A new model for simultaneous dimensionality reduction and time-varying functional connectivity estimation

An important question in neuroscience is whether or not we can interpret spontaneous variations in the pattern of correlation between brain areas, which we refer to as functional connectivity or FC, as an index of dynamic neuronal communication in fMRI. That is, can we measure time-varying FC reliably? And, if so, can FC reflect information transfer between brain regions at relatively fast-time scales? Answering these questions in practice requires dealing with the statistical challenge of having high-dimensional data and a comparatively lower number of time points or volumes. A common strategy is to use PCA to reduce the dimensionality of the data, and then apply some model, such as the hidden Markov model (HMM) or a mixture model of Gaussian distributions, to find a set of distinct FC patterns or states. The distinct spatial properties of these FC states together with the time-resolved switching between them offer a flexible description of time-varying FC. In this work, I show that in this context PCA can suffer from systematic biases and loss of sensitivity for the purposes of finding time-varying FC. To get around these issues, I propose a novel variety of the HMM, named HMM-PCA, where the states are themselves PCA decompositions. Since PCA is based on the data covariance, the state-specific PCA decompositions reflect distinct patterns of FC. I show, theoretically and empirically, that fusing dimensionality reduction and time-varying FC estimation in one single step can avoid these problems and outperform alternative approaches, facilitating the quantification of transient communication in the brain.