Supervised low-rank semi-nonnegative matrix factorization with frequency regularization for forecasting spatio-temporal data
This provides an incremental improvement in forecasting methods for geophysical and potentially other spatio-temporal data by enhancing interpretability through frequency regularization.
The authors tackled forecasting spatio-temporal data by proposing supervised semi-nonnegative matrix factorization with frequency regularization, which decomposes data into spatial and temporal components with nonnegativity constraints and frequency-domain regularization for clearer temporal patterns. When applied to GRACE geophysical data, the results were comparable to previous research but offered improved interpretability.
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.