Abstract
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.
Chapter PDF
Similar content being viewed by others
References
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)
McLachlan, G.J., Peel, D.: Finite mixture models. In: Probability and Statistics – Applied Probability and Statistics Section, vol. 299. Wiley, New York (2000)
Everitt, B.S., Hand, D.J.: Finite mixture distributions. Chapman and Hall, Boca Raton (1981)
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)
Gyllenberg, M., Koski, T.: Probabilistic models for bacterial taxonomy. International Statistical Review 69, 249–276 (2000)
Burdick, D., Calimlim, M., Gehrke, J.: Mafia: A maximal frequent itemset algorithm for transactional databases. In: ICDE, pp. 443–452 (2001)
Hollmén, J., Seppänen, J.K., Mannila, H.: Mixture models and frequent sets: Combining global and local methods fordata. In: SDM (2003)
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)
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)
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)
Bishop, J.F.: Cancer facts: a concise oncology text. Harwood Academic Publishers, Amsterdam (1999)
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)
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)
Gallo, A., Miettinen, P., Mannila, H.: Finding subgroups having several descriptions: Algorithms for redescription mining. In: SDM, pp. 334–345 (2008)
Haiminen, N., Mannila, H., Terzi, E.: Comparing segmentations by applying randomization techniques. BMC Bioinformatics 8(1), 171 (2007)
Schervish, M.J.: P values: What they are and what they are not. American Statistician 50(3), 203–206 (1996)
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)
Besag, J., Clifford, P.: Generalized monte carlo significance tests. Biometrika 76(4), 633–642 (1989)
Holm, S.: A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics 6, 65–70 (1979)
Geisser, S.: A predictive approach to the random effect model. Biometrika 61(1), 101–107 (1974)
Monsteller, F., Tukey, J.: Data analysis including statistics. In: Lindzey, G., Aronson, E. (eds.) Handbook of Social Psychology, vol. 2. Addison-Wesley, Reading (1968)
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)
Wolfe, J.H.: Pattern clustering by multivariate mixture analysis. Multivariate Behavioral Research 5, 329–350 (1970)
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)
Hollmén, J.: BernoulliMix: Program package for finite mixture models of multivariate Bernoulli distributions (May 2009), http://www.cis.hut.fi/jHollmen/BernoulliMix/
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)
Gay, S.D.: Datamining in proteomics: extracting knowledge from peptide mass fingerprinting spectra. PhD thesis, University of Geneva, Geneva (2002)
Mclachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions, 1st edn. Wiley Interscience, Hoboken (November 1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Adhikari, P.R., Hollmén, J. (2010). Preservation of Statistically Significant Patterns in Multiresolution 0-1 Data. In: Dijkstra, T.M.H., Tsivtsivadze, E., Marchiori, E., Heskes, T. (eds) Pattern Recognition in Bioinformatics. PRIB 2010. Lecture Notes in Computer Science(), vol 6282. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16001-1_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-16001-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16000-4
Online ISBN: 978-3-642-16001-1
eBook Packages: Computer ScienceComputer Science (R0)