Modeling and Analyzing Neural Signals with Phase Variability using the Fisher-Rao Registration

The Dynamic Time Warping (DTW) has recently been introduced to analyze neural signals such as EEG and fMRI where phase variability plays an important role in the data. In this study, we propose to adopt a more powerful method, referred to as the Fisher-Rao Registration (FRR), to study the phase variability. We systematically compare the FRR with the DTW in three aspects: 1) basic framework, 2) mathematical properties, and 3) computational efficiency. We show that the FRR has superior performance in all these aspects and the advantages are well illustrated with simulation examples. We then apply the FRR method to two real experimental recordings - one fMRI and one EEG data set. It is found the FRR method properly removes the phase variability in each set. Finally, we use the FRR framework to examine brain networks in these two data sets and the result demonstrates the effectiveness of the new method.