TY - JOUR

T1 - Noninvasive Approximation of Linear Dynamic System Networks Using Polytrees

AU - Sepehr, Firoozeh

AU - Materassi, Donatello

N1 - Publisher Copyright:
© 2014 IEEE.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - 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.

AB - 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.

KW - Linear Dynamic Systems

KW - Network Topology

KW - Non-invasive Approach

KW - Polytree Structure

KW - Topology Approximation

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U2 - 10.1109/tcns.2021.3065646

DO - 10.1109/tcns.2021.3065646

M3 - Article

AN - SCOPUS:85102676788

SN - 2325-5870

VL - 8

SP - 1314

EP - 1323

JO - IEEE Transactions on Control of Network Systems

JF - IEEE Transactions on Control of Network Systems

IS - 3

ER -