Hierarchical clustering and filtering in half-inverse space for MEG and/or EEG hypothesis-free analysis

We propose hierarchical clustering and filtering methods for the analysis of spatio–temporal multidimensional time series, where both methods are based on a new pseudo distance. The pseudo distance is determined between orthogonal matrices, which are derived by eigenvalue decomposition of the variance–covariance matrix of the time series. Because the grouping algorithm is also important in clustering, a modified Ward method grouping criterion is used here. The filtering derives temporal similarity information between two time series, providing information that cannot be evaluated by the clustering. If the time series to be clustered and filtered cannot be obtained directly, different time series reflecting the original time series are used instead. There exists a transform between the time series, and hence, scaling distortion occurs. We also propose a scaling normalization method. As an application example, we present an analysis of a multichannel magnetoencephalography (MEG) and/or electroencephalography (EEG) time series. Each of the MEG and EEG generations is a transform from the same electrophysiological brain activity. We applied these methods to sound localization-related MEG time series and evaluated their effectiveness. These methods may be useful for discovering similarity among many multidimensional time series without a priori information and/or hypotheses.