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.

翻译：我们提出了一种利用带频率正则化的监督半非负矩阵分解（SSNMF）进行时空数据预测的新方法。该方法通过矩阵分解将时空数据分解为空间分量与时间分量。为提高时间模式的清晰度，我们在时间域引入非负约束，并在频率域施加正则化。具体而言，频率域的正则化通过在频域空间进行特征选择，使得频域解释更为便捷。我们提出了频域软正则化与硬正则化两种方法，并给出了相应约束优化问题一阶稳定点的收敛性保证。虽然本研究的主要动机源于基于GRACE（重力恢复与气候实验）数据的地球物理数据分析，但该方法具有更广泛的应用潜力。将本方法应用于GRACE数据时，我们发现所得结果与地球物理科学领域的已有研究具有可比性，同时提供了更清晰的解释性。