Product graph-based higher order contextual similarities for inexact subgraph matching

Abstract

Many algorithms formulate graph matching as an optimization of an objective function of pairwise quantification of nodes and edges of two graphs to be matched. Pairwise measurements usually consider local attributes but disregard contextual information involved in graph structures. We address this issue by proposing contextual similarities between pairs of nodes. This is done by considering the tensor product graph (TPG) of two graphs to be matched, where each node is an ordered pair of nodes of the operand graphs. Contextual similarities between a pair of nodes are computed by accumulating weighted walks (normalized pairwise similarities) terminating at the corresponding paired node in TPG. Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG. We use contextual similarities to construct an objective function and optimize it with a linear programming approach. Since random walk formulation through TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities and better discrimination among the nodes and edges.Experimental results shown on synthetic as well as real benchmarks illustrate that higher order contextual similarities add discriminating power and allow one to find approximate solutions to the subgraph matching problem.

Spatial Location in Integrated Circuits through Infrared Microscopy

“…Among the numerous graph matching methods proposed over the years, we found that the method proposed by Dutta et al [ 54 ] matches our constraints. Indeed, their approach is based on the computation of higher order similarities between pairwise nodes and edges of input graphs.…”

“…In this way, the assignment is solved with linear approximation functions. A recent method [ 54 ] was proposed to compute contextual similarities between pairwise nodes and edges using a remastered random walk. This gives high-order features without dealing with hypergraphs, but still linearly solves the assignment.…”

“…In the second case and in a similar way as in [ 66 ], once pairwise similarities are used as transition probabilities of a walk, the probabilities of a walker ending on node n at instant t are used to compute a new contextual similarity. In [ 54 ], the backtrackless random walk is computed on the PG, from which the new contextual similarity is strengthened compared to usual walks. It is proven that the backtrackless walk has a more discriminating power of the resulting contextual similarities [ 67 ].…”

“…In this experiment, successful location corresponds to both a correct graph matching and a correct projection of this graph on the target one. In [ 68 ], we compared the success rate of our framework with the method proposed in [ 54 ], based on PG. Their overall performances are presented as true/false rates in Figure 7 , where the area under each curve represents the overall location success rate for the corresponding method.…”

A Review of Point Set Registration: From Pairwise Registration to Groupwise Registration

“…Most current GM algorithms are second-order or high-order GM methods [ 22 , 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 ]. Second-order GM methods combine the similarity of vertices-to-vertices and edges-to-edges.…”