Model Identification of a Network as Compressing Sensing
For researchers in network science, this work provides a geometric framework for network identification, but the results are incremental and lack quantitative benchmarks.
The paper addresses the problem of inferring network topology from time-series data without prior knowledge, formulating it as a sparse Wiener filter estimation. The approach is validated on real data and simulations, though no concrete performance numbers are reported.
In many applications, it is important to derive information about the topology and the internal connections of dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology, and unveiling an unknown structure as the estimate of a "sparse Wiener filter". A geometric interpretation of the problem in a pre-Hilbert space for wide-sense stochastic processes is provided. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the solution that "better" satisfies the constraints according to the criterion of approximation. Applications starting from real data and numerical simulations are provided.