A Linear Generative Model for Graph Structure
- Cite this paper as:
- 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
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.
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