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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bonev, B., et al.: Constellations and the Unsupervised Learning of Graphs. In: Escolano, F., Vento, M. (eds.) GbRPR. LNCS, vol. 4538, pp. 340–350. Springer, Heidelberg (2007)
Bunke, H., et al.: Graph Clustering Using the Weighted Minimum Common Supergraph. In: Graph Based Representations in Pattern Recognition, pp. 235–246. Springer, Heidelberg (2003)
Comley, J.W., Dowe, D.L.: General Bayesian networks and asymmetric languages. In: Proc. Hawaii International Conference on Statistics and Related Fields (2003)
Comley, J.W., Dowe, D.L.: Minimum message length and generalized Bayesian nets with asymmetric languages. In: Grünwald, P., Pitt, M.A., Myung, I.J. (eds.) Advances in Minimum Description Length: Theory and Applications (MDL Handbook), pp. 265–294. MIT Press, Cambridge (2005)
Dowe, D.L.: Foreword re C. S. Wallace. Computer Journal 51(5), 523–560 (2008)
Dowe, D.L., Gardner, S., Oppy, G.R.: Bayes not bust! Why simplicity is no problem for Bayesians. British J. for the Philosophy of Science 58(4), 709–754 (2007)
Dickinson, S.J., Pentland, A.P., Rosenfeld, A.: 3-D shape recovery using distributed aspect matching. IEEE Trans. Pattern Anal. Machine Intell. 14(2), 174–198 (1992)
Friedman, N., Koller, D.: Being Bayesian about Network Structure. Machine Learning 50(1-2), 95–125 (2003)
Getoor, L., Friedman, N., Koller, D., Taskar, B.: Learning Probabilistic models of relational structure. In: 8th Int. Conf. on Machine Learning, pp. 170–177 (2001)
Gold, S., Rangarajan, A.: A graduated Assignment Algorithm for Graph Matching. IEEE Trans. Pattern Anal. Machine Intell. 18(4), 377–388 (1995)
Hagenbuchner, M., Sperduti, A., Tsoi, A.C.: A Self-Organizing Map for Adaptive Processing of Structured Data. IEEE Trans. Neural Networks 14, 491–505 (2003)
Ioffe, S., Forsyth, D.A.: Human tracking with mixtures of trees. In: Proc. Int. Conf. Computer Vision, vol. I, pp. 690–695 (2001)
Kimia, B.B., Tannenbaum, A.R., Zucker, S.W.: Shapes, shocks, and deformations I: the components of shape and the reaction-diffusion space. Int. J. Computer Vision 15(3), 189–224 (1995)
Todorovic, S., Ahuja, N.: Extracting Subimages of an unknown category from a set of images. In: IEEE Comp. Soc. conf. Computer Vision and Pattern Recognition, vol. 1, pp. 927–934 (2006)
Torsello, A., Hancock, E.R.: A Skeletal Measure of 2D Shape Similarity. Computer Vision and Image Understanding 95(1), 1–29 (2004)
Torsello, A., Hancock, E.R.: Learning Shape-Classes Using a Mixture of Tree-Unions. IEEE Trans. Pattern Anal. Machine Intell. 28(6), 954–967 (2006)
Wallace, C.S.: Statistical and Inductive Inference by Minimum Message Length. In: Information Science and Statistics. Springer, Heidelberg (2005)
Wallace, C.S., Boulton, D.M.: An information measure for classification. Computer Journal 11(2), 185–194 (1968)
Wallace, C.S., Dowe, D.L.: Minimum message length and Kolmogorov complexity. Computer Journal 42(4), 270–283 (1999)
Wallace, C.S., Freeman, P.R.: Estimation and inference by compact coding. Journal of the Royal Statistical Society series B, 240–252 (1987) (See also Discussion on pp. 252–265)
White, D., Wilson, R.C.: Spectral Generative Models for Graphs. In: Int. Conf. Image Analysis and Processing, pp. 35–42. IEEE Computer Society, Los Alamitos (2007)
Zhu, S.C., Yuille, A.L.: FORMS: A flexible object recognition and modelling system. Int. J. Computer Vision 20(3), 187–212 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Torsello, A., Dowe, D.L. (2008). Learning a Generative Model for Structural Representations. In: Wobcke, W., Zhang, M. (eds) AI 2008: Advances in Artificial Intelligence. AI 2008. Lecture Notes in Computer Science(), vol 5360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89378-3_58
Download citation
DOI: https://doi.org/10.1007/978-3-540-89378-3_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89377-6
Online ISBN: 978-3-540-89378-3
eBook Packages: Computer ScienceComputer Science (R0)