Manuel Gomez-Rodriguez
Jure Leskovec
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Abstract
Information diffusion and virus propagation are fundamental processes taking place in networks. While it is often possible to directly observe when nodes become infected with a virus or publish the information, observing individual transmissions (who infects whom, or who influences whom) is typically very difficult. Furthermore, in many applications, the underlying network over which the diffusions and propagations spread is actually unobserved. We tackle these challenges by developing a method for tracing paths of diffusion and influence through networks and inferring the networks over which contagions propagate. Given the times when nodes adopt pieces of information or become infected, we identify the optimal network that best explains the observed infection times. Since the optimization problem is NP-hard to solve exactly, we develop an efficient approximation algorithm that scales to large datasets and finds provably near-optimal networks.
We demonstrate the effectiveness of our approach by tracing information diffusion in a set of 170 million blogs and news articles over a one year period to infer how information flows through the online media space. We find that the diffusion network of news for the top 1,000 media sites and blogs tends to have a core-periphery structure with a small set of core media sites that diffuse information to the rest of the Web. These sites tend to have stable circles of influence with more general news media sites acting as connectors between them.
- Adar, E. and Adamic, L. A. 2005. Tracking information epidemics in blogspace. In Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence (WI). 207--214. Google Scholar
Digital Library
- Adar, E., Zhang, L., Adamic, L. A., and Lukose, R. M. 2004. Implicit structure and the dynamics of blogspace. In Proceedings of the 13th International World Wide Web Conference (WWW). Workshop on the Weblogging Ecosystem.Google Scholar
- Ahmed, A. and Xing, E. 2009. Recovering time-varying networks of dependencies in social and biological studies. Proc. Nat. Acad. Sci. 106.Google Scholar
- Anderson, R. M. and May, R. M. 2002. Infectious Diseases Of Humans: Dynamics and Control. Oxford Press.Google Scholar
- Backstrom, L. and Leskovec, J. 2011. Supervised random walks: Predicting and recommending links in social networks. In Proceedings of the ACM International Conference on Web Search and Data Mining (WSDM). Google ScholarDigital Library
- Bailey, N. T. J. 1975. The Mathematical Theory of Infectious Diseases and its Applications 2nd Ed. Hafner Press.Google Scholar
- Barabási, A.-L. 2005. The origin of bursts and heavy tails in human dynamics. Nature 435, 207.Google ScholarCross Ref
- Barabási, A.-L. and Albert, R. 1999. Emergence of scaling in random networks. Science 286, 509--512.Google ScholarCross Ref
- Butte, A. and Kohane, I. 2000. Mutual information relevance networks: Functional genomic clustering using pairwise entropy measurements. In Proceedings of the Pacific Symposium on Biocomputing Vol. 5., 418--429.Google Scholar
- Clauset, A., Moore, C., and Newman, M. E. J. 2008. Hierarchical structure and the prediction of missing links in networks. Nature 453, 7191, 98--101.Google Scholar
- Crane, R. and Sornette, D. 2008. Robust dynamic classes revealed by measuring the response function of a social system. Proc. Nat. Acad. Sci. 105, 41, 15649--15653.Google ScholarCross Ref
- Domingos, P. and Richardson, M. 2001. Mining the network value of customers. In Proceedings of the 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). Google ScholarDigital Library
- Edmonds, J. 1967. Optimum branchings. J. Res. Nat Bureau Stand. 71B, 233--240.Google ScholarCross Ref
- Erdős, P. and Rényi, A. 1960. On the evolution of random graphs. Publ. Math. Inst. Hungarian Acad. Sci. 5, 17--67.Google Scholar
- Friedman, N. and Koller, D. 2003. Being Bayesian about network structure. A Bayesian approach to structure discovery in Bayesian networks. Mach. Learn. 50, 1, 95--125.Google ScholarCross Ref
- Friedman, N., Nachman, I., and Pe’er, D. 1999. Learning Bayesian network structure from massive datasets: The “Sparse Candidate” algorithm. In Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence (UAI). Google ScholarDigital Library
