TY - JOUR
T1 - Multiscale dynamical embeddings of complex networks
AU - Schaub, Michael T.
AU - Delvenne, Jean Charles
AU - Lambiotte, Renaud
AU - Barahona, Mauricio
N1 - Funding Information:
J.C.D. and R.L. acknowledge support from FRS-FNRS, the Belgian Network DYSCO (Dynamical Systems, Control, and Optimisation) funded by the Interuniversity Attraction Poles Programme initiated by the Belgian State Science Policy Office, and the ARC (Action de Recherche Concerte) on Mining and Optimization of Big Data Models funded by the Wallonia-Brussels Federation. M.T.S. received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 702410. M.B. acknowledges funding from the EPSRC (Grant No. EP/N014529/1). The funders had no role in the design of this study; the results presented here reflect solely the authors' views. We thank Leto Peel, Mauro Faccin, and Nima Dehmamy for interesting discussions.
Publisher Copyright:
© 2019 American Physical Society.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/6/20
Y1 - 2019/6/20
N2 - Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.
AB - Complex systems and relational data are often abstracted as dynamical processes on networks. To understand, predict, and control their behavior, a crucial step is to extract reduced descriptions of such networks. Inspired by notions from control theory, we propose a time-dependent dynamical similarity measure between nodes, which quantifies the effect a node-input has on the network. This dynamical similarity induces an embedding that can be employed for several analysis tasks. Here we focus on (i) dimensionality reduction, i.e., projecting nodes onto a low-dimensional space that captures dynamic similarity at different timescales, and (ii) how to exploit our embeddings to uncover functional modules. We exemplify our ideas through case studies focusing on directed networks without strong connectivity and signed networks. We further highlight how certain ideas from community detection can be generalized and linked to control theory, by using the here developed dynamical perspective.
UR - http://www.scopus.com/inward/record.url?scp=85068362147&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.99.062308
DO - 10.1103/PhysRevE.99.062308
M3 - Article
AN - SCOPUS:85068362147
SN - 2470-0045
VL - 99
JO - Physical Review E
JF - Physical Review E
IS - 6
M1 - 062308
ER -