Graph seriation using semi-definite programming

Abstract

Graph seriation is concerned with placing the nodes of a graph in a serial order so that edge consecutive constraints are generally preserved. It is an important task in network analysis problem in routine and bioinformatics. In this paper we show how the problem of graph seriation can be solved using semi-definite programming (SDP). This is a convex optimisation procedure that has recently found widespread use in computer vision. The main contribution of the paper is to detail the matrix representation needed to cast the graph-seriation problem in a matrix setting so that it can be solved using SDP. We illustrate the utility of the method for graph-matching and graph-clustering, where it is shown to offer advantages to the graph-spectral approach to seriation. © Springer-Verlag Berlin Heidelberg 2005.