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：时变图信号的恢复是一个基础性问题，在传感器网络和时间序列预测中有着广泛的应用。有效捕捉这些信号中的时空信息对于后续任务至关重要。以往研究通常假设此类图信号的时间差分具有平滑性。然而，当这一先验假设不成立时，平滑性假设可能导致相应应用中的性能下降。在本工作中，我们通过引入学习模块来放宽这一假设的要求。我们提出了一种用于时变图信号恢复的时间图神经网络（Time Graph Neural Network, TimeGNN）。该算法采用编码器-解码器架构，并设计了由均方误差函数和Sobolev平滑算子组成的专用损失函数。在真实数据集上的实验表明，TimeGNN相较于以往方法展现出具有竞争力的性能。