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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

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

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

Matthias Maneck - Journal Club WS 04/05

results combined2
Results – combined

Matthias Maneck - Journal Club WS 04/05

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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