Multivariate data analysis and visualization tools for biological data
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This document discusses various tools for analyzing and visualizing multivariate biological data. It describes univariate, bivariate, and multivariate analysis methods. Univariate analysis examines one variable at a time, bivariate examines two variables jointly, and multivariate examines multiple variables together. Dimensionality reduction techniques like principal component analysis (PCA) and partial least squares (PLS) projection can be used to visualize high-dimensional data. Networks can represent relationships among objects and identify patterns in complex data. Integrative modeling approaches provide a holistic view of biological systems from multivariate data.
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:
- 5. Univariate: Properties vector of length m mean variance
- 7. Univariate: Assumptions Normality
- 8. Univariate: Utility Hypothesis testing α - type I error ( False Positive) β - type II error ( False negative) power - (1– β ) effect size - standardized difference in mean
- 9. Univariate: Limitations Biological definition of the mean ? Relationship between sample size and test power Multiple hypothesis testing False discovery rate
- 10. Old Faithful Data 272 observations time between eruptions 70 ± 14 min duration of eruption 3.5 ± 1 min Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics 39 , 357–365
- 11. Matrix of 2 vectors of length m Bivariate: Properties
- 12. ( X , Y ) Bivariate: Representations
- 13. ( X , Y ) Bivariate: Utility bivariate distribution correlation Variable 2 = m* Variable 1 + b
- 14. http://en.wikipedia.org/wiki/Correlation Bivariate: Limitations correlation coefficient Measure of linear or monotonic relationship
- 15. http://en.wikipedia.org/wiki/Correlation Bivariate: Limitations Sensitive to outliers
- 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
- 17. Old Unfaithful?
- 18. Old Unfaithful? Additional variables Nearby hydrofracking Improve inference based on more information
- 19. Old Unfaithful? Additional variables Nearby hydrofracking Improve inference based on more information
- 20. Challenges data often wide structured integration noise Rewards robust inference signal amplification holistic/systems approach A matrix of n vectors of length m Multivariate: Properties Correlation matrix
- 21. Principal Components Analysis (PCA) Linear n-dimensional encoding of original data Where dimensions are: orthogonal (uncorrelated) Top k dimensions are ordered by variance explained Multivariate: Dimensional Reduction PC 2 PC 1
- 22. 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) Eigenvalue explained variance Scores sample representation based on all variables Loadings variable contribution to scores
- 23. Old Faithful 2.0 272 measurements 8 variables 2 real, 6 random noise A matrix of n vectors of length m Multivariate: Representations
- 24. Multivariate: Representation Identify outliers using all measurements Use known to impute missing Identify interesting groups Evaluate uni- and bivariate observations Number of PCs can be used true data complexity
- 25. PCA: Considerations data pre-treatment outliers noise unsupervised projection no pre-treatment centered and scaled to unit variance
- 26. PCA: Considerations data pre-treatment outliers linear reconstruction noise Independent components analysis (ICA) unsupervised projection Use ICA to calculate statistically independent components
- 27. PCA: Considerations data pre-treatment outliers linear reconstruction noise supervised projection Non-negative matrix factorization (NMF) NMF uses additive parts based encoding Learning the parts of objects by nonnegative matrix factorization, D.D. Lee,H.S. Seung, Zhipeng Zhao, ppt.
- 28. PCA: Considerations data pre-treatment outliers linear reconstruction noise supervised projection Identify projection correlated with class assignment (classification) or continuous variables (regression) Partial Least Squares Projection to Latent Structures (PLS/-DA)
- 29. PLS/-DA: Utility Strengths Predict multiple dependent variables avoids issues of multicollinearity Independent measure of variable importance Weaknesses Need to derive an empirical reference for model performance Poor established model optimization methods
- 30. PLS-DA: Example Data: Old Faithful 2.0 272 observations on 8 variables Latent Variables are analogous to PCs Important Statistics (CV) Q2 = fit RMSEP = error of prediction AU(RO)C = specificity vs. sensitivity Select the appropriate number Latent Variables (LVs) to maximize Q2
- 31. PLS-DA: Performance Use permutation tests to empirically determine model performance
- 32. PLS-DA: Performance Use permutation tests to empirically determine model performance
- 33. PLS: Predictive Performance Split data into training (2/3) and test sets (1/3) Generate model using training set and then predict class assignment for test set Use permutation tests to generate confidence bounds for future predictions
- 35. PLS: Feature Selection Use the PLS-DA as an objective function to identify the most informative variables
- 36. Networks Network: representation of relationships among objects Utility Project statistical results into a biological context Explore informative data aspects in the context of all that was observed. Identify emergent patterns
- 37. Networks Interpret statistical results within a biological context
- 38. Networks Highlight changes in patterns of relationships. non-diabetics type 2 diabetics
- 39. Networks Display complex interactions non-diabetics type 2 diabetics
- 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.