Darya Chudova, Christopher Hart, Eric Mjolsness, Padhraic Smyth
We propose a functional mixture model for simultaneous clustering and alignment of sets of curves measured on a discrete time grid. The model is speciﬁcally tailored to gene expression time course data. Each func- tional cluster center is a nonlinear combination of solutions of a simple linear differential equation that describes the change of individual mRNA levels when the synthesis and decay rates are constant. The mixture of continuous time parametric functional forms allows one to (a) account for the heterogeneity in the observed proﬁles, (b) align the proﬁles in time by estimating real-valued time shifts, (c) capture the synthesis and decay of mRNA in the course of an experiment, and (d) regularize noisy proﬁles by enforcing smoothness in the mean curves. We derive an EM algo- rithm for estimating the parameters of the model, and apply the proposed approach to the set of cycling genes in yeast. The experiments show consistent improvement in predictive power and within cluster variance compared to regular Gaussian mixtures.