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Multiobjective Blockmodeling for Social Network Analysis

Published online by Cambridge University Press:  01 January 2025

Michael Brusco ,
Patrick Doreian ,
Douglas Steinley  and
Cinthia B. Satornino
Michael Brusco*
Affiliation:
College of Business, Florida State University
Patrick Doreian
Affiliation:
Department of Sociology, University of Pittsburgh Faculty of Social Sciences, University of Ljubljana
Douglas Steinley
Affiliation:
Department of Psychological Sciences, University of Missouri, Columbia
Cinthia B. Satornino
Affiliation:
College of Business, Florida State University
*
Requests for reprints should be sent to Michael Brusco, College of Business, Florida State University, Tallahassee, FL 32306-1110, USA. E-mail: mbrusco@fsu.edu
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Abstract

To date, most methods for direct blockmodeling of social network data have focused on the optimization of a single objective function. However, there are a variety of social network applications where it is advantageous to consider two or more objectives simultaneously. These applications can broadly be placed into two categories: (1) simultaneous optimization of multiple criteria for fitting a blockmodel based on a single network matrix and (2) simultaneous optimization of multiple criteria for fitting a blockmodel based on two or more network matrices, where the matrices being fit can take the form of multiple indicators for an underlying relationship, or multiple matrices for a set of objects measured at two or more different points in time. A multiobjective tabu search procedure is proposed for estimating the set of Pareto efficient blockmodels. This procedure is used in three examples that demonstrate possible applications of the multiobjective blockmodeling paradigm.

Keywords

social networksblockmodelingmultiobjective programmingheuristicstabu search

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 3 , July 2013 , pp. 498 - 525
Copyright
Copyright © 2012 The Psychometric Society

