An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Algorithm for Subgraph Isomorphism
Journal of the ACM (JACM)
A Linear Programming Approach for the Weighted Graph Matching Problem
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matching Delauny Triangulations by Probabilistic Relaxation
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
An Inexact Graph Comparison Approach in Joint Eigenspace
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
WSM: a novel algorithm for subgraph matching in large weighted graphs
Journal of Intelligent Information Systems
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In this paper, Umeyama's eigen-decomposition approach to weighted graph matching problems is critically examined. We argue that Umeyama's approach only guarantees to work well for graphs that satisfy three critical conditions: (1) The pair of weighted graphs to be matched must be nearly isomorphic; (2) The eigenvalues of the adjacency matrix of each graph have to be single and isolated enough to each other; (3) The rows of the matrix of the corresponding absolute eigenvetors cannot be very similar to each other. For the purpose of matching general weighted graph pairs without such imposed constraints, we shall propose an approximate formula with a theoretical guarantee of accuracy, from which Umeyama's formula can be deduced as a special case. Based on this approximate formula, a new algorithm for matching weighted graphs is developed. The experimental results demonstrate great improvements to the accuracy of weighted graph matching.