- Friedman, J., Hastie, T., and Tibshirani, R. 2008. Sparse inverse covariance estimation with the graphical lasso. Biostat 9, 3, 432--441.Google ScholarCross Ref
- Getoor, L., Friedman, N., Koller, D., and Taskar, B. 2003. Learning probabilistic models of link structure. J. Mach. Learn. Res. 3, 707. Google ScholarDigital Library
- Ghahramani, Z. 1998. Learning dynamic Bayesian networks. In Adaptive Processing of Sequences and Data Structures, C. Lee Giles, Marco Gori Eds., Springer. Google ScholarDigital Library
- Ghosh, R. and Lerman, K. 2011. A framework for quantitative analysis of cascades on networks. In Proceedings of the 4th ACM International Conference on Web Search and Data Mining (WSDM). 665--674. Google ScholarDigital Library
- Gomez-Rodriguez, M., Balduzzi, D., and Schölkopf, B. 2011. Uncovering the temporal dynamics of diffusion networks. In Proceedings of the 28th International Conference on Machine Learning (ICML). 561--568.Google Scholar
- Goodman, L. A. 1961. Snowball sampling. Annals Math. Statist. 32, 1, 148--170.Google ScholarCross Ref
- Goyal, A., Bonchi, F., and Lakshmanan, L. 2010. Learning influence probabilities in social networks. In Proceedings of the 3rd ACM International Conference on Web Search and Data Mining (WSDM). 241--250. Google ScholarDigital Library
- Gruhl, D., Guha, R., Liben-Nowell, D., and Tomkins, A. 2004. Information diffusion through blogspace. In Proceedings of the 13th International Conference on World Wide Web (WWW). 491--501. Google ScholarDigital Library
- Heckathorn, D. 1997. Respondent-driven sampling: A new approach to the study of hidden populations. Soc. Prob. 44, 2, 174--199.Google ScholarCross Ref
- Hethcote, H. W. 2000. The mathematics of infectious diseases. SIAM Rev. 42, 4, 599--653. Google ScholarDigital Library
- Jansen, R., Yu, H., Greenbaum, D., Kluger, Y., Krogan, N., Chung, S., Emili, A., Snyder, M., Greeblatt, J., and Gerstein, M. 2003. A Bayesian networks approach for predicting protein-protein interactions from genomic data. Science 302, 5644, 449--453.Google Scholar
- Katz, E. and Lazarsfeld, P. 1955. Personal Influence: The Part Played By People in The Flow of Mass Communications. Free Press.Google Scholar
- Kearns, M., Suri, S., and Montfort, N. 2006. An experimental study of the coloring problem on human subject networks. Science 313, 5788, 824.Google ScholarCross Ref
- Kempe, D., Kleinberg, J. M., and Tardos, E. 2003. Maximizing the spread of influence through a social network. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). 137--146. Google ScholarDigital Library
- Khuller, S., Moss, A., and Naor, J. 1999. The budgeted maximum coverage problem. Inform. Process. Lett. 70, 1, 39--45. Google ScholarDigital Library
- Knuth, D. 1968. The Art of Computer Programming. Addison-Wesley.Google Scholar
- Kumar, R., Novak, J., Raghavan, P., and Tomkins, A. 2004. Structure and evolution of blogspace. Comm. ACM 47, 12, 35--39. Google ScholarDigital Library
- Leskovec, J. and Faloutsos, C. 2007. Scalable modeling of real graphs using Kronecker multiplication. In Proceedings of the 24th International Conference on Machine Learning (ICML). 504. Google ScholarDigital Library
- Leskovec, J., Kleinberg, J., and Faloutsos, C. 2005. Graphs over time: Densification laws, shrinking diameters and possible explanations. In Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery In Data Mining (KDD). Google ScholarDigital Library
- Leskovec, J., Adamic, L. A., and Huberman, B. A. 2006a. The dynamics of viral marketing. In Proceedings of the 7th ACM Conference on Electronic Commerce (EC). 228--237. Google ScholarDigital Library
- Leskovec, J., Singh, A., and Kleinberg, J. M. 2006b. Patterns of influence in a recommendation network. In Proceedings of the 10th Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD). 380--389. Google ScholarDigital Library
- Leskovec, J., Kleinberg, J. M., and Faloutsos, C. 2007a. Graph evolution: Densification and shrinking diameters. ACM Trans. Knowl. Discov. Data 1, 1, 2. Google ScholarDigital Library
- Leskovec, J., Krause, A., Guestrin, C., Faloutsos, C., VanBriesen, J., and Glance, N. 2007b. Cost-effective outbreak detection in networks. In Proceedings of the 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). 420--429. Google ScholarDigital Library
- Leskovec, J., McGlohon, M., Faloutsos, C., Glance, N., and Hurst, M. 2007c. Cascading behavior in large blog graphs. In Proceedings of the SIAM Conference on Data Mining (SDM).Google Scholar
