A Skew-t-Normal Multi-level Reduced-Rank Functional PCA Model for the Analysis of Replicated Genomics Time Course Data

  • Maurice Berk
  • Giovanni Montana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7619)


Modelling replicated genomics time series data sets is challenging for two key reasons. Firstly, they exhibit two distinct levels of variation — the between-transcript and, nested within that, the between-replicate. Secondly, the typical assumption of normality rarely holds. Standard practice in light of these issues is to simply treat each transcript independently which greatly simplifies the modelling approach, reduces the computational burden and nevertheless appears to yield good results. We have set out to improve upon this, and in this article we present a multi-level reduced-rank functional PCA model that more accurately reflects the biological reality of these replicated genomics data sets, retains a degree of computational efficiency and enables us to carry out dimensionality reduction.


Functional Principal Component Analysis Functional Principal Component Principal Component Loading Time Series Data Analysis Ionize Radiation Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Bar-Joseph, Z., Gerber, G., Simon, I., Gifford, D.K., Jaakkola, T.S.: Comparing the continuous representation of time-series expression profiles to identify differentially expressed genes. Proceedings of the National Academy of Sciences of the United States of America 100(18), 10146–10151 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  2. Berk, M., Ebbels, T., Montana, G.: A statistical framework for metabolic profiling using longitudinal data. Bioinformatics 27, 1979–1985 (2011)CrossRefGoogle Scholar
  3. Di, C., Crainiceanu, C.M., Kuechenhoff, H., Peters, A.: Multilevel functional principal component analysis. Annals of Applied Statistics 3, 458–488 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. Gómez, H.W., Venegas, O., Bolfarine, H.: Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18(4), 395–407 (2007)MathSciNetCrossRefGoogle Scholar
  5. Ho, H.J., Lin, T.-I.: Robust linear mixed models using the skew t distribution with application to schizophrenia data. Biometrical Journal 52(4), 449–469 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  6. James, G., Hastie, T., Sugar, C.: Principal component models for sparse functional data. Biometrika 87(3), 587–602 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  7. Luan, Y., Li, H.: Clustering of time-course gene expression data using a mixed-effects model with B-splines. Bioinformatics 19(4), 474–482 (2003)CrossRefGoogle Scholar
  8. Ma, P., Castillo-Davis, C.I., Zhong, W., Liu, J.S.: A data-driven clustering method for time course gene expression data. Nucleic Acids Research 34(4), 1261–1269 (2006)CrossRefGoogle Scholar
  9. Nelder, J.A., Mead, R.: A Simplex Method for Function Minimization. The Computer Journal 7(4), 308–313 (1965)zbMATHGoogle Scholar
  10. Storey, J.D., Xiao, W., Leek, J.T., Tompkins, R.G., Davis, R.W.: Significance analysis of time course microarray experiments. Proceedings of the National Academy of Sciences of the United States of America 102(36), 12837–12842 (2005)CrossRefGoogle Scholar
  11. Tusher, V.G., Tibshirani, R., Chu, G.: Significance analysis of microarrays applied to the ionizing radiation response. Proceedings of the National Academy of Sciences of the United States of America 98(9), 5116–5121 (2001)zbMATHCrossRefGoogle Scholar
  12. Wei, G.C.G., Tanner, M.A.: A Monte Carlo Implementation of the EM Algorithm and the Poor Man’s Data Augmentation Algorithms. Journal of the American Statistical Association 85(411), 699–704 (1990)CrossRefGoogle Scholar
  13. Zhou, L., Huang, J.Z., Carroll, R.J.: Joint modelling of paired sparse functional data using principal components. Biometrika 95(3), 601–619 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  14. Zhou, L., Huang, J.Z., Martinez, J.G., Maity, A., Baladandayuthapani, V., Carroll, R.J.: Reduced rank mixed effects models for spatially correlated hierarchical functional data. Journal of the American Statistical Association 105(489), 390–400 (2010)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Maurice Berk
    • 1
  • Giovanni Montana
    • 2
  1. 1.Department of MedicineImperial College LondonUK
  2. 2.Department of MathematicsImperial College LondonUK

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