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Multivariate data analysis and visualization tools for biological data

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Dmitry Grapov
Dmitry Grapov
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Multivariate Data Analysis and Visualization Tools for Understanding Biological Data Dmitry Grapov
Introduction: Systems Oltvai, et al. Science 25 October 2002: 763-764. Emergent Reductionist Deterministic Systems Complex systems Chemical analysis Physiology Biochemistry Graph theory Modeling Informatics
Introduction: Inference
http://www.thefullwiki.org/Hypercube Overview many correlation mean Central Idea: dendrograms heatmaps biplots networks scatter plots histograms densities Representations: matrix matrix vector Properties: Multivariate n-D Bivariate 2-D Univariate 1-D Types:
Univariate: Properties ,[object Object],[object Object],[object Object]
Univariate: Representations
Univariate: Assumptions ,[object Object]
Univariate: Utility ,[object Object],[object Object],[object Object],[object Object],[object Object]
Univariate: Limitations ,[object Object],[object Object],[object Object],[object Object]
Old Faithful Data ,[object Object],[object Object],[object Object],[object Object],[object Object],Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics 39 , 357–365
[object Object],Bivariate: Properties
( X , Y ) Bivariate: Representations
( X , Y ) Bivariate: Utility ,[object Object],[object Object],Variable 2 = m* Variable 1 + b
http://en.wikipedia.org/wiki/Correlation Bivariate: Limitations correlation coefficient ,[object Object]
http://en.wikipedia.org/wiki/Correlation Bivariate: Limitations ,[object Object]
Old Faithful Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics 39 , 357–365
Old Unfaithful?
Old Unfaithful? ,[object Object],[object Object],[object Object]
Old Unfaithful? ,[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A matrix of n vectors of length m Multivariate: Properties Correlation matrix
[object Object],[object Object],[object Object],[object Object],[object Object],Multivariate: Dimensional Reduction PC 2 PC 1
Multivariate: Dimensional Reduction Wall, Michael E., Andreas Rechtsteiner, Luis M. Rocha."Singular value decomposition and principal component analysis". in  A Practical Approach to Microarray Data Analysis . D.P. Berrar, W. Dubitzky, M. Granzow, eds. pp. 91-109, Kluwer: Norwell, MA (2003). LANL LA-UR-02-4001. Scores Loadings Explained variance m x PC PC x PC n x PC Original Data Calculating PCs: singular value decomposition (SVD) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
[object Object],[object Object],[object Object],[object Object],A matrix of n vectors of length m Multivariate: Representations
Multivariate: Representation Identify outliers using all measurements Use known to impute missing Identify interesting groups Evaluate uni- and bivariate observations ,[object Object]
PCA: Considerations ,[object Object],[object Object],[object Object],[object Object],no pre-treatment centered and scaled to unit variance
PCA: Considerations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Use ICA to calculate statistically independent components
PCA: Considerations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],NMF uses additive parts based encoding Learning the parts of objects by nonnegative matrix factorization, D.D. Lee,H.S. Seung, Zhipeng Zhao, ppt.
PCA: Considerations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
PLS/-DA: Utility ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
PLS-DA: Example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Select the appropriate number Latent Variables (LVs) to maximize Q2
PLS-DA: Performance ,[object Object]
PLS-DA: Performance ,[object Object]
PLS: Predictive Performance ,[object Object],[object Object],[object Object]
PLS: Predictive Performance
PLS: Feature Selection Use the PLS-DA as an objective function to identify the most informative variables
Networks ,[object Object],[object Object],[object Object],[object Object],[object Object]
Networks ,[object Object]
Networks ,[object Object],non-diabetics type 2 diabetics
Networks ,[object Object],non-diabetics type 2 diabetics
non-diabetics type 2 diabetics imDEV : interactive modules for Data Exploration and Visualization   An integrated environment for systems level analysis of multivariate data. http:// sourceforge.net/apps/mediawiki/imdev
Acknowledgements Newman Lab Designated Emphasis in Biotechnology (DEB) NIH This project is funded in part by the NIH grant NIGMS-NIH T32-GM008799, USDA-ARS 5306-51530-019-00D, and NIH-NIDDK R01DK078328 -01.

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Multivariate data analysis and visualization tools for biological data

  • 1. Multivariate Data Analysis and Visualization Tools for Understanding Biological Data Dmitry Grapov
  • 2. Introduction: Systems Oltvai, et al. Science 25 October 2002: 763-764. Emergent Reductionist Deterministic Systems Complex systems Chemical analysis Physiology Biochemistry Graph theory Modeling Informatics
  • 4. http://www.thefullwiki.org/Hypercube Overview many correlation mean Central Idea: dendrograms heatmaps biplots networks scatter plots histograms densities Representations: matrix matrix vector Properties: Multivariate n-D Bivariate 2-D Univariate 1-D Types:
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  • 12. ( X , Y ) Bivariate: Representations
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  • 16. Old Faithful Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics 39 , 357–365
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  • 35. PLS: Feature Selection Use the PLS-DA as an objective function to identify the most informative variables
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  • 40. non-diabetics type 2 diabetics imDEV : interactive modules for Data Exploration and Visualization   An integrated environment for systems level analysis of multivariate data. http:// sourceforge.net/apps/mediawiki/imdev
  • 41. Acknowledgements Newman Lab Designated Emphasis in Biotechnology (DEB) NIH This project is funded in part by the NIH grant NIGMS-NIH T32-GM008799, USDA-ARS 5306-51530-019-00D, and NIH-NIDDK R01DK078328 -01.