## Abstract

We consider the problem of approximating a complex network of linear dynamic systems via a simpler network, with the goal of highlighting the most significant connections. Indeed, paradoxically, an approximate network with fewer edges could be more informative in terms of how a system operates than a more accurate representation including a large number of 'weak' links. Broadly, this article explores the meaning of approximating a network belonging to a certain class using another network belonging to a subset of its class (the set of approximators). We posit that any network approximation algorithm is expected to satisfy at least a congruity property. By congruity, we mean that if the approximated network belongs to the set of approximators, then the algorithm should map it into itself. From a technical perspective, we choose a class of dynamic networks with a directed tree (polytree) structure as a set of approximators and analytically derive a technique, which asymptotically satisfies the congruity property when the observation horizon approaches infinity. Also, we test such a technique using high-frequency financial data. Financial data provide a challenging benchmark since they are not expected to meet the theoretical assumptions behind our methodology, such as linearity or stationarity.

Original language | English (US) |
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Pages (from-to) | 1314-1323 |

Number of pages | 10 |

Journal | IEEE Transactions on Control of Network Systems |

Volume | 8 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 2021 |

### Bibliographical note

Funding Information:Manuscript received May 31, 2020; revised June 1, 2020 and December 23, 2020; accepted February 3, 2021. Date of publication March 11, 2021; date of current version September 17, 2021. This work was supported in part by the NSF (CNS CAREER #1553504, and SaTC #1816703). Recommended by Associate Editor M. R. Jovanovic. (Corresponding author: Firoozeh Sepehr.) Firoozeh Sepehr is with the Department of the Electrical Engineering and Computer Science, University of Tennessee Knoxville, Knoxville, TN 37996 USA (e-mail: fsepehr1@vols.utk.edu).

Publisher Copyright:

© 2014 IEEE.

## Keywords

- Linear Dynamic Systems
- Network Topology
- Non-invasive Approach
- Polytree Structure
- Topology Approximation