  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.