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References

Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P. (2008). Mixed-membership stochastic blockmodels. Journal of Machine Learning Research, 9, 1981–2014Google ScholarPubMed
Batagelj, V., Ferligoj, A., Doreian, P. (1992). Direct and indirect methods for structural equivalence. Social Networks, 14, 63–90CrossRefGoogle Scholar
Bickel, P.J., Chen, A. (2009). A nonparametric view of network models and Newman–Girvan and other modularities. Proceedings of the National Academy of Sciences of the United States of America, 106, 21068–2107310.1073/pnas.0907096106CrossRefGoogle ScholarPubMed
Breiger, R.L., Boorman, S.A., Arabie, P. (1975). An algorithm for clustering relational data with applications to social network analysis and comparison to multidimensional scaling. Journal of Mathematical Psychology, 12, 328–38310.1016/0022-2496(75)90028-0CrossRefGoogle Scholar
Brusco, M.J., Cradit, J.D., Stahl, S. (2002). A simulated annealing heuristic for a bicriterion problem in market segmentation. Journal of Marketing Research, 39, 99–10910.1509/jmkr.39.1.99.18932CrossRefGoogle Scholar
Brusco, M.J., Cradit, J.D., Tashchian, A. (2003). Multicriterion clusterwise regression for joint segmentation settings: An application to customer value. Journal of Marketing Research, 40, 225–23410.1509/jmkr.40.2.225.19227CrossRefGoogle Scholar
Brusco, M., Doreian, P., Mrvar, A., Steinley, D. (2011). Linking theory, models, and data to understand social network phenomena: Two algorithms for relaxed structural balance partitioning. Sociological Methods & Research, 40, 57–8710.1177/0049124110384947CrossRefGoogle Scholar
Brusco, M., Doreian, P., Mrvar, A., & Steinley, D. (in press). An exact algorithm for blockmodeling of two-mode network data. The Journal of Mathematical Sociology. Google Scholar
Brusco, M.J., Stahl, S. (2001). An interactive multiobjective programming approach to combinatorial data analysis. Psychometrika, 66, 5–2410.1007/BF02295729CrossRefGoogle Scholar
Brusco, M.J., Stahl, S. (2005). Branch-and-bound applications in combinatorial data analysis, New York: SpringerGoogle Scholar
Brusco, M., Steinley, D. (2007). A variable neighborhood search method for generalized blockmodeling of two-mode binary matrices. Journal of Mathematical Psychology, 51, 325–338CrossRefGoogle Scholar
Brusco, M.J., Steinley, D. (2009). Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence. Journal of Mathematical Psychology, 53, 577–58510.1016/j.jmp.2009.08.003CrossRefGoogle ScholarPubMed
Brusco, M.J., Steinley, D. (2009). Cross validation issues in multiobjective clustering. British Journal of Mathematical & Statistical Psychology, 62, 349–368CrossRefGoogle ScholarPubMed
Brusco, M., Steinley, D. (2010). K-balance partitioning: An exact method with application to generalized structural balance and other psychological contexts. Psychological Methods, 15, 145–15710.1037/a0017738CrossRefGoogle ScholarPubMed
Brusco, M., Steinley, D. (2011). A tabu search heuristic for deterministic two-mode blockmodeling. Psychometrika, 76, 612–633CrossRefGoogle ScholarPubMed
Burt, R.S. (1976). Positions in networks. Social Forces, 55, 93–12210.2307/2577097CrossRefGoogle Scholar
Cartwright, D., Harary, F. (1956). Structural balance: A generalization of Heider’s theory. Psychological Review, 63, 277–29310.1037/h0046049CrossRefGoogle ScholarPubMed
Davis, J.A. (1967). Clustering and structural balance in graphs. Human Relations, 20, 181–18710.1177/001872676702000206CrossRefGoogle Scholar
Delattre, M., Hansen, P. (1980). Bicriterion cluster analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2, 277–29110.1109/TPAMI.1980.4767027CrossRefGoogle ScholarPubMed
Dempster, A.P., Laird, N.M., Rubin, D.B. (1977). Maximum likelihood from incomplete data via the E–M algorithm. Journal of the Royal Statistical Society. Series B, 39, 1–3810.1111/j.2517-6161.1977.tb01600.xCrossRefGoogle Scholar
DeSarbo, W.S., Grisaffe, D. (1998). Combinatorial optimization approaches to constrained market segmentation: An application to industrial market segmentation. Marketing Letters, 9, 115–134CrossRefGoogle Scholar
Doreian, P. (2008). A multiple indicator approach to blockmodeling signed networks. Social Networks, 30, 247–25810.1016/j.socnet.2008.03.005CrossRefGoogle Scholar
Doreian, P., Batagelj, V., Ferligoj, A. (1994). Partitioning networks based on generalized concepts of equivalence. The Journal of Mathematical Sociology, 19, 1–27CrossRefGoogle Scholar
Doreian, P., Batagelj, V., Ferligoj, A. (2004). Generalized blockmodeling of two-mode network data. Social Networks, 26, 29–5310.1016/j.socnet.2004.01.002CrossRefGoogle Scholar
Doreian, P., Batagelj, V., Ferligoj, A. (2005). Generalized blockmodeling, Cambridge: Cambridge University PressGoogle Scholar
Doreian, P., Mrvar, A. (1996). A partitioning approach to structural balance. Social Networks, 18, 149–16810.1016/0378-8733(95)00259-6CrossRefGoogle Scholar
Doreian, P., Mrvar, A. (2009). Partitioning signed social networks. Social Networks, 31, 1–1110.1016/j.socnet.2008.08.001CrossRefGoogle Scholar
Erhgott, M., Gandibleaux, X. (2000). A survey and annotated bibliography on multiobjective combinatorial optimization. OR Spektrum, 22, 425–460CrossRefGoogle Scholar
Ehrgott, M., Wiecek, M.M. (2005). Multiobjective programming. In Figueira, J., Greco, S., Ehrgott, M. (Eds.), Multiple criteria decision analysis: State of the art surveys, New York: Springer 667722CrossRefGoogle Scholar
Ferligoj, A., Batagelj, V. (1992). Direct multicriteria clustering algorithms. Journal of Classification, 9, 43–6110.1007/BF02618467CrossRefGoogle Scholar
