图上的信号处理：非结构化数据的因果建模
Signal Processing on Graphs: Causal Modeling of Unstructured Data
摘要：
许多应用程序收集大量的时间序列，例如，股票交易所中引用的公司的财务数据，访问医院急诊室的所有患者的医疗保健数据，或美国各地气象站连续测量的温度序列。这些数据通常被称为非结构化数据。其分析的第一个任务是导出一个低维表示，一个图或离散流形，它很好地描述了时间序列之间的相互关系和它们在时间上的内在关系。本文提出了一种计算上易于处理的算法来估计这个图结构的数据。所得到的图是有向的和加权的，可能捕获因果关系，而不仅仅是文献中许多现有方法中的相互关系。进行了收敛性分析。在随机图数据集和真实网络时间序列数据集上对算法进行了验证，并与相关算法进行了性能比较。新方法估计的邻接矩阵与模拟数据中的真实图接近，与测试数据中的先验物理知识一致。
英文摘要：
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences continuously measured by weather stations across the US. These data are often referred to as unstructured. A first task in its analytics is to derive a low dimensional representation, a graph or discrete manifold, that describes well the interrelations among the time series and their intrarelations across time. This paper presents a computationally tractable algorithm for estimating this graph that structures the data. The resulting graph is directed and weighted, possibly capturing causal relations, not just reciprocal correlations as in many existing approaches in the literature. A convergence analysis is carried out. The algorithm is demonstrated on random graph datasets and real network time series datasets, and its performance is compared to that of related methods. The adjacency matrices estimated with the new method are close to the true graph in the simulated data and consistent with prior physical knowledge in the real dataset tested.
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