Bounded-observation Kalman filtering of correlation in multivariate neural recordings

A persistent question in multivariate neural signal processing is how best to characterize the statistical association between brain regions known as functional connectivity. Of the many metrics available for determining such association, the standard Pearson correlation coefficient (i.e., the zero-lag cross-correlation) remains widely used, particularly in neuroimaging. Generally, the cross-correlation is computed over an entire trial or recording session, with the assumption of within-trial stationarity. Increasingly, however, the length and complexity of neural data requires characterizing transient effects and/or non-stationarity in the temporal evolution of the correlation. That is, to estimate dynamics in the association between brain regions. Here, we present a simple, data-driven Kalman filter-based approach to tracking correlation dynamics. The filter explicitly accounts for the bounded nature of correlation measurements through the inclusion of a Fisher transform in the measurement equation. An output linearization facilitates a straightforward implementation of the standard recursive filter equations, including admittance of covariance identification via an autoregressive least squares method. We demonstrate the efficacy and utility of the approach in an example of multivariate neural functional magnetic resonance imaging data.