# Exact Topology Learning in a Network of Cyclostationary Processes

## TL;DR

This paper introduces an exact topology learning algorithm for networks of cyclostationary processes, leveraging a lifting technique and Wiener filter properties, with demonstrated accuracy on a resistor-capacitor network.

## Contribution

It is the first method to guarantee exact network topology recovery for cyclostationary processes without structural assumptions.

## Key findings

- Accurate reconstruction demonstrated on resistor-capacitor network.
- Performance improves with increasing sample size.
- First to guarantee exact recovery in this context.

## Abstract

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.