Modeling and Multiway Analysis of Chatroom Tensors

  • Evrim Acar
  • Seyit A. Çamtepe
  • Mukkai S. Krishnamoorthy
  • Bülent Yener
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3495)


This work identifies the limitations of n-way data analysis techniques in multidimensional stream data, such as Internet chatroom communications data, and establishes a link between data collection and performance of these techniques. Its contributions are twofold. First, it extends data analysis to multiple dimensions by constructing n-way data arrays known as high order tensors. Chatroom tensors are generated by a simulator which collects and models actual communication data. The accuracy of the model is determined by the Kolmogorov-Smirnov goodness-of-fit test which compares the simulation data with the observed (real) data. Second, a detailed computational comparison is performed to test several data analysis techniques including svd [1], and multiway techniques including Tucker1, Tucker3 [2], and Parafac [3].


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  1. 1.
    Golub, G., Loan, C.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  2. 2.
    Tucker, L.: Some mathematical notes on three mode factor analysis. Psychometrika 31, 279–311 (1966)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Harshman, R.: Foundations of the parafac procedure: Model and conditions for an explanatory multi-mode factor analysis. UCLA WPP 16, 1–84 (1970)Google Scholar
  4. 4.
    Kalt, C.: Internet Relay Chat. RFC 2810, 2811, 2812, 2813 (2000)Google Scholar
  5. 5.
    Krebs, V.: An introduction to social network analysis (2004), (accessed February 2004)
  6. 6.
    Magdon-Ismail, M., Goldberg, M., Siebecker, D., Wallace, W.: Locating hidden groups in communication networks using hidden markov models. In: Chen, H., Miranda, R., Zeng, D.D., Demchak, C.C., Schroeder, J., Madhusudan, T. (eds.) ISI 2003. LNCS, vol. 2665, pp. 126–137. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Goldberg, M., Horn, P., Magdon-Ismail, M., Riposo, J., Siebecker, D., Wallace, W., Yener, B.: Statistical modeling of social groups on communication networks. In: First conference of the North American Association for Computational Social and Organizational Science, NAACSOS 2003 (2003)Google Scholar
  8. 8.
    Camtepe, S., Krishnamoorthy, M., Yener, B.: A tool for internet chatroom surveillance. In: Chen, H., Moore, R., Zeng, D.D., Leavitt, J. (eds.) ISI 2004. LNCS, vol. 3073, pp. 252–265. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Camtepe, S., Goldberg, M., Magdon-Ismail, M., Krishnamoorty, M.: Detecting conversing groups of chatters: A model, algorithms, and tests. In: IADIS International Conference on Applied Computing (2005)Google Scholar
  10. 10.
    Mutton, P., Golbeck, J.: Visualization of semantic metadata and ontologies. In: Seventh International Conference on Information Visualization (IV 2003), pp. 300–305. IEEE, Los Alamitos (2003)CrossRefGoogle Scholar
  11. 11.
    Mutton, P.: Piespy social network bot (2001), (accessed January 2005)
  12. 12.
    Viegas, F., Donath, J.: Chat circles. In: ACM SIGCHI, pp. 9–16. ACM, New York (1999)Google Scholar
  13. 13.
    Kroonenberg, P.: Three-mode Principal Component Analysis: Theory and Applications. DSWO Press, Leiden (1983)Google Scholar
  14. 14.
    Leibovici, D., Sabatier, R.: A singular value decomposition of a k-ways array for a principal component analysis of multi-way data, the pta-k. Linear Algebra and its Applications 269, 307–329 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Lathauwer, L., Moor, B., Van de walle, J.: On the best rank-1 and rank-(r1,r2,.,rn) approximation of higher-order tensors. SIAM J. Matrix Analysis and Applications 21, 1324–1342 (2000)zbMATHCrossRefGoogle Scholar
  16. 16.
    Zhang, T., Golub, G.: Rank-one approximation to higher order tensors. SIAM J. Matrix Analysis and Applications 23, 534–550 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Kolda, T.: Orthogonal tensor decompositions. SIAM J. Matrix Analysis and Applications 23, 243–255 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Kofidis, E., Regalia, P.: On the best rank-1 approximation of higher-order supersymmetric tensors. SIAM J. Matrix Analysis and Applications 22, 863–884 (2002)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Kolda, T.: A counter example to the possibility of an extension of the eckart-young low-rank approximation theorem for the orthogonal rank tensor decomposition. SIAM J. Matrix Analysis and Applications 24, 762–767 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Kolda, T., Bader, B.: Matlab tensor classes for fast algorithm prototyping. Technical Report SAND2004-5187, Sandia National Laboratories (2004)Google Scholar
  21. 21.
    Andersson, C., Bro, R.: The N-way Toolbox for MATLAB. Chemometrics and Intelligent Laboratory Systems (2000)Google Scholar
  22. 22.
    Andrews, D.: Plots of high-dimensional data. Biometrics 28, 125–136 (1972)CrossRefGoogle Scholar
  23. 23.
    Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algoritms. Plenum Press, New York (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Evrim Acar
    • 1
  • Seyit A. Çamtepe
    • 1
  • Mukkai S. Krishnamoorthy
    • 1
  • Bülent Yener
    • 1
  1. 1.Department of Computer ScienceRensselaer Polytechnic InstituteTroy

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