Pattern Detection of Multivariate Hormonal Systems

A method of data analysis which aims at the detection of the significant periodicities as well as of the irregular high frequency oscillations (perturbations) in biological time series (TS) is proposed. The significant frequency modes are detected by application of a statistical significance criterion on the periodogram derived from the given TS; they are used to construct the significant periodic series. The latter is then subtracted from the original TS in order to obtain the detrended TS defined as the perturbation series which is considered as the outcome of a stochastic process. Under the assumption of Gaussian characteristics for the stochastic process, evidence of which is available, a probabilistic basis for both univariate and bivariate analysis is provided. A ``surprisal'' measure defined as the reciprocal of the probability for an outcome of a stochastic process (or a pair of correlated porcesses) is introduced to account for both the average as well as the localized perturbation of the TS (or the correlation between the pair of TS). A dependence tree configuration that maximizes the overall mutual information or dependence among branches is proposed as an optimal representation of a multivariate system. Lag-correlation analysis and cospectrum tests are adopted for validation and modification of the configuration generated. Simulated systems are employed to test the extent of linear approximation of various nonlinear functions as well as the sensitivity of the proposed method when the simulated system is subject to disturbances of varied type and degree.