Collective Sampling and Analysis of High Order Tensors for Chatroom Communications

  • Evrim Acar
  • Seyit A. Çamtepe
  • Bülent Yener
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3975)


This work investigates the accuracy and efficiency tradeoffs between centralized and collective (distributed) algorithms for (i) sampling, and (ii) n-way data analysis techniques in multidimensional stream data, such as Internet chatroom communications. Its contributions are threefold. First, we use the Kolmogorov-Smirnov goodness-of-fit test to show that statistical differences between real data obtained by collective sampling in time dimension from multiple servers and that of obtained from a single server are insignificant. Second, we show using the real data that collective data analysis of 3-way data arrays (users x keywords x time) known as high order tensors is more efficient than centralized algorithms with respect to both space and computational cost. Furthermore, we show that this gain is obtained without loss of accuracy. Third, we examine the sensitivity of collective constructions and analysis of high order data tensors to the choice of server selection and sampling window size. We construct 4-way tensors (users x keywords x time x servers) and analyze them to show the impact of server and window size selections on the results.


Singular Value Decomposition Singular Vector Server Selection Interarrival Time Message Size 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Acar, E., Çamtepe, S.A., Krishnamoorthy, M.S., Yener, B.: Modeling and multiway analysis of chatroom tensors. In: Kantor, P., Muresan, G., Roberts, F., Zeng, D.D., Wang, F.-Y., Chen, H., Merkle, R.C. (eds.) ISI 2005. LNCS, vol. 3495, pp. 256–268. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    Golub, G.H., Loan, C.F.V.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)zbMATHGoogle Scholar
  3. 3.
    Kargupta, H., Huang, W., Sivakumar, K., Johnson, E.: Distributed Clustering Using Collective Principal Component Analysis. Knowledge and Information Systems Journal 3(4), 422–448 (2001)zbMATHCrossRefGoogle Scholar
  4. 4.
    Timmerman, M., Kiers, H.A.L.: Three-mode principal component analysis: Choosing the numbers of components and sensitivity to local optima. British Journal of Mathematical and Statistical Psychology 53, 1–16 (2000)CrossRefGoogle Scholar
  5. 5.
    Kiers, H.A.L., der Kinderen, A.: A fast method for choosing the numbers of components in Tucker3 analysis. British Journal of Mathematical and Statistical Psychology 56, 119–125 (2003)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Lathauwer, L.D., Moor, B.D., Vanderwalle, J.: A Multilinear Singular Value Decomposition. SIAM Journal on Matrix Analysis and Applications 21(4), 1253–1278 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    MacQueen, J.B.: Some Methods for classification and Analysis of Multivariate Observations. In: Proceedings of 5-th Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297. University of California Press, Berkeley (1967)Google Scholar
  8. 8.
    Smilde Age, K., Westerhuis, J.A., Boque, R.: Multiway Multiblock Component and Covariates Regression Models. J. Chemometrics 14, 301–331 (2000)CrossRefGoogle Scholar
  9. 9.
    Tucker, L.: Some mathematical notes on three mode factor analysis. Psychometrika 31, 279–311 (1966)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Wansbeek, T., Verhees, J.: Models for multidimensional matrices in econometrics and psychometrics. In: Coppi, R., Bolasco, S. (eds.) Multiway Data Analysis. North Holland, AmsterdamGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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