Independent components analysis of starch deficient pgm mutants

Matthias Maneck - Journal Club WS 04/05

GCB 2004

M. Scholz, Y. Gibon, M. Stitt, J. Selbig

Overview

Introduction Methods

PCA – Principal Component Analysis ICA – Independent Component AnalysisKurtosis

Results Summary

Introduction – techniques

visualization techniques supervised

biological background informationunsupervised

present major global information General questions about the underlying data

structure. Detect relevant components independent from

background knowledge.

Introduction – techniques

PCAdimensionality reductionextracts relevant information related to the

highest variance ICA

Optimizes independence conditionComponents represent different non-

overlapping information

Introduction - experiments

Micro plate assays of enzymes form Arabidopsis thaliana. pgm mutant vs. wild type continuous night

data j Samples

Introduction – workflow

j Samples

1st IC

2nd IC

j SamplesIC

PCA ICA KurtosisData ICs

PCA – principal component analysis

-4 -3 -2 -1 0 1 2 3 4-4

Enzyme 1

-4 -3 -2 -1 0 1 2 3 4-4

Enzyme 1

2. Principal Component

-4 -3 -2 -1 0 1 2 3 4-4

PCA – calculation

j Samples

i Enzymes

Eigenvectors

x1 ... ... xi

- mean

Data-Matrix Cov-Matrix

Eigenvalues

PCA – dimensionality reductionP

i Enzymes

j Samples

Reduced Data MatrixData MatrixSelected Components

-4 -3 -2 -1 0 1 2 3 4-4

Enzyme 1

-4 -3 -2 -1 0 1 2 3 4-4

Minimizes correlation between components. Components are orthogonal to each other. Delivers transformation matrix, that gives the influence of

the enzymes on the principal components. PCs ordered by size of eigenvalues of cov-matrix

i Enzymes

j Samples

Reduced Data Matrix Data MatrixSelected Components

ICA – independent component analysis

Person 1

Person 3

Person 2

Mike 1

Mike 3

Mike 2

microphone signals are mixed speech signals

)()()()(

3332321313

3232221212

3132121111

tsatsatsatx

ICA – independent component analysism

time tmixingspeech

time t

time tdemixingspeech

time t

Microphone Signals X Mixing Matrix A Speech Signals S

Microphone signals XDemixing matrix A-1 Speech signals S

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0 0.5 1 1.5 2 2.5 30

The sum of distribution of the same time is more Gaussian.

Maximizes independence (non Gaussianity) between components.

ICA doesn’t work with purely Gaussian distributed data. Components are not orthogonal to each other. Delivers transformation matrix, that gives the influence of the PCs

on the independent components. ICs are unordered

j Samples

ICs Demixing Matrix Data Matrix

Kurtosis – significant components

measure of non Gaussianity

z – random variable (IC) μ – mean σ – standard deviation

positive kurtosis super Gaussian

negative kurtosis sub Gaussian

zzkurtosis

Kurtosis – significant components

Influence Values

Which enzymes have most influence on ICs?

si Enzymes

j Samples

Reduced Data Matrix Data MatrixSelected Components

j Samples

ICs Demixing Matrix Data Matrix

Influence Values

i Enzymes

Selected Components

Demixing Matrix

i Enzymes

Influence Matrix

j Samples

Data Matrix

i Enzymes

Influence Matrix

j Samples

Results

pgm mutantcompares wild type and pgm mutant17 enzymes,125 samples

wild type, pgm mutant

continuous nightresponse to carbon starvation17 enzymes, 55 samples

+0, +2, +4, +8, +24, +48, +72, +148 h

Results – pgm mutant

Results – continuous night

Results – combined

Summary

ICA in combination with PCA has higher discriminating power than only PCA.

Kurtosis is used for selection optimal PCA dimension and ordering of ICs.

pgm experiment, 1st IC discriminates between mutant and wild type.

Continuous night, 2nd IC represents time component.

The two most strongly implicated enzymes are identical.

References

Scholz M., Gibon Y., Stitt M., Selbig J.: Independent components analysis of starch deficient pgm mutants.

Scholz M., Gatzek S., Sterling A., Fiehn O., Selbig J.: Metabolite fingerprinting: an ICA approach.

Blaschke, T., Wiskott, L.: CuBICA: Independent Component Analysis by Simultaneous Third- and Fourth-Order Cumulant Diagonalization. IEEE Transactions on Signal Processing, 52(5):1250-1256.http://itb.biologie.hu-berlin.de/~blaschke/

Hyvärinen A., Karhunen J., Oja E.: Independent Component Analysis. J. Wiley. 2001.

Independent components analysis of starch deficient pgm mutants

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