, we make use of relational graphs to represent 2D chemical structures, 27 and it is difficult to define the necessary statistical quantities, such as the mean and variance of a set of graphs. 28,29 There have been several proposed solutions [30][31][32][33][34] to this problem for generic graphs. One approach 32 is to construct a canonical representation of each graph using a graph alignment algorithm 35 and then embed [36][37][38][39] each ordered graph in a vector space.…”