DELTACON: A Principled Massive-Graph Similarity Function with Attribution
Abstract
How much did a network change since yesterday? How different is the wiring between Bob's brain (a left-handed male) and Alice's brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DeltaCon, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customers of a mobile carrier). In our experiments on various synthetic and real graphs we showcase the advantages of our method over existing similarity measures. We also employ DeltaCon to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.
- Authors:
-
- Carnegie Mellon Univ., Pittsburgh, PA (United States). Computer Science Dept.
- Duke Univ., Durham, NC (United States). Dept. of Statistical Science
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1343040
- Report Number(s):
- LLNL-JRNL-677691
Journal ID: ISSN 1556-4681
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- ACM Transactions on Knowledge Discovery from Data
- Additional Journal Information:
- Journal Volume: 10; Journal Issue: 3; Conference: SIAM International Conference on Data Mining, Austin, Texas, USA, 5/02/2013 - 5/04/2013; Journal ID: ISSN 1556-4681
- Publisher:
- Association for Computing Machinery
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 99 GENERAL AND MISCELLANEOUS; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; algorithms; experimentation; graph similarity; graph comparison; anomaly detection; network monitoring; graph classification; node attribution; edge attribution
Citation Formats
Koutra, Danai, Shah, Neil, Vogelstein, Joshua T., Gallagher, Brian, and Faloutsos, Christos. DELTACON: A Principled Massive-Graph Similarity Function with Attribution. United States: N. p., 2014.
Web. doi:10.1145/2824443.
Koutra, Danai, Shah, Neil, Vogelstein, Joshua T., Gallagher, Brian, & Faloutsos, Christos. DELTACON: A Principled Massive-Graph Similarity Function with Attribution. United States. https://doi.org/10.1145/2824443
Koutra, Danai, Shah, Neil, Vogelstein, Joshua T., Gallagher, Brian, and Faloutsos, Christos. 2014.
"DELTACON: A Principled Massive-Graph Similarity Function with Attribution". United States. https://doi.org/10.1145/2824443. https://www.osti.gov/servlets/purl/1343040.
@article{osti_1343040,
title = {DELTACON: A Principled Massive-Graph Similarity Function with Attribution},
author = {Koutra, Danai and Shah, Neil and Vogelstein, Joshua T. and Gallagher, Brian and Faloutsos, Christos},
abstractNote = {How much did a network change since yesterday? How different is the wiring between Bob's brain (a left-handed male) and Alice's brain (a right-handed female)? Graph similarity with known node correspondence, i.e. the detection of changes in the connectivity of graphs, arises in numerous settings. In this work, we formally state the axioms and desired properties of the graph similarity functions, and evaluate when state-of-the-art methods fail to detect crucial connectivity changes in graphs. We propose DeltaCon, a principled, intuitive, and scalable algorithm that assesses the similarity between two graphs on the same nodes (e.g. employees of a company, customers of a mobile carrier). In our experiments on various synthetic and real graphs we showcase the advantages of our method over existing similarity measures. We also employ DeltaCon to real applications: (a) we classify people to groups of high and low creativity based on their brain connectivity graphs, and (b) do temporal anomaly detection in the who-emails-whom Enron graph.},
doi = {10.1145/2824443},
url = {https://www.osti.gov/biblio/1343040},
journal = {ACM Transactions on Knowledge Discovery from Data},
issn = {1556-4681},
number = 3,
volume = 10,
place = {United States},
year = {Thu May 22 00:00:00 EDT 2014},
month = {Thu May 22 00:00:00 EDT 2014}
}
Web of Science
Works referenced in this record:
Measuring Graph Similarity Using Spectral Geometry
book, June 2008
- ElGhawalby, Hewayda; Hancock, Edwin R.
