Abstract
The aim in this paper is to show how the problem of learning the modes of structural variation in sets of graphs can be solved by converting the graphs to strings. We commence by showing how the problem of converting graphs to strings, or seriation, can be solved using semi-definite programming (SDP). This is a convex optimisation procedure that has recently found widespread use in computer vision for problems including image segmentation and relaxation labelling. We detail the representation needed to cast the graph-seriation problem in a matrix setting so that it can be solved using SDP. We show how to perform PCA on the strings delivered by our method. By projecting the seriated graphs on to the leading eigenvectors of the sample covariance matrix, we pattern spaces suitable for graph clustering.
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Yu, H., Hancock, E.R. (2005). Eigenspaces from Seriated Graphs. In: Gagalowicz, A., Philips, W. (eds) Computer Analysis of Images and Patterns. CAIP 2005. Lecture Notes in Computer Science, vol 3691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556121_23
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DOI: https://doi.org/10.1007/11556121_23
Publisher Name: Springer, Berlin, Heidelberg
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