On a relation between graph edit distance and maximum common subgraph
Pattern Recognition Letters
Error Correcting Graph Matching: On the Influence of the Underlying Cost Function
IEEE Transactions on Pattern Analysis and Machine Intelligence
Inexact Multisubgraph Matching Using Graph Eigenspace and Clustering Models
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Efficiently Computing Weighted Tree Edit Distance Using Relaxation Labeling
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Normalized Cuts and Image Segmentation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Pattern Spaces from Graph Polynomials
ICIAP '03 Proceedings of the 12th International Conference on Image Analysis and Processing
Graph Manifolds from Spectral Polynomials
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Structure Is a Visual Class Invariant
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
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The spectra of graphs has been widely used to characterise and extract information from their structures. Applications include matching, segmentation and indexing. One of the key questions about this approach is the stability and representational power of the spectrum under changes in the graphs. There is also a wide variety of graph matrix representations from which the spectrum can be extracted. In this paper we discuss the issue of stability of various graph representation methods and compare five main graph representations; the adjacency matrix, combinatorial Laplacian, normalized Laplacian matrix, heat kernel and path length distribution matrix. We show that the Euclidean distance between spectra tracks the edit distance over a wide range of edit costs, and we analyse the stability of this relationship. We then use the spectra to match and classify the graphs and demonstrate the effect of the graph matrix formulation on error rates.