Network identification via multivariate correlation analysis

In this thesis an innovative approach to assess connectivity in a complex network was proposed. In network connectivity studies, a major problem is to estimate the links between the elements of a system in a robust and reliable way. To address this issue, a statistical method based on Pearson’s correlation coefficient was proposed. The former inherits the versatility of the latter, declined in a general applicability to any kind of system and the capability to evaluate cross–correlation of time series pairs both simultaneously and at different time lags. In addition, our method has an increased “investigation power”, allowing to estimate correlation at different time scale–resolutions. The method was tested on two very different kind of systems: the brain and a set of meteorological stations in the Trentino region. In both cases, the purpose was to reconstruct the existence of significant links between the elements of the two systems at different temporal resolutions. In the first case, the signals used to reconstruct the networks are magnetoencephalographic (MEG) recordings acquired from human subjects in resting–state. Zero–delays cross–correlations were estimated on a set of MEG time series corresponding to the regions belonging to the default mode network (DMN) to identify the structure of the fully–connected brain networks at different time scale resolutions. A great attention was devoted to test the correlation significance, estimated by means of surrogates of the original signal. The network structure is defined by means of the selection of four parameter values: the level of significance α, the efficiency η0, and two ranking parameters, R1 and R2, used to merge the results obtained from the whole dataset in a single average behav- ior. In the case of MEG signals, the functional fully–connected networks estimated at different time scale resolutions were compared to identify the best observation window at which the network dynamics can be highlighted. The resulting best time scale of observation was ∼ 30 s, in line with the results present in the scientific liter- ature. The same method was also applied to meteorological time series to possibly assess wind circulation networks in the Trentino region. Although this study is pre- liminary, the first results identify an interesting clusterization of the meteorological stations used in the analysis.