Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this work, we aim to learn a graph from incomplete time-series observations. From another viewpoint, we consider the problem of semi-blind recovery of time-varying graph signals where the underlying graph model is unknown. We propose an algorithm based on the method of block successive upperbound minimization (BSUM), for simultaneous inference of the signal and the graph from incomplete data. Simulation results on synthetic and real time-series demonstrate the performance of the proposed method for graph learning and signal recovery.

翻译：从数据中学习图结构是利用图信号处理工具的关键。传统的图学习算法大多需要完整的数据统计特征，而某些场景下这些统计信息可能无法获取。本研究旨在从不完整的时间序列观测中学习图结构。从另一视角出发，我们考虑当底层图模型未知时，时变图信号的半盲恢复问题。我们提出一种基于块连续上界最小化（BSUM）方法的算法，用于从不完整数据中同时推断信号与图结构。在合成时间序列和真实时间序列上的仿真结果表明，所提方法在图学习与信号恢复任务中均具有良好性能。