Visualization of Multivariate Data

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Visualization of Multivariate Data Christine
Steinhoff Max Planck Institute for Molecular
Genetics Berlin, Germany
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Outline
Motivation DATA INTEGRATION
Data types EXPRESSION aCGH Patients
Information Problems DISTRIBUTION, SCALE
Procedure DISCRETIZATION FILTERING
INDICATOR MATRIX MCA TOWARDS DISTANCE
DEFINITION
Results
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Data Sources
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DATA INTEGRATION
Patients Covariates Information on Patients
under study
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Gene x3 Loss
DATA INTEGRATION
Gene x1 Overexpressed
Gene x2 Amplified
Gene x4 Overexpressed
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PROBLEMS
Discrete categories
After appropriate normalization Approx
lognormal symmetric
Not symmetric skew
Scale and Distribution differ!
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Data INPUT
Procedure
Discretization
Filtering
Indicator coding
Multiple Correspondence Analysis
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Step 1 Discretization
Patients covariates
arrayCGH
Expression
Categorical e.g. Staging Grading Smoking Mutatio
n ....
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Step 1 Discretization
arrayCGH
Expression
For example CBS Package DNAcopy Segmentation
and discretization of arrayCGH data
For example Fold Change Criterion
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Step 1 Discretization
Patients covariates
arrayCGH
Expression
Typically n23,000 -gt reduce number
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Step 2 Filtering (optional)

• Suggestion
• Neglect all genes with no change in any patient
• Select for high Correlation between arrayCGH and
  expression

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Step 3 Indicator Matrix - Binary Coding
Indicator matrix With binary coding
Original matrix With categories
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Step 3 Indicator Matrix - Binary Coding
Indicator matrix With binary coding
Original matrix With categories
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Step 4 Appending Matrices
A
E
P
Experimental
SupplementalCovariates
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Multiple Correspondence Analysis with
supplementary Information
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Multiple Correspondence Analysis
Gene 251 state 1
G1 (-1) G1 (0) G1 (1) G2 (-1) ...
G1 (-1) G1 (0) G1 (1) G2 (-1) ...
t(E)E
t(E)A
t(A)E
t(A)A
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Multiple Correspondence Analysis
How to read Gene states cluster according to
- Distance from origin - Angle
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Patients Information
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Towards Distance Definition

• Determine
• Angle
• Vector length
• - Select genes according to a predefined angle
• Or
• - Select genes according to angle and length

a
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EXAMPLE PUBLISHED DATA
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EXAMPLE PUBLISHED DATA
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EXAMPLE PUBLISHED DATA
P0.006
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EXAMPLE PUBLISHED DATA
P0.005
P0.008
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SUMMARY
Pipeline for joint visualization of (a)
experimental continuous data e.g. arrayCGH and
expression data (b) Patients covariates
Application Data set parallel investigation of
arrayCGH and expression in breast cancer
patients covariate data available Determinati
on of candidate gene sets enrichment of specific
cancer related pathways
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FURTHER DIRECTIONS AND OPEN QUESTIONS

• Integration of variable datasources
• Appropriate discretization methods
• Avoid filtering by choosing algorithm for
  decomposition of sparse matrices
• Evaluation scheme (problem of simulation and
  noise adding)
• Appropriate comparision with Berger et al
  approach on continuous data
• (no implementation of patients covariates)
• ...

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ACKNOWLEDGEMENT
Sensor Lab, CNR-INFM
Max Planck Institute for Molecular Genetics
Martin Vingron
Matteo Pardo