Detecting multivariate cross-correlation between brain regions

Abstract

The problem of identifying functional connectivity from multiple time series data recorded in each of two or more brain areas arises in many neuroscientific investigations. For a single stationary time series in each of two brain areas statistical tools such as cross-correlation and Granger causality may be applied. On the other hand, to examine multivariate interactions at a single time point, canonical correlation, which finds the linear combinations of signals that maximize the correlation, may be used. We report here a new method that produces interpretations much like these standard techniques and, in addition, 1) extends the idea of canonical correlation to 3-way arrays (with dimensionality number of signals by number of time points by number of trials), 2) allows for nonstationarity, 3) also allows for nonlinearity, 4) scales well as the number of signals increases, and 5) captures predictive relationships, as is done with Granger causality. We demonstrate the effectiveness of the method through simulation studies and illustrate by analyzing local field potentials recorded from a behaving primate. NEW & NOTEWORTHY Multiple signals recorded from each of multiple brain regions may contain information about cross-region interactions. This article provides a method for visualizing the complicated interdependencies contained in these signals and assessing them statistically. The method combines signals optimally but allows the resulting measure of dependence to change, both within and between regions, as the responses evolve dynamically across time. We demonstrate the effectiveness of the method through numerical simulations and by uncovering a novel connectivity pattern between hippocampus and prefrontal cortex during a declarative memory task.

Nonlinear demixed component analysis for neural population data as a low-rank kernel regression problem

“…In summary, both dPCA and kdPCA recovered similar independent stimulus and time dimensions when the simulated activity depended on linearly separable temporal and stimulus components. As expected, kdPCA with a linear kernel produced identical results to dPC, demonstrating that these two formulations are equivalent (Rodu et al, 2018). With a Gaussian kernel, kdPCA achieved close to the same performance as dPCA (the optimal method for this example).…”

“…I present an extension to dPCA to find nonlinear task-related components. This method is related to kernel-based extensions of standard principal component analysis (PCA) (Schölkopf et al, 1998), canonical correlation analysis (CCA) (Lai & Fyfe, 2000;Hardoon et al, 2004;Rodu et al, 2018), and kernel regularized least-squares regression (Hainmueller & Hazlett, 2014). In this method, the data points are projected from neural activity space (R N ) into a potentially higher-dimensional space (A).…”

Disentangling the flow of signals between populations of neurons

“…5). This characterization would have been difficult with existing time series methods that incorporate dimensionality reduction but discard within-area activity as noise [54, 55].…”

“…5). This characterization would have been difficult with existing time series methods that incorporate dimensionality reduction but discard within-area activity as noise [54,55]. DLAG also offers unique advantages when characterizing the temporal structure of activity within and across areas.…”

Correlating Physiologic Measures of Stress: Exploring Dyads in Clinical Surgical Teams

“…Li & Chen, 2006;Shmueli et al, 2007). In the past, much work has been done to improve CCA for time series data correlation, such as multilinear CCA (Lu, 2013), kernel CCA (Bießmann et al, 2010), and dynamic kernel CCA (Rodu et al, 2018). While useful for providing global measures for predefined time intervals, these techniques can be computationally expensive or difficult to use in evaluating acute stress response or temporal stress correlation changes.…”