Properties of a singular value decomposition based dynamical model of gene expression data

Krzysztof Simek

International Journal of Applied Mathematics and Computer Science (2003)

  • Volume: 13, Issue: 3, page 337-345
  • ISSN: 1641-876X

Abstract

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Recently, data on multiple gene expression at sequential time points were analyzed using the Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by the fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model, we formulate a nonlinear optimization problem and present how to solve it numerically using the standard MATLAB procedures. We use freely available data to test the approach. We discuss the possible consequences of data regularization, called sometimes ``polishing'', on the outcome of the analysis, especially when the model is to be used for prediction purposes. Then, we investigate the sensitivity of the method to missing measurements and its abilities to reconstruct the missing data. Summarizing, we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics, but may also lead to unexpected difficulties, like overfitting problems.

How to cite

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Simek, Krzysztof. "Properties of a singular value decomposition based dynamical model of gene expression data." International Journal of Applied Mathematics and Computer Science 13.3 (2003): 337-345. <http://eudml.org/doc/207648>.

@article{Simek2003,
abstract = {Recently, data on multiple gene expression at sequential time points were analyzed using the Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by the fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model, we formulate a nonlinear optimization problem and present how to solve it numerically using the standard MATLAB procedures. We use freely available data to test the approach. We discuss the possible consequences of data regularization, called sometimes ``polishing'', on the outcome of the analysis, especially when the model is to be used for prediction purposes. Then, we investigate the sensitivity of the method to missing measurements and its abilities to reconstruct the missing data. Summarizing, we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics, but may also lead to unexpected difficulties, like overfitting problems.},
author = {Simek, Krzysztof},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {multiple gene expression; dynamical model of gene expression data; singular value decomposition},
language = {eng},
number = {3},
pages = {337-345},
title = {Properties of a singular value decomposition based dynamical model of gene expression data},
url = {http://eudml.org/doc/207648},
volume = {13},
year = {2003},
}

TY - JOUR
AU - Simek, Krzysztof
TI - Properties of a singular value decomposition based dynamical model of gene expression data
JO - International Journal of Applied Mathematics and Computer Science
PY - 2003
VL - 13
IS - 3
SP - 337
EP - 345
AB - Recently, data on multiple gene expression at sequential time points were analyzed using the Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by the fitting of a linear discrete-time dynamical system in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model, we formulate a nonlinear optimization problem and present how to solve it numerically using the standard MATLAB procedures. We use freely available data to test the approach. We discuss the possible consequences of data regularization, called sometimes ``polishing'', on the outcome of the analysis, especially when the model is to be used for prediction purposes. Then, we investigate the sensitivity of the method to missing measurements and its abilities to reconstruct the missing data. Summarizing, we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics, but may also lead to unexpected difficulties, like overfitting problems.
LA - eng
KW - multiple gene expression; dynamical model of gene expression data; singular value decomposition
UR - http://eudml.org/doc/207648
ER -

References

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