Abstract
This paper shows how to construct a linear deformable model for graph structure by performing principal components analysis (PCA) on the vectorised adjacency matrix. We commence by using correspondence information to place the nodes of each of a set of graphs in a standard reference order. Using the correspondences order, we convert the adjacency matrices to long-vectors and compute the long-vector covariance matrix. By projecting the vectorised adjacency matrices onto the leading eigenvectors of the covariance matrix, we embed the graphs in a pattern-space. We illustrate the utility of the resulting method for shape-analysis.
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
Christmas, W.J., Kittler, J., Petrou, M.: Structural matching in computer vision using probabilistic relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(8), 749–764 (1995)
Wilson, R.C., Hancock, E.R.: Structural matching by discrete relaxation. IEEE Transactions on Pattern Analysis and Machine Intelligence 19(6), 634–648 (1997)
Roweis, S., Saul, L.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)
Luo, B., Wilson, R.C., Hancock, E.R.: Spectral embedding of graphs. Pattern Recognition 36, 2213–2230 (2003)
Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active Shape Models - Their Training and Application. Computer Vision and Image Understanding 61, 38–59 (1995)
Luo, B., Hancock, E.R.: Structural graph matching using the em algorithm and singular value decomposition. IEEE PAMI 23(10), 1120–1136 (2001)
Murase, H., Nayar, S.K.: Illumination planning for object recognition using parametric eigenspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence 16(12), 1219–1227 (1994)
Chatfield, C., Collins, A.J.: Introduction to multivariate analysis. Chapman & Hall, Boca Raton (1980)
Frischholz, R., Dieckmann, U.: BioID: A multimodal biometric identification system. IEEE Computer 33(2), 64–68 (2000)
Bagdanov, A.D., Worring, M.: First Order Gaussian Graphs for Efficient Structure Classification. Pattern Recogntion 36, 1311–1324 (2003)
Wong, A.K.C., Constant, J., You, M.L.: Random Graphs Syntactic and Structural Pattern Recognition. World Scientific, Singapore (1990)
Heckerman, D., Geiger, D., Chickering, D.M.: Learning Bayesian Networks: The combination of knowledge and statistical data. Machine Learning 20, 197–243 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Luo, B., Wilson, R.C., Hancock, E.R. (2005). A Linear Generative Model for Graph Structure. In: Brun, L., Vento, M. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2005. Lecture Notes in Computer Science, vol 3434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31988-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-31988-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25270-2
Online ISBN: 978-3-540-31988-7
eBook Packages: Computer ScienceComputer Science (R0)