1. 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

2. Matthias Maneck - Journal Club WS 04/05 Overview Introduction Methods  PCA – Principal Component Analysis  ICA – Independent Component Analysis  Kurtosis Results Summary

3. Matthias Maneck - Journal Club WS 04/05 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.

4. Matthias Maneck - Journal Club WS 04/05 Introduction – techniques PCA  dimensionality reduction  extracts relevant information related to the highest variance ICA  Optimizes independence condition  Components represent different non- overlapping information

5. Matthias Maneck - Journal Club WS 04/05 Introduction - experiments Micro plate assays of enzymes form Arabidopsis thaliana.  pgm mutant vs. wild type  continuous night data

6. Matthias Maneck - Journal Club WS 04/05 Introduction – workflow PCAICAKurtosisDataICs

7. Matthias Maneck - Journal Club WS 04/05 PCA – principal component analysis

8. Matthias Maneck - Journal Club WS 04/05 PCA – principal component analysis 2. Principal Component 1. Principal Component

9. Matthias Maneck - Journal Club WS 04/05 PCA – principal component analysis

10. Matthias Maneck - Journal Club WS 04/05 PCA – calculation

11. Matthias Maneck - Journal Club WS 04/05 PCA – dimensionality reduction = Reduced Data MatrixData MatrixSelected Components

12. Matthias Maneck - Journal Club WS 04/05 PCA – principal component analysis 1. Principal Component 2. Principal Component

13. Matthias Maneck - Journal Club WS 04/05 PCA – principal component analysis

14. Matthias Maneck - Journal Club WS 04/05 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 MatrixData MatrixSelected Components

15. Matthias Maneck - Journal Club WS 04/05 ICA – independent component analysis microphone signals are mixed speech signals

16. Matthias Maneck - Journal Club WS 04/05 ICA – independent component analysis = = Microphone Signals XMixing Matrix ASpeech Signals S Microphone signals XDemixing matrix A -1 Speech signals S

17. Matthias Maneck - Journal Club WS 04/05 ICA – independent component analysis The sum of distribution of the same time is more Gaussian.

18. Matthias Maneck - Journal Club WS 04/05 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 = ICsDemixing MatrixData Matrix

19. Matthias Maneck - Journal Club WS 04/05 Kurtosis – significant components measure of non Gaussianity  z – random variable (IC)  μ – mean  σ – standard deviation positive kurtosis  super Gaussian negative kurtosis  sub Gaussian

20. Matthias Maneck - Journal Club WS 04/05 Kurtosis – significant components

21. Matthias Maneck - Journal Club WS 04/05 Influence Values Which enzymes have most influence on ICs? = Reduced Data MatrixData MatrixSelected Components = ICs Demixing MatrixData Matrix

22. Matthias Maneck - Journal Club WS 04/05 Influence Values Selected ComponentsDemixing Matrix = Influence Matrix Data MatrixInfluence MatrixICs =

23. Matthias Maneck - Journal Club WS 04/05 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

24. Matthias Maneck - Journal Club WS 04/05 Results – pgm mutant

25. Matthias Maneck - Journal Club WS 04/05

26. Results – continuous night

27. Matthias Maneck - Journal Club WS 04/05 Results – combined

28. Matthias Maneck - Journal Club WS 04/05 Results – combined

29. Matthias Maneck - Journal Club WS 04/05 Results – combined

30. Matthias Maneck - Journal Club WS 04/05 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.

31. Matthias Maneck - Journal Club WS 04/05 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.