Normalized linear variance decay dimension density and its application of dynamical complexity detection in physiological (fMRI) time series

The upper and lower bounds of the linear variance decay (LVD) dimension density are analytically deduced using multivariate series with uncorrelated and perfectly correlated component series. Then, the normalized LVD dimension density (δnormLVDδnormLVD) is introduced. In order to measure the complexity of a scalar series with δnormLVDδnormLVD, a pseudo-multivariate series was constructed from the scalar time series using time-delay embedding. Thus, δnormLVDδnormLVD is used to characterize the complexity of the pseudo-multivariate series. The results from the model systems and fMRI data of anxiety subjects reveal that this method can be used to analyze short and noisy time series.

► Deducing the upper and lower bounds of δLVDδLVD dimension density analytically.
► Proposing the normalized LVD dimension density (δnormLVDδnormLVD).
► Measuring the complexity of a scalar time series by δnormLVDδnormLVD.
► Voxel-base analysis of fMRI data set of anxiety disease by δnormLVDδnormLVD.