Practical issues in the detection of multiscale spatial synchronization using empirical mode decomposition

Approaches based on assumptions of normality, linearity or stationarity are not well suited to biology. High throughtput gene expression data is noisy asymptotically approximates a power law amplitude distribution. Such data requires careful selection of interpolating spline in the sifting step of empirical mode decomposition as this markedly eects the decomposition result. The rationale for choice of interpolating spline is based upon cri- teria such as parsimonious decomposition, amplitude modulation, stopping criteria and hysteresis. Decomposition of noisy data requires stringent em- pirical tests of periodicity based on random permutations of experimental data. Intrinsic mode functions within a decomposition are only orthogonal in amplitude whereas their frequency energy may be correlated. Thus, each intrinsic mode function cannot be considered in isolation from the rest of the decomposition. Autocorrelation synchronisation metrics provide a powerful way of investigating multiscale interdependency between intrinsic mode functions within a decompostion and between replicate experimental datasets