Independent components analysis of starch deficient pgm mutants
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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 Analysis Kurtosis Results Summary. Introduction – techniques.

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Independent components analysis of starch deficient pgm mutants

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Independent components analysis of starch deficient pgm mutants

Independent components analysis of starch deficient pgm mutants

GCB 2004

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

Matthias Maneck - Journal Club WS 04/05


Overview

Overview

  • Introduction

  • Methods

    • PCA – Principal Component Analysis

    • ICA – Independent Component Analysis

    • Kurtosis

  • Results

  • Summary

Matthias Maneck - Journal Club WS 04/05


Introduction techniques

Introduction – techniques

  • visualization techniques

    • supervised

      • biological background information

    • unsupervised

      • present major global information

      • General questions about the underlying data structure.

      • Detect relevant components independent from background knowledge.

Matthias Maneck - Journal Club WS 04/05


Introduction techniques1

Introduction – techniques

  • PCA

    • dimensionality reduction

    • extracts relevant information related to the highest variance

  • ICA

    • Optimizes independence condition

    • Components represent different non-overlapping information

Matthias Maneck - Journal Club WS 04/05


Introduction experiments

Introduction - experiments

  • Micro plate assays of enzymes form Arabidopsis thaliana.

    • pgm mutant vs. wild type

    • continuous night

  • data

Matthias Maneck - Journal Club WS 04/05


Introduction workflow

Introduction – workflow

Data

PCA

ICA

Kurtosis

ICs

Matthias Maneck - Journal Club WS 04/05


Pca principal component analysis

PCA – principal component analysis

Matthias Maneck - Journal Club WS 04/05


Pca principal component analysis1

PCA – principal component analysis

1. Principal Component

2. Principal Component

Matthias Maneck - Journal Club WS 04/05


Pca principal component analysis2

PCA – principal component analysis

Matthias Maneck - Journal Club WS 04/05


Pca calculation

PCA – calculation

Matthias Maneck - Journal Club WS 04/05


Pca dimensionality reduction

PCA – dimensionality reduction

Selected Components

Data Matrix

Reduced Data Matrix

=

Matthias Maneck - Journal Club WS 04/05


Pca principal component analysis3

PCA – principal component analysis

1. Principal Component

2. Principal Component

Matthias Maneck - Journal Club WS 04/05


Pca principal component analysis4

PCA – principal component analysis

Matthias Maneck - Journal Club WS 04/05


Pca principal component analysis5

PCA – principal component analysis

  • 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

Reduced Data Matrix

Selected Components

Data Matrix

=

Matthias Maneck - Journal Club WS 04/05


Ica independent component analysis

ICA – independent component analysis

  • microphone signals are mixed speech signals

Matthias Maneck - Journal Club WS 04/05


Ica independent component analysis1

ICA – independent component analysis

Microphone Signals X

Mixing Matrix A

Speech Signals S

=

Demixing matrix A-1

Microphone signals X

Speech signals S

=

Matthias Maneck - Journal Club WS 04/05


Ica independent component analysis2

ICA – independent component analysis

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

Matthias Maneck - Journal Club WS 04/05


Ica independent component analysis3

ICA – independent component analysis

  • 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

ICs

Demixing Matrix

Data Matrix

=

Matthias Maneck - Journal Club WS 04/05


Kurtosis significant components

Kurtosis – significant components

  • measure of non Gaussianity

    • z – random variable (IC)

    • μ – mean

    • σ – standard deviation

  • positive kurtosis super Gaussian

  • negative kurtosis sub Gaussian

Matthias Maneck - Journal Club WS 04/05


Kurtosis significant components1

Kurtosis – significant components

Matthias Maneck - Journal Club WS 04/05


Influence values

Influence Values

  • Which enzymes have most influence on ICs?

Reduced Data Matrix

Selected Components

Data Matrix

=

ICs

Demixing Matrix

Data Matrix

=

Matthias Maneck - Journal Club WS 04/05


Influence values1

Influence Values

Influence Matrix

Demixing Matrix

Selected Components

=

ICs

Influence Matrix

Data Matrix

=

Matthias Maneck - Journal Club WS 04/05


Results

Results

  • pgm mutant

    • compares wild type and pgm mutant

    • 17 enzymes,125 samples

      • wild type, pgm mutant

  • continuous night

    • response to carbon starvation

    • 17 enzymes, 55 samples

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

Matthias Maneck - Journal Club WS 04/05


Results pgm mutant

Results – pgm mutant

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Independent components analysis of starch deficient pgm mutants

Matthias Maneck - Journal Club WS 04/05


Results continuous night

Results – continuous night

Matthias Maneck - Journal Club WS 04/05


Results combined

Results – combined

Matthias Maneck - Journal Club WS 04/05


Results combined1

Results – combined

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Results combined2

Results – combined

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Summary

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.

Matthias Maneck - Journal Club WS 04/05


References

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.

Matthias Maneck - Journal Club WS 04/05


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