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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. 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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  1. 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

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

  3. 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

  4. 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

  5. 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

  6. Introduction – workflow Data PCA ICA Kurtosis ICs Matthias Maneck - Journal Club WS 04/05

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

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

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

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

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

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

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

  14. 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

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

  16. 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

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

  18. 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

  19. 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

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

  21. 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

  22. Influence Values Influence Matrix Demixing Matrix Selected Components = ICs Influence Matrix Data Matrix = Matthias Maneck - Journal Club WS 04/05

  23. 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

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

  25. Matthias Maneck - Journal Club WS 04/05

  26. Results – continuous night Matthias Maneck - Journal Club WS 04/05

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

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

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

  30. 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

  31. 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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