Clustering Time Series Gene Expression Data Based on Sum-of-Exponentials Fitting

Abstract

This paper presents a method based on fitting a sum-of-exponentials model to the nonuniformly sampled data, for clustering the time series of gene expression data. The structure of the model is estimated by using the minimum description length (MDL) principle for nonlinear regression, in a new form, incorporating a normalized maximum-likelihood (NML) model for a subset of the parameters. The performance of the structure estimation method is studied using simulated data, and the superiority of the new selection criterion over earlier criteria is demonstrated. The accuracy of the nonlinear estimates of the model parameters is analyzed with respect to the Cramér-Rao lower bounds. Clustering examples of gene expression data sets from a developmental biology application are presented, revealing gene grouping into clusters according to functional classes.