- Lecture Notes in Computer Science
Graph based anomaly detection and description: a survey
journal, July 2014
- Akoglu, Leman; Tong, Hanghang; Koutra, Danai
- Data Mining and Knowledge Discovery, Vol. 29, Issue 3
Authoritative sources in a hyperlinked environment
journal, September 1999
- Kleinberg, Jon M.
- Journal of the ACM, Vol. 46, Issue 5
Graph Comparison Using Fine Structure Analysis
conference, August 2010
- Macindoe, Owen; Richards, Whitman
- 2010 IEEE Second International Conference on Social Computing (SocialCom)
Fast anomaly detection despite the duplicates
conference, January 2013
- Lee, Jay Yoon; Kang, U.; Koutra, Danai
- Proceedings of the 22nd International Conference on World Wide Web - WWW '13 Companion
Thirty Years of Graph Matching in Pattern Recognition
journal, May 2004
- Conte, D.; Foggia, P.; Sansone, C.
- International Journal of Pattern Recognition and Artificial Intelligence, Vol. 18, Issue 03
Patterns amongst Competing Task Frequencies: Super-Linearities, and the Almond-DG Model
book, January 2013
- Koutra, Danai; Koutras, Vasileios; Prakash, B. Aditya
- Advances in Knowledge Discovery and Data Mining
Graph-based anomaly detection
conference, January 2003
- Noble, Caleb C.; Cook, Diane J.
- Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '03
Anomaly detection in dynamic networks: a survey
journal, March 2015
- Ranshous, Stephen; Shen, Shitian; Koutra, Danai
- Wiley Interdisciplinary Reviews: Computational Statistics, Vol. 7, Issue 3
BIG-ALIGN: Fast Bipartite Graph Alignment
conference, December 2013
- Koutra, Danai; Tong, Hanghang; Lubensky, David
- 2013 IEEE International Conference on Data Mining (ICDM), 2013 IEEE 13th International Conference on Data Mining
TimeCrunch: Interpretable Dynamic Graph Summarization
conference, January 2015
- Shah, Neil; Koutra, Danai; Zou, Tianmin
- Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - KDD '15
Topic-sensitive pagerank: A context-sensitive ranking algorithm for web search
journal, July 2003
- Haveliwala, T. H.
- IEEE Transactions on Knowledge and Data Engineering, Vol. 15, Issue 4
Web graph similarity for anomaly detection
journal, February 2010
- Papadimitriou, Panagiotis; Dasdan, Ali; Garcia-Molina, Hector
- Journal of Internet Services and Applications, Vol. 1, Issue 1
Eigenspace-based anomaly detection in computer systems
conference, January 2004
- IdÉ, Tsuyoshi; Kashima, Hisashi
- Proceedings of the 2004 ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '04
Network similarity via multiple social theories
conference, January 2013
- Berlingerio, Michele; Koutra, Danai; Eliassi-Rad, Tina
- Proceedings of the 2013 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining - ASONAM '13
Revealing the Hidden Language of Complex Networks
journal, April 2014
- Yaveroğlu, Ömer Nebil; Malod-Dognin, Noël; Davis, Darren
- Scientific Reports, Vol. 4, Issue 1
Shortest-Path Kernels on Graphs
conference, January 2005
- Borgwardt, K. M.; Kriegel, H.
- Fifth IEEE International Conference on Data Mining (ICDM'05)
A Set of Measures of Centrality Based on Betweenness
journal, March 1977
- Freeman, Linton C.
- Sociometry, Vol. 40, Issue 1
Algebraic connectivity of graphs [Algebraic connectivity of graphs]
journal, January 1973
- Fiedler, Miroslav
- Czechoslovak Mathematical Journal, Vol. 23, Issue 2
On Graph Kernels: Hardness Results and Efficient Alternatives
book, January 2003
- Gärtner, Thomas; Flach, Peter; Wrobel, Stefan
- Learning Theory and Kernel Machines
Propagation of trust and distrust
conference, January 2004
- Guha, R.; Kumar, Ravi; Raghavan, Prabhakar
- Proceedings of the 13th conference on World Wide Web - WWW '04
SNARE: a link analytic system for graph labeling and risk detection
conference, January 2009
- McGlohon, Mary; Bay, Stephen; Anderle, Markus G.
- Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '09
Honeycomb: Visual Analysis of Large Scale Social Networks
book, January 2009
- van Ham, Frank; Schulz, Hans-Jörg; Dimicco, Joan M.
- Human-Computer Interaction – INTERACT 2009
The anatomy of a large-scale hypertextual Web search engine
journal, April 1998
- Brin, Sergey; Page, Lawrence
- Computer Networks and ISDN Systems, Vol. 30, Issue 1-7
Cyclic pattern kernels for predictive graph mining
conference, January 2004
- Horváth, Tamás; G?rtner, Thomas; Wrobel, Stefan
- Proceedings of the 2004 ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '04
Locality Statistics for Anomaly Detection in Time Series of Graphs
journal, February 2014
- Wang, Heng; Tang, Minh; Park, Youngser
- IEEE Transactions on Signal Processing, Vol. 62, Issue 3
Graph kernels based on tree patterns for molecules
journal, October 2008
- Mahé, Pierre; Vert, Jean-Philippe
- Machine Learning, Vol. 75, Issue 1
A study of graph spectra for comparing graphs and trees
journal, September 2008
- Wilson, Richard C.; Zhu, Ping
- Pattern Recognition, Vol. 41, Issue 9
Personalized PageRank vectors for tag recommendations: inside FolkRank
conference, January 2011
- Kim, Heung-Nam; El Saddik, Abdulmotaleb
- Proceedings of the fifth ACM conference on Recommender systems - RecSys '11
Net-Ray: Visualizing and Mining Billion-Scale Graphs
book, January 2014
- Kang, U.; Lee, Jay-Yoon; Koutra, Danai
- Advances in Knowledge Discovery and Data Mining
MultiAspectForensics: Pattern Mining on Large-Scale Heterogeneous Networks with Tensor Analysis
conference, July 2011
- Maruhashi, Koji; Guo, Fan; Faloutsos, Christos
- 2011 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2011)
Temporal Scale of Processes in Dynamic Networks
conference, December 2011
- Caceres, Rajmonda Sulo; Berger-Wolf, Tanya; Grossman, Robert
- 2011 IEEE International Conference on Data Mining Workshops (ICDMW), 2011 IEEE 11th International Conference on Data Mining Workshops
VOG: Summarizing and Understanding Large Graphs
conference, April 2014
- Koutra, Danai; Kang, U.; Vreeken, Jilles
- Proceedings of the 2014 SIAM International Conference on Data Mining
On the evolution of user interaction in Facebook
conference, January 2009
- Viswanath, Bimal; Mislove, Alan; Cha, Meeyoung
- Proceedings of the 2nd ACM workshop on Online social networks - WOSN '09
Fast Random Walk Graph Kernel
conference, December 2013
- Kang, U.; Tong, Hanghang; Sun, Jimeng
- Proceedings of the 2012 SIAM International Conference on Data Mining
Graph evolution: Densification and shrinking diameters
journal, March 2007
- Leskovec, Jure; Kleinberg, Jon; Faloutsos, Christos
- ACM Transactions on Knowledge Discovery from Data, Vol. 1, Issue 1
Locality Sensitive Outlier Detection: A ranking driven approach
conference, April 2011
- Wang, Ye; Parthasarathy, Srinivasan; Tatikonda, Shirish
- 2011 IEEE International Conference on Data Engineering (ICDE 2011), 2011 IEEE 27th International Conference on Data Engineering
Visual Graph Comparison
conference, July 2009
- Andrews, Keith; Wohlfahrt, Martin; Wurzinger, Gerhard
- 2009 13th International Conference Information Visualisation, IV
D elta C on : A Principled Massive-Graph Similarity Function
conference, December 2013
- Koutra, Danai; Vogelstein, Joshua T.; Faloutsos, Christos
- Proceedings of the 2013 SIAM International Conference on Data Mining
A measure of betweenness centrality based on random walks
journal, January 2005
- Newman, M. E. J.
