An Integrated QAP-Based Approach to Visualize Patterns of Gene Expression Similarity

  • Mario Inostroza-Ponta
  • Alexandre Mendes
  • Regina Berretta
  • Pablo Moscato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4828)


This paper illustrates how the Quadratic Assignment Problem (QAP) is used as a mathematical model that helps to produce a visualization of microarray data, based on the relationships between the objects (genes or samples). The visualization method can also incorporate the result of a clustering algorithm to facilitate the process of data analysis. Specifically, we show the integration with a graph-based clustering algorithm that outperforms the results against other benchmarks, namely k −means and self-organizing maps. Even though the application uses gene expression data, the method is general and only requires a similarity function being defined between pairs of objects. The microarray dataset is based on the budding yeast (S. cerevisiae). It is composed of 79 samples taken from different experiments and 2,467 genes. The proposed method delivers an automatically generated visualization of the microarray dataset based on the integration of the relationships coming from similarity measures, a clustering result and a graph structure.


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  1. 1.
    Shannon, P., Markiel, A., Ozier, O., Baliga, N., Wang, J., Ramage, D., Amin, N., Schwikowski, B., Ideker, T.: Cytoscape: A software environment for integrated models of biomolecular interaction networks. Genome Research 13, 2498–2504 (2003)CrossRefGoogle Scholar
  2. 2.
    Kohler, J., Baumbach, J., Taubert, J., Specht, M., Skusa, A., Ruegg, A., Rawlings, C., Verrier, P., Philippi, S.: Graph-based analysis and visualization of experimental results with ondex. Bioinformatics 22(11), 1383–1390 (2006)CrossRefGoogle Scholar
  3. 3.
    Eisen, M., Spellman, P., Brown, P., Botstein, D.: Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA 95, 14863–14868 (1998)CrossRefGoogle Scholar
  4. 4.
    Tavazoie, S., Hughes, J., Campbell, M., Cho, R., Church, G.: Systematic determination of genetic network architecture. Nat. Genet. (22), 281–285 (1999)CrossRefGoogle Scholar
  5. 5.
    Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Kitareewan, S., Dmitrovsky, E., Lander, E., Golub, T.: Interpreting patterns of gene expression with self-organizing maps: methods and application to hematopoietic differentiation. Proc. Natl. Acad. Sci. (96), 2907–2912 (1999)CrossRefGoogle Scholar
  6. 6.
    Burkard, R., Çela, E., Pardalos, P., Pitsoulis, L.: The quadratic assignment problem. In: Pardalos, P., Du, D. (eds.) Handbook of Combinatorial Optimization, pp. 241–338. Kluwer Academic Publishers, Dordrecht (1998)Google Scholar
  7. 7.
    Taillard, E.: Robust taboo search for the quadratic assignment problem. Parallel Computing 17(4-5), 443–455 (1991)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Oliveira, C., Pardalos, P., Resende, M.: Grasp with path-relinking for the quadratic assignment problem. In: Ribeiro, C.C., Martins, S.L. (eds.) WEA 2004. LNCS, vol. 3059, pp. 356–368. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    González-Barrios, J., Quiroz, A.: A clustering procedure based on the comparison between the k nearest neighbors graph and the minimal spanning tree. Statistics & Probability Letters 62(1), 23–34 (2003)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Inostroza-Ponta, M., Berretta, R., Mendes, A., Moscato, P.: An automatic graph layout procedure to visualize correlated data. In: Bramer, M. (ed.) Artificial Intelligence in Theory and Practice: Ifip 19th World Computer Congress. IFIP International Federation for Information Processing, vol. 217, pp. 179–188. Springer, Heidelberg (2006)Google Scholar
  11. 11.
    Shamir, R., Maron-Katz, A., Tanay, A., Linhart, C., Steinfeld, I., Sharan, R., Shiloh, Y., Elkon, R.: Expander-an integrative program suite for microarray data analysis. BMC Bioinformatics 6(232) (2005)Google Scholar
  12. 12.
    Gasch, A., Eisen, M.: Exploring the conditional coregulation of yeast gene expression through fuzzy k-means clustering. Genome Biology 3(11) (2002)Google Scholar
  13. 13.
    Handl, J., Knowles, J.: Multiobjective clustering with automatic determination of the number of clusters. Technical Report TR-COMPSYSBIO-2004-02, UMIST, Manchester, UK (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Mario Inostroza-Ponta
    • 1
  • Alexandre Mendes
    • 1
  • Regina Berretta
    • 1
  • Pablo Moscato
    • 1
  1. 1.Centre for Bioinformatics, Biomarker Discovery and Information-based Medicine, The University of Newcastle, Callaghan, NSW, 2308Australia

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