Structural Pattern Recognition with Graph Edit Distance: Approximation Algorithms and Applications PDF
Preview Structural Pattern Recognition with Graph Edit Distance: Approximation Algorithms and Applications
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 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland 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
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