Table Of ContentSPRINGER BRIEFS IN COMPLEXITY
Derek Doran
Network Role
Mining and
Analysis
123
SpringerBriefs in Complexity
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Derek Doran
Network Role Mining
and Analysis
123
Derek Doran
Department ofComputer Science
andEngineering
Wright State University
Dayton,OH
USA
ISSN 2191-5326 ISSN 2191-5334 (electronic)
SpringerBriefs inComplexity
ISBN978-3-319-53885-3 ISBN978-3-319-53886-0 (eBook)
DOI 10.1007/978-3-319-53886-0
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Preface
Theadventoflarge-scaleonlinesocialnetworks,webservicesandsystemsthatare
inherently social, and our unprecedented ability to capture “big” meta-data about
entitiesincountlesssystemshaveledtoasurgeofrecentdevelopmentstodiscover
the roles of entities in networks by sociologists, mathematicians, statisticians, and
computer scientists. This monograph presents an overview of network role mining
and analysis techniques. It organizes methods into five classes, representing
methods of varying computational sophistication and interpretability. Techniques
within each class are presented with an eye towards their actual implementation in
computer algorithms and systems. The monograph also discusses the broad char-
acteristics of methods in each class, enabling high-level comparisons that guide
practitioners toward choosing the appropriate technique for a given analysis task.
Themonographtargetsresearchersandpractitionerswithlittletonobackgroundin
network role mining, those with experience in a limited number of methods, or
thosethatfeeltheyhavejustanarrowperspectiveofthiskindofnetworkanalytics.
The structure and components of almost any complex system can be examined
fromtheperspectiveoftherolesitscomponentsplay.Thismonographwillserveas
aguidepostforcomputationalsocialscientists,computerscientists,andstatisticians
toaidintheirunderstandingofthesemethods,tofindtherightkindofroleanalysis
tobeusedintheirproblemofinterest,andtoinspirenewresearchdirectionsinthis
important field.
Dayton, OH, USA Derek Doran
December 2016
v
Acknowledgements
I would like to thank my collaborators and students who engaged me in conver-
sations leading to the development of this monograph. Thank you to Kyle Brown,
JaceRobinson,andJibrilIkharofortheirhelpfuleditsandcommentsthatimproved
thereadabilityandcontentofthisbook.IespeciallywanttoacknowledgeKylewho
assisted me in various aspects of the blockmodeling chapters and engaged me in
manyconversationsconcerningthetopicsofthisbookbeforeitsconception.Thank
youalsotoChristopherCoughlin,whoseinterestingconversationsduringthe2015
IEEE/ACM International Conference at Social Network Analysis and Mining in
Paris, France provided the initial spark for this brief. Finally thanks to Zandra
Zweber, Dan Ford, and Andre Keuck for volunteering their time as professional
meteorological and extraordinary individuals consultants.
vii
Contents
1 Network Role Mining and Analysis: An Overview.. .... ..... .... 1
1.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 1
1.2 Defining Roles .. .... ..... .... .... .... .... .... ..... .... 2
1.2.1 Networks. .... ..... .... .... .... .... .... ..... .... 3
1.2.2 Positions in Networks.... .... .... .... .... ..... .... 5
1.3 Mining Roles ... .... ..... .... .... .... .... .... ..... .... 6
1.3.1 Relationship to Graph Partitioning and Community
Detection. .... ..... .... .... .... .... .... ..... .... 10
1.4 Purpose and Outline of This Monograph ... .... .... ..... .... 11
References.. .... .... .... ..... .... .... .... .... .... ..... .... 11
2 Implied Role Mining. .... ..... .... .... .... .... .... ..... .... 15
2.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 15
2.2 The Implied Role Mining Process .... .... .... .... ..... .... 17
2.3 Illustrations with Usenet.... .... .... .... .... .... ..... .... 18
2.3.1 Golder et al.’s Taxonomy. .... .... .... .... ..... .... 19
2.3.2 Nolker et al.’s Hierarchy.. .... .... .... .... ..... .... 22
2.4 Analysis of Implied Role Mining. .... .... .... .... ..... .... 25
2.4.1 Qualitative Nature... .... .... .... .... .... ..... .... 25