- Leskovec, J., Lang, K. J., Dasgupta, A., and Mahoney, M. W. 2008. Statistical properties of community structure in large social and information networks. In Proceedings of the 17th International Conference on World Wide Web (WWW). Google ScholarDigital Library
- Leskovec, J., Backstrom, L., and Kleinberg, J. 2009. Meme-tracking and the dynamics of the news cycle. In Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD). ACM, New York, NY, 497--506. Google ScholarDigital Library
- Liben-Nowell, D. and Kleinberg, J. 2003. The link prediction problem for social networks. In Proceedings of the International Conference on Information and Knowledge Management (CIKM). 556--559. Google ScholarDigital Library
- Liben-Nowell, D. and Kleinberg, J. 2008. Tracing the flow of information on a global scale using Internet chain-letter data. Proc. Nat. Acad. Sci. 105, 12, 4633--4638.Google ScholarCross Ref
- Lippert, C., Stegle, O., Ghahramani, Z., and Borgwardt, K. 2009. A kernel method for unsupervised structured network inference. In Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS).Google Scholar
- Malmgren, R. D., Stouffer, D. B., Motter, A. E., and Amaral, L. A. A. N. 2008. A Poissonian explanation for heavy tails in e-mail communication. Proc. Nat. Acad. Sci. 105, 47, 18153--18158.Google ScholarCross Ref
- Meinshausen, N. and Buehlmann, P. 2006. High-dimensional graphs and variable selection with the lasso. Annals Statist. 34, 1436--1462.Google ScholarCross Ref
- Myers, S. and Leskovec, J. 2010. On the convexity of latent social network inference. In Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS).Google Scholar
- Nemhauser, G., Wolsey, L., and Fisher, M. 1978. An analysis of approximations for maximizing submodular set functions. Math. Prog. 14, 1, 265--294.Google ScholarDigital Library
- Rogers, E. M. 1995. Diffusion of Innovations Fourth Ed. Free Press, New York.Google Scholar
- Romero, D., Meeder, B., and Kleinberg, J. 2011. Differences in the mechanics of information diffusion across topics: Idioms, political hashtags, and complex contagion on Twitter. In Proceedings of the 20th International Conference on World Wide Web (WWW). ACM, 695--704. Google ScholarDigital Library
- Sadikov, S., Medina, M., Leskovec, J., and Garcia-Molina, H. 2011. Correcting for missing data in information cascades. In Proceedings of the ACM International Conference on Web Search and Data Mining (WSDM). Google ScholarDigital Library
- Schmidt, M., Niculescu-Mizil, A., and Murphy, K. 2007. Learning graphical model structure using L1-regularization paths. In Proceedings of the 21st Conference on Artificial Intelligence (AAAI). Vol. 22. Google ScholarDigital Library
- Song, L., Kolar, M., and Xing, E. 2009. Time-varying dynamic Bayesian networks. In Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS).Google Scholar
- Strang, D. and Soule, S. A. 1998. Diffusion in organizations and social movements: From hybrid corn to poison pills. Annual Rev. Sociology 24, 265--290.Google ScholarCross Ref
- Taskar, B., Wong, M. F., Abbeel, P., and Koller, D. 2003. Link prediction in relational data. In Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS).Google Scholar
- Tutte, W. 1948. The disection of equilateral triangles into equilateral triangles. Proc. Cambridge Philos. Soc. 44, 63--482.Google ScholarCross Ref
- Ver Steeg, G., Ghosh, R., and Lerman, K. 2011. What stops social epidemics? In Proceedings of the 5th International Conference on Weblogs and Social Media (ICWSM0).Google Scholar
- Vert, J. and Yamanishi, Y. 2005. Supervised graph inference. In Proceedings of the Conference on Advances in Neural Information Processing Systems (NIPS).Google Scholar
- Wainwright, M. J., Ravikumar, P., and Lafferty, J. D. 2006. High-dimensional graphical model selection using l1-regularized logistic regression. Proc. Nat. Acad. Sci.Google Scholar
- Wallinga, J. and Teunis, P. 2004. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Amer. J. Epidemiology 160, 6, 509--516.Google ScholarCross Ref
- Watts, D. J. and Dodds, P. S. 2007. Influentials, networks, and public opinion formation. J. Consumer Res. 34, 4, 441--458.Google ScholarCross Ref
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- Inferring Networks of Diffusion and Influence
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