Preservation of Statistically Significant Patterns in Multiresolution 0-1 Data

  • Prem Raj Adhikari
  • Jaakko Hollmén
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6282)


Measurements in biology are made with high throughput and high resolution techniques often resulting in data in multiple resolutions. Currently, available standard algorithms can only handle data in one resolution. Generative models such as mixture models are often used to model such data. However, significance of the patterns generated by generative models has so far received inadequate attention. This paper analyses the statistical significance of the patterns preserved in sampling between different resolutions and when sampling from a generative model. Furthermore, we study the effect of noise on the likelihood with respect to the changing resolutions and sample size. Finite mixture of multivariate Bernoulli distribution is used to model amplification patterns in cancer in multiple resolutions. Statistically significant itemsets are identified in original data and data sampled from the generative models using randomization and their relationships are studied. The results showed that statistically significant itemsets are effectively preserved by mixture models. The preservation is more accurate in coarse resolution compared to the finer resolution. Furthermore, the effect of noise on data on higher resolution and with smaller number of sample size is higher than the data in lower resolution and with higher number of sample size.


Multiresolution data statistical significance frequent itemset mixture modelling 


  1. 1.
    Shaffer, L.G., Tommerup, N.: ISCN 2005: An International System for Human Cytogenetic Nomenclature(2005) Recommendations of the International Standing Committee on Human Cytogenetic Nomenclature. Karger (2005)Google Scholar
  2. 2.
    McLachlan, G.J., Peel, D.: Finite mixture models. In: Probability and Statistics – Applied Probability and Statistics Section, vol. 299. Wiley, New York (2000)Google Scholar
  3. 3.
    Everitt, B.S., Hand, D.J.: Finite mixture distributions. Chapman and Hall, Boca Raton (1981)CrossRefGoogle Scholar
  4. 4.
    Hollmén, J., Tikka, J.: Compact and understandable descriptions of mixtures of bernoulli distributions. In: Berthold, M.R., Shawe-Taylor, J., Lavrač, N. (eds.) IDA 2007. LNCS (LNAI), vol. 4723, pp. 1–12. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Gyllenberg, M., Koski, T.: Probabilistic models for bacterial taxonomy. International Statistical Review 69, 249–276 (2000)CrossRefGoogle Scholar
  6. 6.
    Burdick, D., Calimlim, M., Gehrke, J.: Mafia: A maximal frequent itemset algorithm for transactional databases. In: ICDE, pp. 443–452 (2001)Google Scholar
  7. 7.
    Hollmén, J., Seppänen, J.K., Mannila, H.: Mixture models and frequent sets: Combining global and local methods fordata. In: SDM (2003)Google Scholar
  8. 8.
    Agrawal, R., Imieliński, T., Swami, A.: Mining association rules between sets of items in large databases. In: SIGMOD ’93: Proceedings of the 1993 ACM SIGMOD international conference on Management of data, pp. 207–216. ACM, New York (1993)CrossRefGoogle Scholar
  9. 9.
    Mannila, H., Toivonen, H., Verkamo, A.I.: Efficient algorithms for discovering association rules. In: Fayyad, U.M., Uthurusamy, R. (eds.) AAAI Workshop on Knowledge Discovery in Databases (KDD-94), Seattle, Washington, pp. 181–192. AAAI Press, Menlo Park (1994)Google Scholar
  10. 10.
    Adhikari, P.R., Hollmén, J.: Patterns from multiresolution 0-1 data. In: UP ’10: Proceedings of the 16th ACM SIGKDD. ACM, New York (to appear, 2010)Google Scholar
  11. 11.
    Bishop, J.F.: Cancer facts: a concise oncology text. Harwood Academic Publishers, Amsterdam (1999)Google Scholar
  12. 12.
    Myllykangas, S., Tikka, J., Böhling, T., Knuutila, S., Hollmén, J.: Classification of human cancers based on DNA copy number amplification modeling. BMC Medical Genomics 1, 15 (2008)CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Gionis, A., Mannila, H., Mielikäinen, T., Tsaparas, P.: Assessing data mining results via swap randomization. ACM Transactions on Knowledge Discovery from Data 1(3), 14 (2007)CrossRefGoogle Scholar
  14. 14.
    Gallo, A., Miettinen, P., Mannila, H.: Finding subgroups having several descriptions: Algorithms for redescription mining. In: SDM, pp. 334–345 (2008)Google Scholar
  15. 15.
    Haiminen, N., Mannila, H., Terzi, E.: Comparing segmentations by applying randomization techniques. BMC Bioinformatics 8(1), 171 (2007)CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Schervish, M.J.: P values: What they are and what they are not. American Statistician 50(3), 203–206 (1996)Google Scholar
  17. 17.
    De La Horra, J., Rodriguez-Bernal, M.T.: Posterior predictive p-values: What they are and what they are not. Test 10(1), 75–86 (2001)CrossRefGoogle Scholar
  18. 18.
    Besag, J., Clifford, P.: Generalized monte carlo significance tests. Biometrika 76(4), 633–642 (1989)CrossRefGoogle Scholar
  19. 19.
    Holm, S.: A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65–70 (1979)Google Scholar
  20. 20.
    Geisser, S.: A predictive approach to the random effect model. Biometrika 61(1), 101–107 (1974)CrossRefGoogle Scholar
  21. 21.
    Monsteller, F., Tukey, J.: Data analysis including statistics. In: Lindzey, G., Aronson, E. (eds.) Handbook of Social Psychology, vol. 2. Addison-Wesley, Reading (1968)Google Scholar
  22. 22.
    Tikka, J., Hollmén, J., Myllykangas, S.: Mixture modeling of DNA copy number amplification patterns in cancer. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 972–979. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  23. 23.
    Wolfe, J.H.: Pattern clustering by multivariate mixture analysis. Multivariate Behavioral Research 5, 329–350 (1970)CrossRefPubMedGoogle Scholar
  24. 24.
    Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 39(1), 1–38 (1977)Google Scholar
  25. 25.
    Hollmén, J.: BernoulliMix: Program package for finite mixture models of multivariate Bernoulli distributions (May 2009),
  26. 26.
    Hanhijärvi, S., Ojala, M., Vuokko, N., Puolamäki, K., Tatti, N., Mannila, H.: Tell me something I don’t know: randomization strategies for iterative data mining. In: KDD ’09: Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 379–388. ACM, New York (2009)CrossRefGoogle Scholar
  27. 27.
    Gay, S.D.: Datamining in proteomics: extracting knowledge from peptide mass fingerprinting spectra. PhD thesis, University of Geneva, Geneva (2002)Google Scholar
  28. 28.
    Mclachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions, 1st edn. Wiley Interscience, Hoboken (November 1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Prem Raj Adhikari
    • 1
  • Jaakko Hollmén
    • 1
  1. 1.Department of Information and Computer ScienceAalto University School of Science and TechnologyAalto, EspooFinland

Personalised recommendations