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
Structural Matching by Discrete Relaxation
IEEE Transactions on Pattern Analysis and Machine Intelligence
On a relation between graph edit distance and maximum common subgraph
Pattern Recognition Letters
The advantages of forward thinking in generating rooted and free trees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Error Correcting Graph Matching: On the Influence of the Underlying Cost Function
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
Inexact Multisubgraph Matching Using Graph Eigenspace and Clustering Models
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical 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
Enumeration of cospectral graphs
European Journal of Combinatorics - Special issue on algebraic combinatorics: in memory of J.J. Seidel
A POCS-Based Graph Matching Algorithm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning Shape-Classes Using a Mixture of Tree-Unions
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Riemannian approach to graph embedding
Pattern Recognition
The Representation and Matching of Pictorial Structures
IEEE Transactions on Computers
Indexing through laplacian spectra
Computer Vision and Image Understanding
Retrieving articulated 3-d models using medial surfaces and their graph spectra
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Spectral Embedding of Feature Hypergraphs
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
Indexing tree and subtree by using a structure network
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
A polynomial characterization of hypergraphs using the Ihara zeta function
Pattern Recognition
Detecting anomalies in people's trajectories using spectral graph analysis
Computer Vision and Image Understanding
Learning generative graph prototypes using simplified von neumann entropy
GbRPR'11 Proceedings of the 8th international conference on Graph-based representations in pattern recognition
Isomorphism of (mis)labeled graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
An information theoretic approach to learning generative graph prototypes
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
The missing models: a data-driven approach for learning how networks grow
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Robust point pattern matching based on spectral context
Pattern Recognition
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The spectrum of a graph has been widely used in graph theory to characterise the properties of a graph and extract information from its structure. It has also been employed as a graph representation for pattern matching since it is invariant to the labelling of the graph. There are, however, a number of potential drawbacks in using the spectrum as a representation of a graph. Firstly, more than one graph may share the same spectrum. It is well known, for example, that very few trees can be uniquely specified by their spectrum. Secondly, the spectrum may change dramatically with a small change structure. There are a wide variety of graph matrix representations from which the spectrum can be extracted. Among these are the adjacency matrix, combinatorial Laplacian, normalised Laplacian and unsigned Laplacian. Spectra can also be derived from the heat kernel matrix and path length distribution matrix. The choice of matrix representation clearly has a large effect on the suitability of spectrum in a number of pattern recognition tasks. In this paper we investigate the performance of the spectra as a graph representation in a variety of situations. Firstly, we investigate the cospectrality of the various matrix representations over large graph and tree sets, extending the work of previous authors. We then show that the Euclidean distance between spectra tracks the edit distance between graphs over a wide range of edit costs, and we analyse the accuracy of this relationship. We then use the spectra to both cluster and classify the graphs and demonstrate the effect of the graph matrix formulation on error rates. These results are produced using both synthetic graphs and trees and graphs derived from shape and image data.