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On Multivariate Markov Chains for Common and Non-Common Objects in Multiple Networks

Published online by Cambridge University Press:  28 May 2015

Xutao Li ,
Wen Li ,
Michael K. Ng  and
Yunming Ye
Xutao Li*
Affiliation:
Department of Computer Science, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
Wen Li*
Affiliation:
School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China
Michael K. Ng*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Yunming Ye*
Affiliation:
Department of Computer Science, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, 518055, China
*
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
Corresponding author.Email address:[email protected]
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Abstract

Node importance or centrality evaluation is an important methodology for network analysis. In this paper, we are interested in the study of objects appearing in several networks. Such common objects are important in network-network interactions via object-object interactions. The main contribution of this paper is to model multiple networks where there are some common objects in a multivariate Markov chain framework, and to develop a method for solving common and non-common objects’ stationary probability distributions in the networks. The stationary probability distributions can be used to evaluate the importance of common and non-common objects via network-network interactions. Our experimental results based on examples of co-authorship of researchers in different conferences and paper citations in different categories have shown that the proposed model can provide useful information for researcher-researcher interactions in networks of different conferences and for paper-paper interactions in networks of different categories.

Keywords

60J1091D3005C81transition probability multivariate Markov chainsstationary probability distributionirreduciblemultiple networks
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 5 , Issue 3 , August 2012 , pp. 384 - 402
Copyright
Copyright © Global Science Press Limited 2012

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References

[1]Bini, D., Del Corso, G., and Romani, F., Evaluating scientific products by means of citation-based models: a first analysis and validation. Electronic Transactions on Numerical Analysis, 33:1–16, 2008.Google Scholar
[2]Bini, D., Del Corso, G., and Romani, F., A combined approach for evaluating papers, authors and scientific journals. Journal of computational and applied mathematics, 234(11):3104–3121, 2010.Google Scholar
[3]Borgatti, S., Centrality and network flow. Social Networks, 27(1):55–71, 2005.CrossRefGoogle Scholar
[4]Brandes, U., On variants of shortest-path betweenness centrality and their generic computation. Social Networks, 30(2):136–145, 2008.CrossRefGoogle Scholar
[5]Ching, W., Fung, E., and Ng, M., A multivariate Markov chain model for categorical data sequences and its applications in demand predictions. IMA Journal of Management Mathematics, 13(3):187, 2002.Google Scholar
[6]Cohn, D. and Chang, H., Learning to probabilistically identify authoritative documents. In Proc. of International Conference on Machine Learning, pp. 167–174, 2000.Google Scholar
[7]Del Corso, G. and Romani, F., Versatile weighting strategies for a citation-based research evaluation model. Bulletin of the Belgian Mathematical Society-Simon Stevin, 16(4):723–743, 2009.CrossRefGoogle Scholar
[8]Deng, H., Lyu, M., and King, I., A generalized Co-HITS algorithm and its application to bipartite graphs. In Proc. of ACM SIGKDD, pp. 239–248, 2009.Google Scholar
[9]Ercsey-Ravasz, M. and Toroczkai, Z., Centrality scaling in large networks. Phys. Rev. Lett., 105(3):038701, Jul 2010.CrossRefGoogle ScholarPubMed
[10]Freeman, L., A set of measures of centrality based on betweenness. Sociometry, pp. 35–41, 1977.Google Scholar
[11]Freeman, L., Centrality in social networks conceptual clarification. Social networks, 1(3):215–239, 1979.Google Scholar
[12]Haveliwala, T. H., Topic-sensitive PageRank. In Proc. of ACM World Wide Web, 2002.Google Scholar
[13]Kleinberg, J., Authoritative sources in a hyperlinked environment. Journal of the ACM (JACM), 46(5):604–632, 1999.CrossRefGoogle Scholar
[14]Kolda, T., Bader, B., and Kenny, J., Higher-order web link analysis using multilinear algebra. In Proc. of IEEE International Conference on Data Mining, pp. 242–249, 2005.Google Scholar
[15]Latora, V. and Marchiori, M., A measure of centrality based on network efficiency. New Journal of Physics, 9:188, 2007.CrossRefGoogle Scholar
[16]Meyer, C., Stochastic complementation, uncoupling Markov chains and the theory of nearly reducible systems. SIAM Rev., 31(2):240–272, 1989.CrossRefGoogle Scholar
[17]Newman, M., A measure of betweenness centrality based on random walks. Social networks, 27(1):39–54, 2005.CrossRefGoogle Scholar
[18]Nie, Z., Zhang, Y., Wen, J., and Ma, W., Object-level ranking: Bringing order to web objects. In Proc. of ACM World Wide Web, pp. 567–574, 2005.Google Scholar
[19]Page, L., Brin, S., Motwani, R., and Winograd, T., The pagerank citation ranking: Bringing order to the web. Technical report, Stanford Digital Library Technologies Project, 1998.Google Scholar
[20]Puzis, R., Elovici, Y., and Dolev, S., Fast algorithm for successive computation of group betweenness centrality. Phys. Rev. E, 76(5):056709, Nov 2007.CrossRefGoogle ScholarPubMed
[21]Zhou, D., Orshanskiy, S., Zha, H., and Giles, C., Co-ranking authors and documents in a heterogeneous network. In Proc. of IEEE International Conference on Data Mining, 2007.Google Scholar