  We propose a new solution to the blind source separation problem that factors
mixed time-series signals into a sum of spatiotemporal modes, with the
constraint that the temporal components are intrinsic mode functions (IMF's).
The key motivation is that IMF's allow the computation of meaningful Hilbert
transforms of non-stationary data, from which instantaneous time-frequency
representations may be derived. Our spatiotemporal intrinsic mode decomposition
(STIMD) method leverages spatial correlations to generalize the extraction of
IMF's from one-dimensional signals, commonly performed using the empirical mode
decomposition (EMD), to multi-dimensional signals. Further, this data-driven
method enables future-state prediction. We demonstrate STIMD on several
synthetic examples, comparing it to common matrix factorization techniques,
namely singular value decomposition (SVD), independent component analysis
(ICA), and dynamic mode decomposition (DMD). We show that STIMD outperforms
these methods at reconstruction and extracting interpretable modes. Next, we
apply STIMD to analyze two real-world datasets, gravitational wave data and
neural recordings from the rodent hippocampus.