- Social Networks, Vol. 27, Issue 1
SimRank: a measure of structural-context similarity
conference, January 2002
- Jeh, Glen; Widom, Jennifer
- Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '02
MalSpot: Multi2 Malicious Network Behavior Patterns Analysis
book, January 2014
- Mao, Hing-Hao; Wu, Chung-Jung; Papalexakis, Evangelos E.
- Advances in Knowledge Discovery and Data Mining
Robust Outlier Detection Using Commute Time and Eigenspace Embedding
book, January 2010
- Khoa, Nguyen Lu Dang; Chawla, Sanjay
- Advances in Knowledge Discovery and Data Mining
Comparison of graphs by their number of spanning trees
journal, November 1976
- Kelmans, A. K.
- Discrete Mathematics, Vol. 16, Issue 3
Fast computation of SimRank for static and dynamic information networks
conference, January 2010
- Li, Cuiping; Han, Jiawei; He, Guoming
- Proceedings of the 13th International Conference on Extending Database Technology - EDBT '10
Gelling, and melting, large graphs by edge manipulation
conference, January 2012
- Tong, Hanghang; Prakash, B. Aditya; Eliassi-Rad, Tina
- Proceedings of the 21st ACM international conference on Information and knowledge management - CIKM '12
Metric forensics: a multi-level approach for mining volatile graphs
conference, January 2010
- Henderson, Keith; Eliassi-Rad, Tina; Faloutsos, Christos
- Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '10
More is simpler: effectively and efficiently assessing node-pair similarities based on hyperlinks
journal, September 2013
- Yu, Weiren; Lin, Xuemin; Zhang, Wenjie
- Proceedings of the VLDB Endowment, Vol. 7, Issue 1
Magnetic Resonance Connectome Automated Pipeline: An Overview
journal, March 2012
- Gray, W. R.; Bogovic, J. A.; Vogelstein, J. T.
- IEEE Pulse, Vol. 3, Issue 2
TensorSplat: Spotting Latent Anomalies in Time
conference, October 2012
- Koutra, Danai; Papalexakis, Evangelos E.; Faloutsos, Christos
- 2012 16th Panhellenic Conference on Informatics (PCI)
Interactive graph matching and visual comparison of graphs and clustered graphs
conference, January 2012
- Hascoët, Mountaz; Dragicevic, Pierre
- Proceedings of the International Working Conference on Advanced Visual Interfaces - AVI '12
Weighted graph comparison techniques for brain connectivity analysis
conference, January 2013
- Alper, Basak; Bach, Benjamin; Henry Riche, Nathalie
- Proceedings of the SIGCHI Conference on Human Factors in Computing Systems - CHI '13
OPAvion: mining and visualization in large graphs
conference, January 2012
- Akoglu, Leman; Chau, Duen Horng; Kang, U.
- Proceedings of the 2012 international conference on Management of Data - SIGMOD '12
Localizing anomalous changes in time-evolving graphs
conference, January 2014
- Sricharan, Kumar; Das, Kamalika
- Proceedings of the 2014 ACM SIGMOD international conference on Management of data - SIGMOD '14
Visual comparison for information visualization
journal, September 2011
- Gleicher, Michael; Albers, Danielle; Walker, Rick
- Information Visualization, Vol. 10, Issue 4
CopyCatch: stopping group attacks by spotting lockstep behavior in social networks
conference, January 2013
- Beutel, Alex; Xu, Wanhong; Guruswami, Venkatesan
- Proceedings of the 22nd international conference on World Wide Web - WWW '13
Aligning graphs and finding substructures by a cavity approach
journal, February 2010
- Bradde, S.; Braunstein, A.; Mahmoudi, H.
