Independent components analysis of starch deficient pgm mutants

Matthias Maneck - Journal Club WS 04/05

Independent components analysis of starch deficient pgm mutants

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

i Enz

ymes


Introduction – workflow

j Samples

i Enz

ymes

j Samples

PC

’s

1st IC

2nd IC

j SamplesIC

s

PCA ICA KurtosisData ICs


PCA – principal component analysis

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

-3

-2

-1

0

1

2

3

4

Enzyme 1

Enz

yme

2


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

-3

-2

-1

0

1

2

3

4

Enzyme 1

Enz

yme

2


2. Principal Component




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

-3

-2

-1

0

1

2

3

4

1. PC

2. P

C


PCA – calculation

j Samples

i Enz

ymes

i Enz

ymes

i Enzymes

Eigenvectors

x1 ... ... xi

- mean

- mean

- mean

- mean

Data-Matrix Cov-Matrix

Eigenvalues

λ1

λi


PCA – dimensionality reductionP

Cs

i Enzymes

j Samples

i Enz

ymes

j Samples

PC

s

=

Reduced Data MatrixData MatrixSelected Components


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

-3

-2

-1

0

1

2

3

4

Enzyme 1

Enz

yme

2






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

-3

-2

-1

0

1

2

3

4

1. PC



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

PC

s

i Enzymes

j Samples

i Enz

ymes

j Samples

PC

s

=

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

tsatsatsatx

tsatsatsatx


ICA – independent component analysism

icro

phon

esi

gnal

s

time tmixingspeech

mic

roph

one

time t

spee

chsi

gnal

s

=m

icro

phon

esi

gnal

s

time tdemixingspeech

spea

ker

time t

spee

chsi

gnal

s

=

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

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

20

25

30

35

0 0.5 1 1.5 2 2.5 30

10

20

30

40

50

60

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

PC

s

j Samples

ICs

PCs

=

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

3)1(

)()(

41

4

n

zzkurtosis

n

ii


Kurtosis – significant components


Influence Values

Which enzymes have most influence on ICs?

PC

si Enzymes

j Samples

i Enz

ymes

j Samples

PC

s

=

Reduced Data Matrix Data MatrixSelected Components

j Samples

PC

s

j Samples

ICs

PCs

=

ICs Demixing Matrix Data Matrix


Influence Values

PC

s

i Enzymes

Selected Components

PCs

Demixing Matrix

i Enzymes

ICs

=

Influence Matrix

j Samples

i Enz

ymes

Data Matrix

i Enzymes

ICs

Influence Matrix

j Samples

ICs

ICs

=


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.

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Independent components analysis of starch deficient pgm mutants