Structural Pattern Recognition with Graph Edit Distance: Approximation Algorithms and Applications

164 Pages·2015·3.1 MB·English

by  Kaspar Riesen (auth.)

Advances in Computer Vision and Pattern Recognition
Kaspar Riesen
Structural Pattern
Recognition
with Graph Edit
Distance
Approximation Algorithms and
Applications
Advances in Computer Vision and Pattern
Recognition
Founding editor
Sameer Singh, Rail Vision, Castle Donington, UK
Series editor
Sing Bing Kang, Microsoft Research, Redmond, WA, USA
Advisory Board
Horst Bischof, Graz University of Technology, Austria
Richard Bowden, University of Surrey, Guildford, UK
Sven Dickinson, University of Toronto, ON, Canada
Jiaya Jia, The Chinese University of Hong Kong, Hong Kong
Kyoung Mu Lee, Seoul National University, South Korea
Yoichi Sato, The University of Tokyo, Japan
Bernt Schiele, Max Planck Institute for Computer Science, Saarbrücken, Germany
Stan Sclaroff, Boston University, MA, USA
More information about this series at http://www.springer.com/series/4205
Kaspar Riesen
Structural Pattern
Recognition with Graph
Edit Distance
Approximation Algorithms and Applications
123
Kaspar Riesen
Institut für Wirtschaftsinformatik
Fachhochschule Nordwestschweiz
Olten
Switzerland
ISSN 2191-6586 ISSN 2191-6594 (electronic)
Advances in Computer Vision andPattern Recognition
ISBN978-3-319-27251-1 ISBN978-3-319-27252-8 (eBook)
DOI 10.1007/978-3-319-27252-8
LibraryofCongressControlNumber:2015958905
©SpringerInternationalPublishingSwitzerland2015
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To Madeleine, Emilie, and Maxime
Preface
The present book is concerned with the use of graphs in the field of structural
patternrecognition.Infact,graphsarerecognizedasversatilealternativetofeature
vectors and thus, they found widespread application in pattern recognition and
related fields (yet, the present book is actually focused on the field of pattern
recognition only). In the last four decades, a huge number of procedures for graph
distancecomputation,whichisactuallyabasicrequirementforpatternrecognition,
havebeenproposedintheliterature.Grapheditdistance,introducedabout30years
ago,isstilloneofthemostflexiblegraphdistancemodelsavailableandsubjectof
various recent research activities.
The objective of the present book is twofold. First, it gives a general and
thorough introduction into the field of structural pattern recognition with a partic-
ular focus on graph edit distance (including a survey of graph edit distance
applications that emerged during the last decade). Second, it presents a compre-
hensive compilation of diverse novel methods related to graph edit distance that
have been developed and researched in the course of a recent research project that
has been conducted under my supervision. In particular, the second part of the
present book summarizes and consolidates the results of the following articles.1
1. Kaspar Riesen, Horst Bunke: Improving Bipartite Graph Edit Distance
Approximation using Various Search Strategies. Pattern Recognition 48(4):
1349–1363 (2015).
2. Kaspar Riesen, Andreas Fischer, Horst Bunke: Estimating Graph Edit Distance
Using Lower and Upper Bounds of Bipartite Approximations. IJPRAI 29(2)
(2015).
3. Miquel Ferrer, Francesc Serratosa, Kaspar Riesen: Improving Bipartite Graph
Matching by Assessing the Assignment Confidence. Pattern Recognition
Letters, 2015. Accepted for Publication.
1Wereuseseveraltextexcerpts,tables,andfiguresfromthecorrespondingoriginalpublications
withpermissionfromElsevier,WorldScientific,andIEEE.
vii
viii Preface
4. KasparRiesen,MiquelFerrer:PredictingtheCorrectnessofNodeAssignments
in Bipartite Graph Matching. Pattern Recognition Letters, 2015. Accepted for
Publication.
5. Kaspar Riesen, Miquel Ferrer, HorstBunke: Approximate Graph Edit Distance
in Quadratic Time. IEEE/ACM Transactions on Computational Biology and
Bioinformatics (TCBB), 2015. Accepted for Publication.
Bern Kaspar Riesen
September 2015
Acknowledgments
IamdeeplygratefultoHorstBunkeforintroducingmetotheworldofgraphsand
pattern recognition about 10 years ago. His excellent advice and open attitude
towards new ideas have strongly influenced my scientific development.
Although only one author is mentioned on the front cover of this book, various
colleagues contributed invaluable parts to this work. In particular, I would like to
thanktheco-authorsofthepapers,whichactuallybuildthebasisofthisbook,viz.,
Andreas Fischer, Miquel Ferrer, Rolf Dornberger, Francesc Serratosa, and Horst
Bunke.
Moreover, I would like to thank Thomas Strahm for his support in all admin-
istrative concerns as well as for encouraging me for writing the present book.
I would also like to acknowledge the funding by the Hasler Foundation
Switzerland and the Swiss National Science Foundation (Project 200021 153249).
Furthermore, I would like to thank Simon Rees and Wayne Wheeler from
Springer for their guidance and support.
Last but not least, I am very grateful to my family for their understanding and
encouragement.
ix
Contents
Part I Foundations and Applications of Graph Edit Distance
1 Introduction and Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Pattern Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.1 Statistical and Structural Pattern Recognition . . . . . . . . . . 4
1.2 Graph and Subgraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Graph Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Exact Graph Matching. . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Error-Tolerant Graph Matching. . . . . . . . . . . . . . . . . . . . 15
1.4 Outline of the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Graph Edit Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1 Basic Definition and Properties . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.1.1 Conditions on Edit Cost Functions . . . . . . . . . . . . . . . . . 31
2.1.2 Example Definitions of Cost Functions . . . . . . . . . . . . . . 33
2.2 Computation of Exact Graph Edit Distance. . . . . . . . . . . . . . . . . 35
2.3 Graph Edit Distance-Based Pattern Recognition. . . . . . . . . . . . . . 38
2.3.1 Nearest-Neighbor Classification. . . . . . . . . . . . . . . . . . . . 38
2.3.2 Kernel-Based Classification. . . . . . . . . . . . . . . . . . . . . . . 39
2.3.3 Classification of Vector Space Embedded Graphs . . . . . . . 41
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 Bipartite Graph Edit Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 Graph Edit Distance as Quadratic Assignment Problem . . . . . . . . 45
3.2 Bipartite Graph Edit Distance . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.1 Deriving Upper and Lower Bounds on the Graph
Edit Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3 Experimental Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
xi