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Mixture Models from Multiresolution 0-1 Data

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 8140)

Abstract

Multiresolution data has received considerable research interest due to the practical usefulness in combining datasets in different resolutions into a single analysis. Most models and methods can only model a single data resolution, that is, vectors of the same dimensionality, at a time. This is also true for mixture models, the model of interest. In this paper, we propose a multiresolution mixture model capable of modeling data in multiple resolutions. Firstly, we define the multiresolution component distributions of mixture models from the domain ontology. We then learn the parameters of the component distributions in the Bayesian network framework. Secondly, we map the multiresolution data in a Bayesian network setting to a vector representation to learn the mixture coefficients and the parameters of the component distributions. We investigate our proposed algorithms on two data sets. A simulated data allows us to have full data observations in all resolutions. However, this is unrealistic in all practical applications. The second data consists of DNA aberrations data in two resolutions. The results with multiresolution models show improvement in modeling performance with regards to the likelihood over single resolution mixture models.

Keywords

  • Multiresolution data
  • Mixture Models
  • Bayesian Networks

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References

  1. Garland, M.: Multiresolution Modeling: Survey & Future Opportunities. In: Eurographics 1999 – State of the Art Reports, pp. 111–131 (1999)

    Google Scholar 

  2. Willsky, A.S.: Multiresolution Markov Models for Signal and Image Processing. Proceedings of the IEEE 90(8), 1396–1458 (2002)

    CrossRef  Google Scholar 

  3. 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 

  4. Lindeberg, T.: Scale-space theory: A basic tool for analysing structures at different scales. Journal of Applied Statistics 21(2), 224–270 (1994)

    Google Scholar 

  5. Vetterli, M., Kovačevic, J.: Wavelets and Subband Coding. Prentice-Hall, Inc., Upper Saddle River (1995)

    MATH  Google Scholar 

  6. Russell, B.: On the Relations of Universals and Particulars. Proceedings of the Aristotelian Society 12, 1–24 (1911)

    Google Scholar 

  7. Everitt, B.S., Hand, D.J.: Finite Mixture Distributions. Chapman and Hall, London (1981)

    CrossRef  MATH  Google Scholar 

  8. McLachlan, G.J., Peel, D.: Finite Mixture Models. Probability and Statistics – Applied Probability and Statistics Section, vol. 299. Wiley, New York (2000)

    CrossRef  MATH  Google Scholar 

  9. Moore, A.: Very Fast EM-based Mixture Model Clustering Using Multiresolution KD–trees. In: Kearns, M., Cohn, D. (eds.) Advances in Neural Information Processing Systems, pp. 543–549. Morgan Kaufmann (April 1999)

    Google Scholar 

  10. Meilâ, M., Jordan, M.I.: Learning with mixtures of trees. Journal of Machine Learning Research 1, 1–48 (2000)

    Google Scholar 

  11. 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) (May 2008)

    Google Scholar 

  12. Marlin, B.M.: Missing data problems in machine learning. PhD thesis, University of Toronto (2008)

    Google Scholar 

  13. Kirsch, I.R.: The Causes and Consequences of Chromosomal Aberrations, 1st edn. CRC Press (December 1992)

    Google Scholar 

  14. Adhikari, P.R., Hollmén, J.: Patterns from multiresolution 0-1 data. In: Proceedings of the ACM SIGKDD Workshop on Useful Patterns, UP 2010, pp. 8–16. ACM, New York (2010)

    CrossRef  Google Scholar 

  15. Adhikari, P.R., Hollmén, J.: Multiresolution Mixture Modeling using Merging of Mixture Components. In: Hoi, S.C.H., Buntine, W. (eds.) Proceedings of the Fourth Asian Conference on Machine Learning, ACML 2012, JMLR Workshop and Conference Proceedings, Singapore, vol. 25, pp. 17–32 (2012)

    Google Scholar 

  16. Wilson, R.: MGMM: multiresolution Gaussian mixture models for computer vision. In: Proceedings of 15th International Conference on Pattern Recognition, vol. 1, pp. 212–215 (2000)

    Google Scholar 

  17. Ng, S.-K., McLachlan, G.J.: Robust Estimation in Gaussian Mixtures Using Multiresolution Kd-trees. In: Sun, C., Talbot, H., Ourselin, S., Adriaansen, T. (eds.) Proceedings of the 7th International Conference on Digital Image Computing: Techniques and Applications, pp. 145–154. CSIRO Publishing (2003)

    Google Scholar 

  18. Bellot, D.: Approximate discrete probability distribution representation using a multi–resolution binary tree. In: Proceedings of 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 498–503 (2003)

    Google Scholar 

  19. Sanchís, F.A., Aznar, F., Sempere, M., Pujol, M., Rizo, R.: Learning Discrete Probability Distributions with a Multi-resolution Binary Tree. In: Corchado, E., Yin, H., Botti, V., Fyfe, C. (eds.) IDEAL 2006. LNCS, vol. 4224, pp. 472–479. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  20. Bianchini, M., Maggini, M., Sarti, L.: Object Recognition Using Multiresolution Trees. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR&SPR 2006. LNCS, vol. 4109, pp. 331–339. Springer, Heidelberg (2006)

    CrossRef  Google Scholar 

  21. Huerta, J., Chover, M., Quiros, R., Vivo, R., Ribelles, J.: Binary space partitioning trees: a multiresolution approach. In: Proceedings of 1997 IEEE Conference on Information Visualization, pp. 148–154 (1997)

    Google Scholar 

  22. Barber, D.: Bayesian Reasoning and Machine Learning. Cambridge University Press (2012)

    Google Scholar 

  23. Jordan, M.I.: Graphical Models. Statistical Science (2004)

    Google Scholar 

  24. Heckerman, D.: A Tutorial on Learning With Bayesian Networks. In: Jordan, M.I. (ed.) Learning in Graphical Models, pp. 301–354. MIT Press, USA (1999)

    Google Scholar 

  25. Enders, C.K.: Applied Missing Data Analysis, 1st edn. The Guilford Press (2010)

    Google Scholar 

  26. 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)

    MathSciNet  MATH  Google Scholar 

  27. Adhikari, P.R., Hollmén, J.: Fast Progressive Training of Mixture Models for Model Selection. In: Ganascia, J.-G., Lenca, P., Petit, J.-M. (eds.) DS 2012. LNCS (LNAI), vol. 7569, pp. 194–208. Springer, Heidelberg (2012)

    CrossRef  Google Scholar 

  28. 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)

    CrossRef  Google Scholar 

  29. Lu, X., Shaw, C.A., Patel, A., Li, J., Cooper, M.L., Wells, W.R., Sullivan, C.M., Sahoo, T., Yatsenko, S.A., Bacino, C.A., Stankiewicz, P., Ou, Z., Chinault, A.C., Beaudet, A.L., Lupski, J.R., Cheung, S.W., Ward, P.A.: Clinical Implementation of Chromosomal Microarray Analysis: Summary of 2513 Postnatal Cases. PLoS ONE 2(3), e327 (2007)

    Google Scholar 

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Adhikari, P.R., Hollmén, J. (2013). Mixture Models from Multiresolution 0-1 Data. In: Fürnkranz, J., Hüllermeier, E., Higuchi, T. (eds) Discovery Science. DS 2013. Lecture Notes in Computer Science(), vol 8140. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40897-7_1

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  • DOI: https://doi.org/10.1007/978-3-642-40897-7_1

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