Signal Processing on Graphs: Modeling (Causal) Relations in Big Data

Many big data 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. A first task in the analytics of these data 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 structure from the available data. This graph is directed and weighted, possibly representing causation relations, not just correlations as in most existing approaches in the literature. The algorithm is demonstrated on random graph 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.