2.4.2 Compatibility . ..... .... .... .... .... .... ..... .... 26
2.4.3 Simplicity and Interpretability.. .... .... .... ..... .... 27
2.5 Conclusion. .... .... ..... .... .... .... .... .... ..... .... 29
References.. .... .... .... ..... .... .... .... .... .... ..... .... 30
3 Equivalence-Based Role Mining. .... .... .... .... .... ..... .... 31
3.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 31
3.2 Structural Equivalence ..... .... .... .... .... .... ..... .... 32
3.2.1 Finding Structural Equivalences .... .... .... ..... .... 32
ix
x Contents
3.3 Automorphic Equivalence... .... .... .... .... .... ..... .... 34
3.3.1 Finding Automorphic Equivalences.. .... .... ..... .... 35
3.3.2 Quantifying Automorphic Similarity. .... .... ..... .... 37
3.4 Regular Equivalence.. ..... .... .... .... .... .... ..... .... 40
3.4.1 Finding Regular Equivalences.. .... .... .... ..... .... 40
3.4.2 Quantifying Regular Similarity. .... .... .... ..... .... 45
3.5 Conclusion. .... .... ..... .... .... .... .... .... ..... .... 46
References.. .... .... .... ..... .... .... .... .... .... ..... .... 46
4 Deterministic Blockmodeling ... .... .... .... .... .... ..... .... 49
4.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 49
4.2 The Blockmodeling Framework .. .... .... .... .... ..... .... 52
4.2.1 Similarity Measures.. .... .... .... .... .... ..... .... 52
4.2.2 Blocktypes ... ..... .... .... .... .... .... ..... .... 56
4.3 Goodness of Fit . .... ..... .... .... .... .... .... ..... .... 58
4.3.1 A Goodness-of-Fit Measure for Positional Analysis .. .... 59
4.3.2 A Goodness-of-Fit Measure for Network Compression.... 60
4.4 Conclusion. .... .... ..... .... .... .... .... .... ..... .... 60
References.. .... .... .... ..... .... .... .... .... .... ..... .... 61
5 Stochastic Blockmodeling . ..... .... .... .... .... .... ..... .... 63
5.1 Introduction .... .... ..... .... .... .... .... .... ..... .... 63
5.2 SBM Specification ... ..... .... .... .... .... .... ..... .... 64
5.3 The Infinite Relational Model.... .... .... .... .... ..... .... 65
5.3.1 Parameter Inference for the IRM.... .... .... ..... .... 67
5.3.2 Summary. .... ..... .... .... .... .... .... ..... .... 70
5.4 The Dynamic Stochastic Blockmodel.. .... .... .... ..... .... 70
5.4.1 DSBM Network Generation ... .... .... .... ..... .... 71
5.4.2 Parameter Inference for the DSBM.. .... .... ..... .... 73
5.5 Conclusion. .... .... ..... .... .... .... .... .... ..... .... 75
References.. .... .... .... ..... .... .... .... .... .... ..... .... 75
6 Advanced Computational Methods .. .... .... .... .... ..... .... 77
6.1 Factor Graphs: The Social Roles and Statuses Factor Graph
Model. .... .... .... ..... .... .... .... .... .... ..... .... 78
6.1.1 Social Features ..... .... .... .... .... .... ..... .... 79
6.1.2 A Factor Graph Model ... .... .... .... .... ..... .... 80
6.2 Multi-view Learning: Dual-View Uncertainty Regularization. .... 82
6.2.1 Graph Co-regularization .. .... .... .... .... ..... .... 83
6.2.2 Uncertainty Regularization and Objective Function... .... 84
6.3 Bayesian Modeling: Co-discovery of Roles in Communities . .... 85
6.4 Matrix Factorization: RolX.. .... .... .... .... .... ..... .... 87
Contents xi
6.5 Iterative Quadratic Programming: Synergistic Co-discovery
of Communities and Roles.. .... .... .... .... .... ..... .... 89
6.5.1 Initializing Communities (InitCom).. .... .... ..... .... 90
6.5.2 Initializing Roles (InitRole).... .... .... .... ..... .... 90
6.5.3 Updating Communities... .... .... .... .... ..... .... 91
6.5.4 Updating Roles..... .... .... .... .... .... ..... .... 92
6.6 Conclusion. .... .... ..... .... .... .... .... .... ..... .... 92
References.. .... .... .... ..... .... .... .... .... .... ..... .... 93
7 Concluding Remarks. .... ..... .... .... .... .... .... ..... .... 95
7.1 Emerging Trends in Role Mining. .... .... .... .... ..... .... 96
7.2 Tension Between Rigor and Interpretability . .... .... ..... .... 98
References.. .... .... .... ..... .... .... .... .... .... ..... .... 100