Fienberg, S.E., Meyer, M.M., Wasserman, S.S. (1985). Statistical analysis of multiple sociometric relations. Journal of the American Statistical Association, 80, 51–6710.1080/01621459.1985.10477129CrossRefGoogle Scholar
Gilks, W.R., Richardson, S., Spieglhalter, D.J. (1996). Markov chain Monte Carlo in practice, New York: Chapman & HallGoogle Scholar
Glover, F. (1989). Tabu search—Part I. ORSA Journal on Computing, 1, 190–206CrossRefGoogle Scholar
Glover, F. (1990). Tabu search—Part II. ORSA Journal on Computing, 2, 4–32CrossRefGoogle Scholar
Glover, F., Laguna, M. (1993). Tabu search. In Reeves, C. (Eds.), Modern heuristic techniques for combinatorial problems, Oxford: Blackwell 70141Google Scholar
Goldenberg, A., Zheng, A., Fienberg, S.E., Airoldi, E.M. (2009). A survey of statistical network models. Foundations and Trends in Machine Learning, 2, 1–117Google Scholar
Govaert, G., Nadif, M. (2003). Clustering with block mixture models. Pattern Recognition, 36, 463–47310.1016/S0031-3203(02)00074-2CrossRefGoogle Scholar
Handcock, M.S., Raftery, A.E., Tantrum, J. (2007). Model-based clustering for social networks (with discussion). Journal of the Royal Statistical Society. Series A, 170, 301–35410.1111/j.1467-985X.2007.00471.xCrossRefGoogle Scholar
Handl, J., Kell, D.B., Knowles, J. (2007). Multiobjective optimization in bioinformatics and computational biology. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 4, 279–29210.1109/TCBB.2007.070203CrossRefGoogle ScholarPubMed
Handl, J., Knowles, J. (2007). An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation, 11, 56–76CrossRefGoogle Scholar
Hartigan, J. (1972). Direct clustering of a data matrix. Journal of the American Statistical Association, 67, 123–12910.1080/01621459.1972.10481214CrossRefGoogle Scholar
Heider, F. (1946). Attitudes and cognitive organization. The Journal of Psychology, 21, 107–11210.1080/00223980.1946.9917275CrossRefGoogle ScholarPubMed
Holland, P.W., Laskey, K.B., Leinhardt, S. (1983). Stochastic blockmodels: First steps. Social Networks, 5, 109–13710.1016/0378-8733(83)90021-7CrossRefGoogle Scholar
Karrer, B., Newman, M.E.J. (2011). Stochastic blockmodels and community structure in networks. Physical Review E, 83 10.1103/PhysRevE.83.016107CrossRefGoogle ScholarPubMed
Kulturel-Konak, S., Coit, D.W., Baheranwala, F. (2008). Pruned Pareto-optimal sets for the system redundancy allocation problem based on prioritized objectives. Journal of Heuristics, 14, 335–35710.1007/s10732-007-9041-3CrossRefGoogle Scholar
Kulturel-Konak, S., Smith, A.E., Norman, B.A. (2006). Multi-objective tabu search using a multinomial probability mass function. European Journal of Operational Research, 169, 918–93110.1016/j.ejor.2004.08.026CrossRefGoogle Scholar
Lemann, T.B., Solomon, R.L. (1952). Group characteristics as revealed in sociometric patterns and personality ratings. Sociometry, 15, 7–90CrossRefGoogle Scholar
Liu, Y., Ram, S., Lusch, R., Brusco, M. (2010). Multicriterion market segmentation: A new model, implementation and evaluation. Marketing Science, 29, 880–89410.1287/mksc.1100.0565CrossRefGoogle Scholar
Lorrain, F., White, H.C. (1971). Structural equivalence of individuals in social networks. The Journal of Mathematical Sociology, 1, 49–80CrossRefGoogle Scholar
McCormick, W.T., Schweitzer, P.J., White, T.W. (1972). Problem decomposition and data reorganization by a clustering technique. Operations Research, 20, 993–100910.1287/opre.20.5.993CrossRefGoogle Scholar
Newcomb, T.N. (1961). The acquaintance process, New York: Holt, Rinehart & Winston 10.1037/13156-000CrossRefGoogle Scholar
Nowicki, K., Snijders, T.A.B. (2001). Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association, 96, 1077–108710.1198/016214501753208735CrossRefGoogle Scholar
Ripon, K.S.N., Tsang, C.-H., Kwong, S., Ip, M.-K. (2006). Multi-objective evolutionary clustering using variable-length real jumping genes genetic algorithm. Proceedings of the 18th international conference on pattern recognition, 12001203Google Scholar
Saha, S., Bandyopadhyay, S. (2010). A new multiobjective clustering technique based on the concepts of stability and symmetry. Knowledge and Information Systems, 23, 1–2710.1007/s10115-009-0204-4CrossRefGoogle Scholar
Sampson, S.F. (1968). A novitiate in a period of change: An experimental case study of relationships. Unpublished Ph.D. dissertation, Department of Sociology, Cornell University, Ithaca, NY. Google Scholar
Steinley, D., Brusco, M.J., Wasserman, S. (2011). Clusterwise p ∗ models for social network analysis. Statistical Analysis and Data Mining, 4, 487–49610.1002/sam.10139CrossRefGoogle Scholar
Ulungu, E., Teghem, J. (1994). The two-phase method: An efficient procedure to solve biobjective combinatorial optimization problems. Foundations of Computing and Decision Sciences, 20, 149–165Google Scholar
Wasserman, S., Faust, K. (1994). Social network analysis: methods and applications, Cambridge: Cambridge University PressCrossRefGoogle Scholar
Wasserman, S., Pattison, P. (1996). Logit models and logistic regression for social networks: I. An introduction to Markov graphs and p ∗. Psychometrika, 61, 401–42510.1007/BF02294547CrossRefGoogle Scholar
White, H.C., Boorman, S.A., Brieger, R.L. (1976). Social structure from multiple networks. I. Blockmodels of roles and positions. American Journal of Sociology, 81, 730–77910.1086/226141CrossRefGoogle Scholar
Žnidaršič, A., Ferligoj, A., Doreian, P. (2012). Non-response in social networks: The impact of different non-response treatments on the stability of blockmodels. Social Networks, 34, 438–45010.1016/j.socnet.2012.02.002CrossRefGoogle Scholar