Robust Dynamics Estimation of Gene Expression Data

In this paper, we apply a nonlinear filtering algorithm based on SVD and compression-based filtering, to estimate the characteristic modes of observed gene expression data with independently identically distributed (i.i.il.) random variables of Gaussian density of zero mean. The essence of the technique is that when the proposed lossy data compression algorithm, with the allowed loss set equal to the noise strength, is applied to a noisy gene expression data, the loss and the noise tend to cancel. Then we use the estimated noise strength as a threshold to determine the effective characteristic modes for reconstructing the gene expression profiles, followed by 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. Furthermore, the time evolution of expression values by using the translation matrix to predict future expression values was investigated. Finally the publicly available data set of yeast from microarray experiments on the synchronized cell cycle (CDC15) is given to exemplify the implementation of the proposed technique.