Mining natural associations from high-dimensional spatiotemporal signals plays an important role in various fields including biology, climatology, and financial analysis. However, most existing works have mainly studied time-independent signals without considering the correlations of spatiotemporal signals that achieve high learning accuracy. This paper aims to learn graphs that better reflect underlying data relations by leveraging the long- and short-term characteristics of spatiotemporal signals. First, a spatiotemporal signal model is presented that considers both spatial and temporal relations. In particular, we integrate a low-rank representation and a Gaussian Markov process to describe the temporal correlations. Then, the graph learning problem is formulated as a joint low-rank component estimation and graph Laplacian inference. Accordingly, we propose a low rank and spatiotemporal smoothness-based graph learning method (GL-LRSS), which introduces a spatiotemporal smoothness prior into time-vertex signal analysis. By jointly exploiting the low rank of long-time observations and the smoothness of short-time observations, the overall learning performance can be effectively improved. Experiments on both synthetic and real-world datasets demonstrate substantial improvements in the learning accuracy of the proposed method over the state-of-the-art low-rank component estimation and graph learning methods.

中文翻译：

---

具有长期和短期特征的时空信号图学习

从高维度的时空信号中挖掘自然联系在生物学，气候学和财务分析等各个领域都发挥着重要作用。然而，大多数现有的工作主要研究了与时间无关的信号，而没有考虑达到高学习精度的时空信号的相关性。本文旨在学习通过利用时空信号的长期和短期特征更好地反映基础数据关系的图。首先，提出了时空信号模型，该模型同时考虑了时空关系。特别是，我们集成了低秩表示和高斯马尔可夫过程来描述时间相关性。然后，将图学习问题公式化为联合低秩分量估计和图拉普拉斯推论。因此，我们提出了一种基于低秩和时空平滑度的图学习方法（GL-LRSS），该方法将时空平滑度引入到时间-顶点信号分析中。通过共同利用长期观测的低等级和短期观测的平稳性，可以有效地提高整体学习成绩。在合成数据集和实际数据集上进行的实验表明，与最新的低秩分量估计和图形学习方法相比，该方法的学习准确性有了显着提高。通过共同利用长期观测的低等级和短期观测的平稳性，可以有效地提高整体学习成绩。在合成数据集和实际数据集上进行的实验表明，与最新的低秩分量估计和图形学习方法相比，该方法的学习准确性有了显着提高。通过共同利用长期观测的低等级和短期观测的平稳性，可以有效地提高整体学习成绩。在合成数据集和实际数据集上进行的实验表明，与最新的低秩分量估计和图形学习方法相比，该方法的学习准确性有了显着提高。