Incremental Matrix Reordering for Similarity-Based Dynamic Data Sets

  • Parisa RastinEmail author
  • Basarab Matei
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10638)


Visualization methods are important to describe the underlying structure of a data set. When the data is not described as a vector of numerical values, a visualization can be obtained through the reordering of the corresponding similarity matrix. Although several methods of reordering exist, they all need the complete similarity matrix in memory. However, this is not possible for the analysis of dynamic data sets. The goal of this paper is to propose an original algorithm for the incremental reordering of a similarity matrix adapted to dynamic data sets. The proposed method is compared with state-of-the-art algorithms for static data-sets and applied to a dynamic data-set in order to demonstrate its efficiency.


Matrix reordering Incremental Relational data Dynamic data sets 


  1. 1.
    Bar-Joseph, Z., Gifford, D.K., Jaakkola, T.S.: Fast optimal leaf ordering for hierarchical clustering. Bioinformatics 17(Suppl. 1), S22–S29 (2001)CrossRefGoogle Scholar
  2. 2.
    Barnard, S.T., Pothen, A., Simon, H.D.: A spectral algorithm for envelope reduction of sparse matrices. In: Proceedings of the 1993 ACM/IEEE Conference on Supercomputing 1993, pp. 493–502. ACM, New York (1993)Google Scholar
  3. 3.
    Behrisch, M., Bach, B., Riche, N.H., Schreck, T., Fekete, J.D.: Matrix reordering methods for table and network visualization. In: Computer Graphics Forum (2016)Google Scholar
  4. 4.
    Bezdek, J.C., Hathaway, R.J.: VAT: a tool for visual assessment of (cluster) tendency. In: International Joint Conference on Neural Networks (IJCNN), vol. 3, pp. 2225–2230 (2002)Google Scholar
  5. 5.
    Buja, A., Swayne, D.F., Littman, M.L., Dean, N., Hofmann, H., Chen, L.: Data visualization with multidimensional scaling. J. Comput. Graph. Stat. 17(2), 444–472 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Caraux, G., Pinloche, S.: Permutmatrix: a graphical environment to arrange gene expression profiles in optimal linear order. Bioinformatics 21(7), 1280–1281 (2005)CrossRefGoogle Scholar
  7. 7.
    Chen, C.H., Hrdle, W., Unwin, A.: Handbook of Data Visualization, 1st edn. Springer-Verlag TELOS, Santa Clara (2008). doi: 10.1007/978-3-540-33037-0 Google Scholar
  8. 8.
    Conover, W.J.: Practical Nonparametric Statistics. Wiley, New York (1981)zbMATHGoogle Scholar
  9. 9.
    Ding, C., He, X.: Linearized cluster assignment via spectral ordering. In: International Conference on Machine Learning, New York, NY, USA, p. 30 (2004)Google Scholar
  10. 10.
    Gama, J.: Knowledge Discovery from Data Streams, 1st edn. Chapman & Hall/CRC, Boca Raton (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Gruvaeus, G., Wainer, H.: Two additions to hierarchical cluster analysis. Br. J. Math. Stat. Psychol. 25(2), 200–206 (1972)CrossRefGoogle Scholar
  12. 12.
    Hahsler, M., Hornik, K., Buchta, C.: Getting things in order: an introduction to the R package seriation. J. Stat. Softw. 25(3), 1–34 (2008)CrossRefGoogle Scholar
  13. 13.
    Han, J., Kamber, M.: Data Mining: Concepts and Techniques, 2nd edn., USA (2006)Google Scholar
  14. 14.
    Liiv, I.: Seriation and matrix reordering methods: an historical overview. Stat. Anal. Data Mining 3(2), 70–91 (2010)MathSciNetGoogle Scholar
  15. 15.
    Mount, D.W.: Sequence and genome analysis. Bioinformatics: Cold Spring Harbour Laboratory Press: Cold Spring Harbour 2 (2004)Google Scholar
  16. 16.
    Rastin, P., Matei, B., Cabanes, G., El Baghdadi, I.: Signal-based autonomous clustering for relational data. In: International Joint Conference on Neural Networks, IJCNN 2017 (2017)Google Scholar
  17. 17.
    Rosenkrantz, D.J., Stearns, R.E., Lewis II, P.M.: An analysis of several heuristics for the traveling salesman problem. SIAM J. Comput. 6(3), 563–581 (1977)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LIPN-CNRS, UMR 7030, Université Paris 13VilletaneuseFrance

Personalised recommendations