The recovery of time-varying graph signals is a fundamental problem with numerous applications in sensor networks and forecasting in time series. Effectively capturing the spatio-temporal information in these signals is essential for the downstream tasks. Previous studies have used the smoothness of the temporal differences of such graph signals as an initial assumption. Nevertheless, this smoothness assumption could result in a degradation of performance in the corresponding application when the prior does not hold. In this work, we relax the requirement of this hypothesis by including a learning module. We propose a Time Graph Neural Network (TimeGNN) for the recovery of time-varying graph signals. Our algorithm uses an encoder-decoder architecture with a specialized loss composed of a mean squared error function and a Sobolev smoothness operator.TimeGNN shows competitive performance against previous methods in real datasets.
翻译:时间变化图形信号的恢复是传感器网络和时间序列预测中许多应用中的一个基本问题。 有效捕捉这些信号中的时空信息对于下游任务至关重要。 以前的研究已经将此类图形信号的时间差异的平滑性作为初步假设。 然而,这种平稳性假设可能会在先前的不维持的情况下导致相应应用的性能下降。 在这项工作中,我们通过纳入学习模块来放松这一假设的要求。 我们提议为恢复时间变化图形信号建立一个时间图形网络(TimeGNN ) 。 我们的算法使用了由平均平方差错误函数和索博列夫滑动操作员组成的专门损失的编码解码器结构。 TimeGNN 显示在真实数据集中比以往的方法有竞争力。