Time-evolving data analysis is crucial for understanding complex systems such as the brain. Methods that assume static networks have successfully recovered spatial networks of connectivity from neuroimaging data. Still, discovering both underlying networks and their evolution is a challenging task.

To capture temporal evolution of connectivity networks, we arrange dynamic data as a tensor and use a tensor factorization method called PARAFAC2. PARAFAC2 deciphers the hidden structure of dynamic networks and yields unique and interpretable components. Preliminary results using PARAFAC2 in neuroimaging data analysis are promising. However, the constant cross-product constraint on the time-evolving mode hinders the use of additional constraints or regularization (e.g. spatial smoothness) on this mode. Currently, the only way to regularize the time-evolving mode of a PARAFAC2 model is with a flexible coupling approach, which finds the solution through regularized least-squares subproblems. Instead, we use an alternating direction method of multipliers (ADMM) based approach to widen the possible regularization penalties to any proximable function.

Our numerical experiments demonstrate that the proposed ADMM-based algorithmic approach for PARAFAC2 can accurately recover the underlying evolving components, is flexible in terms of imposing constraints and also computationally efficient.