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：我们提出了一种新颖的时空数据预测方法，该方法采用带频率正则化的有监督半非负矩阵分解（SSNMF）。矩阵分解用于将时空数据分解为空间分量和时间分量。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，频率域正则化涉及在频率空间中选择特征，使得频率域解释更加便捷。我们提出了两种频率域方法：软正则化和硬正则化，并给出了对应约束优化问题收敛至一阶稳定点的保证。虽然我们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。因此，当将本方法应用于GRACE数据时，我们发现方法所得结果与地球物理科学领域的先前研究水平相当，但可解释性更为清晰。