  We propose a novel methodology for forecasting spatio-temporal data using
supervised semi-nonnegative matrix factorization (SSNMF) with frequency
regularization. Matrix factorization is employed to decompose spatio-temporal
data into spatial and temporal components. To improve clarity in the temporal
patterns, we introduce a nonnegativity constraint on the time domain along with
regularization in the frequency domain. Specifically, regularization in the
frequency domain involves selecting features in the frequency space, making an
interpretation in the frequency domain more convenient. We propose two methods
in the frequency domain: soft and hard regularizations, and provide convergence
guarantees to first-order stationary points of the corresponding constrained
optimization problem. While our primary motivation stems from geophysical data
analysis based on GRACE (Gravity Recovery and Climate Experiment) data, our
methodology has the potential for wider application. Consequently, when
applying our methodology to GRACE data, we find that the results with the
proposed methodology are comparable to previous research in the field of
geophysical sciences but offer clearer interpretability.
