Skip to main content
Log in

Management and analysis of DNA microarray data by using weighted trees

  • Original Paper
  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

Abstract

We investigate discrete structures and combinatoric modeling of weighted prefix trees for managing and analyzing DNA microarray data. We describe the algorithms to construct the weighted trees for these data. Using these weighted trees with our algorithms, we propose methods to compute the appearance probability of a DNA microarray, to compare the informational distances in the expression of genes between the DNA microarrays, to search the characteristic microarrays and the group of candidate genes suggestive of a pathology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Salomaa, A.: Theory of automata. Pergamon Press (1969)

  2. Jacob, G.: Langages, Automates, Séries Formelles. Publications no 107, Laboratoire d’Informatique, USTL (1978)

  3. Inza I. (2004). Filter versus wrapper gene selection approaches in DNA microarray domains. Artif. Intell. Med. 31: 91–103

    Article  Google Scholar 

  4. Berstel J., Reutenauer, C.: Les séries rationnelles et leurs langage. Masson (1984)

  5. Boulicaut, J.F., Gandrillon, O.: Informatique pour l’analyse du transcriptome. Hermee-Lavoisier, (2004)

  6. Bourdon J. (2001). Size and path length of Patricia tries: dynamical soures context. Random Struct Algorithms 19(3–4): 289–315

    Article  Google Scholar 

  7. Quackenbush, J.: Computational analysis of microarray data. Nat Genet 32, 509–514 (2001)

    Google Scholar 

  8. Sakarovitch, J.: Elements de theorie des automates. Vuibert Informatique (2003)

  9. Brown, M., Grundy, W., et al.: Knowledge-based analysis of microarray gene expression data by using support vector machines. University of California (1999)

  10. Crochemore, M., et al.: Algorithmique du texte. Vuibert Informatique (2001)

  11. Eisen M. and Botstein D. (1998). Cluster analysis and display genome-wide expression patterns. Pro. Natl. Acad. Sci 95(25): 14863–14868

    Article  Google Scholar 

  12. Fliess, M.: Automates stochastiques et séries rationnelles non commutatives. In: Nivat, M.~(ed.), Proceedings International Colloquium on Automata. Languages and Programming (ICALP), pp. 397–411 (1972)

  13. Kerr M. and Churchill G. (2001). Experimental design for gene expression microarrays. Biostatistics 2: 183–201

    Article  Google Scholar 

  14. Lothaire, M.: Combinatorics on Words. Addison-Wesley Publishing (1983)

  15. Flajolet, P., Sedgewick, R.: An Introduction to the Analysis of Algorithms. Addison-Wesley (1996)

  16. Walker P. and Famili A. (2004). Data mining of gene expression changes in Alzheimer brain. Artif. Intell. Med 31: 137–154

    Article  Google Scholar 

  17. Peeter R. (2000). The maximum edge biclique problem is NP-complete. Discrete Appl. Math. 131(3): 651–654

    Article  Google Scholar 

  18. Cover, T.M., Thomas, J.A.: Elements of Information Theory. Wiley Interscience Publication (1991)

  19. Tran, T., Nguyen, C.C., Minh, H.N.: Data mining of gene expression microarray via weighted prefix trees. In: Proceedings PAKDD’05, LNAI 3518, pp. 21–31. Springer Verlag (2005)

  20. Tran, T., Nguyen, C.C., Minh, H.N.: Bi-clustering des donns de biopuces par les arbres pondérés de plus long préfixe, accepté. TSI. vol. Modisation et Simulation pour la Post-Gomique, Hemes-Lavoisier (2006)

  21. Szpankowski, W.: Average Case Analysis of Algorithms on Sequences. Wiley (2001)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Trang Tran.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tran, T., Nguyen, C.C. & Hoang, N.M. Management and analysis of DNA microarray data by using weighted trees. J Glob Optim 39, 623–645 (2007). https://doi.org/10.1007/s10898-007-9158-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-007-9158-9

Keywords

Navigation