- EPL (Europhysics Letters), Vol. 89, Issue 3
Linearized and single-pass belief propagation
journal, January 2015
- Gatterbauer, Wolfgang; Günnemann, Stephan; Koutra, Danai
- Proceedings of the VLDB Endowment, Vol. 8, Issue 5
Unifying Guilt-by-Association Approaches: Theorems and Fast Algorithms
book, January 2011
- Koutra, Danai; Ke, Tai-You; Kang, U.
- Machine Learning and Knowledge Discovery in Databases
MIGRAINE: MRI Graph Reliability Analysis and Inference for Connectomics
conference, December 2013
- Gray Roncal, William; Koterba, Zachary H.; Mhembere, Disa
- 2013 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
Message-Passing Algorithms for Sparse Network Alignment
journal, March 2013
- Bayati, Mohsen; Gleich, David F.; Saberi, Amin
- ACM Transactions on Knowledge Discovery from Data, Vol. 7, Issue 1
Graph-based anomaly detection
conference, January 2003
- Noble, Caleb C.; Cook, Diane J.
- Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '03
Graph-based Anomaly Detection
book, July 2013
- Samatova, Nagiza F.; Hendrix, William; Jenkins, John
- Practical Graph Mining with R
Locality statistics for anomaly detection in time series of graphs
preprint, January 2013
- Wang, Heng; Tang, Minh; Park, Youngser
- arXiv
Graph kernels based on tree patterns for molecules
preprint, January 2006
- Mahé, Pierre; Vert, Jean-Philippe
- arXiv
Works referencing / citing this record:
Fast network discovery on sequence data via time-aware hashing
journal, December 2018
- Safavi, Tara; Sripada, Chandra; Koutra, Danai
- Knowledge and Information Systems, Vol. 61, Issue 2
Automated assessment of knowledge hierarchy evolution: comparing directed acyclic graphs
journal, December 2018
- Nayak, Guruprasad; Dutta, Sourav; Ajwani, Deepak
- Information Retrieval Journal, Vol. 22, Issue 3-4
Non-backtracking cycles: length spectrum theory and graph mining applications
journal, June 2019
- Torres, Leo; Suárez-Serrato, Pablo; Eliassi-Rad, Tina
- Applied Network Science, Vol. 4, Issue 1
Unsupervised network embeddings with node identity awareness
journal, October 2019
- Gutiérrez-Gómez, Leonardo; Delvenne, Jean-Charles
- Applied Network Science, Vol. 4, Issue 1
Wisdom of stakeholder crowds in complex social–ecological systems
journal, January 2020
- Aminpour, Payam; Gray, Steven A.; Jetter, Antonie J.
- Nature Sustainability, Vol. 3, Issue 3
Hierarchical Change Point Detection on Dynamic Networks
conference, June 2017
- Wang, Yu; Chakrabarti, Aniket; Sivakoff, David
- WebSci '17: ACM Web Science Conference, Proceedings of the 2017 ACM on Web Science Conference
Graph Summarization Methods and Applications: A Survey
journal, July 2018
- Liu, Yike; Safavi, Tara; Dighe, Abhilash
- ACM Computing Surveys, Vol. 51, Issue 3
Discovering and deciphering relationships across disparate data modalities
journal, January 2019
- Vogelstein, Joshua T.; Bridgeford, Eric W.; Wang, Qing
- eLife, Vol. 8
Discovering and Deciphering Relationships Across Disparate Data Modalities
text, January 2016
- Vogelstein, Joshua T.; Bridgeford, Eric; Wang, Qing
- arXiv
Discovering and Deciphering Relationships Across Disparate Data Modalities
text, January 2016
- Vogelstein, Joshua T.; Bridgeford, Eric; Wang, Qing
- arXiv