Exact Topology Learning in a Network of Cyclostationary Processes
It solves the exact topology recovery problem for cyclostationary data, which is relevant to power grids, biology, and finance, and is the first to guarantee exact recovery without structural assumptions.
This work presents the first algorithm for exact topology learning in networks of cyclostationary processes without any assumptions on the underlying structure, demonstrated on a Resistor-Capacitor network with accuracy varying by sample size.
Learning the structure of a network from time series data, in particular cyclostationary data, is of significant interest in many disciplines such as power grids, biology and finance. In this article, an algorithm is presented for reconstruction of the topology of a network of cyclostationary processes. To the best of our knowledge, this is the first work to guarantee exact recovery without any assumptions on the underlying structure. The method is based on a lifting technique by which cyclostationary processes are mapped to vector wide sense stationary processes and further on semi-definite properties of matrix Wiener filters for the said processes.We demonstrate the performance of the proposed algorithm on a Resistor-Capacitor network and present the accuracy of reconstruction for varying sample sizes.