SIAM Review
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
New approximation techniques for some ordering problems
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Semidefinite programming relaxations for the graph partitioning problem
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Edit Distance from Spectral Seriation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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The aim in this paper is to show how the problem of learning the class-structure and 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 the strings delivered by our method can be used for graph-clustering and the construction of graph eigenspaces.