Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks

This work exploits Riemannian manifolds to build a sequential-clustering framework able to address a wide variety of clustering tasks in dynamic multilayer (brain) networks via the information extracted from their nodal time-series. The discussion follows a bottom-up path, starting from feature extr...

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Autores principales:	Cong Ye, Konstantinos Slavakis, Johan Nakuci, Sarah F. Muldoon, John Medaglia
Formato:	article
Lenguaje:	EN
Publicado:	IEEE 2021
Materias:	Clustering multilayer network Riemannian manifold sequential time-series Electrical engineering. Electronics. Nuclear engineering TK1-9971
Acceso en línea:	https://doaj.org/article/8f51f7bb7a254092b4f80807399cb5a5
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id	oai:doaj.org-article:8f51f7bb7a254092b4f80807399cb5a5
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spelling	oai:doaj.org-article:8f51f7bb7a254092b4f80807399cb5a52021-11-20T00:03:10ZFast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks2644-132210.1109/OJSP.2021.3051453https://doaj.org/article/8f51f7bb7a254092b4f80807399cb5a52021-01-01T00:00:00Zhttps://ieeexplore.ieee.org/document/9321498/https://doaj.org/toc/2644-1322This work exploits Riemannian manifolds to build a sequential-clustering framework able to address a wide variety of clustering tasks in dynamic multilayer (brain) networks via the information extracted from their nodal time-series. The discussion follows a bottom-up path, starting from feature extraction from time-series and reaching up to Riemannian manifolds (feature spaces) to address clustering tasks such as state clustering, community detection (a.k.a. network-topology identification), and subnetwork-sequence tracking. Kernel autoregressive-moving-average modeling and kernel (partial) correlations serve as case studies of generating features in the Riemannian manifolds of Grassmann and positive-(semi)definite matrices, respectively. Feature point-clouds form clusters which are viewed as submanifolds through the Riemannian multi-manifold modeling. A novel sequential-clustering scheme of Riemannian features is also established: landmark points are first identified in a <italic>non-random</italic> way to reveal the underlying geometric information of the feature point-cloud, and, then, a fast sequential-clustering scheme is brought forth that takes advantage of Riemannian distances and the angular information on tangent spaces. By virtue of the landmark points and the sequential processing of the Riemannian features, the computational complexity of the framework is rendered free from the length of the available time-series data. The effectiveness and computational efficiency of the proposed framework is validated by extensive numerical tests against several state-of-the-art manifold-learning and (brain-)network-clustering schemes on synthetic as well as real functional-magnetic-resonance-imaging (fMRI) and electro-encephalogram (EEG) data.Cong YeKonstantinos SlavakisJohan NakuciSarah F. MuldoonJohn MedagliaIEEEarticleClusteringmultilayernetworkRiemannian manifoldsequentialtime-seriesElectrical engineering. Electronics. Nuclear engineeringTK1-9971ENIEEE Open Journal of Signal Processing, Vol 2, Pp 67-84 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Clustering multilayer network Riemannian manifold sequential time-series Electrical engineering. Electronics. Nuclear engineering TK1-9971
spellingShingle	Clustering multilayer network Riemannian manifold sequential time-series Electrical engineering. Electronics. Nuclear engineering TK1-9971 Cong Ye Konstantinos Slavakis Johan Nakuci Sarah F. Muldoon John Medaglia Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks
description	This work exploits Riemannian manifolds to build a sequential-clustering framework able to address a wide variety of clustering tasks in dynamic multilayer (brain) networks via the information extracted from their nodal time-series. The discussion follows a bottom-up path, starting from feature extraction from time-series and reaching up to Riemannian manifolds (feature spaces) to address clustering tasks such as state clustering, community detection (a.k.a. network-topology identification), and subnetwork-sequence tracking. Kernel autoregressive-moving-average modeling and kernel (partial) correlations serve as case studies of generating features in the Riemannian manifolds of Grassmann and positive-(semi)definite matrices, respectively. Feature point-clouds form clusters which are viewed as submanifolds through the Riemannian multi-manifold modeling. A novel sequential-clustering scheme of Riemannian features is also established: landmark points are first identified in a <italic>non-random</italic> way to reveal the underlying geometric information of the feature point-cloud, and, then, a fast sequential-clustering scheme is brought forth that takes advantage of Riemannian distances and the angular information on tangent spaces. By virtue of the landmark points and the sequential processing of the Riemannian features, the computational complexity of the framework is rendered free from the length of the available time-series data. The effectiveness and computational efficiency of the proposed framework is validated by extensive numerical tests against several state-of-the-art manifold-learning and (brain-)network-clustering schemes on synthetic as well as real functional-magnetic-resonance-imaging (fMRI) and electro-encephalogram (EEG) data.
format	article
author	Cong Ye Konstantinos Slavakis Johan Nakuci Sarah F. Muldoon John Medaglia
author_facet	Cong Ye Konstantinos Slavakis Johan Nakuci Sarah F. Muldoon John Medaglia
author_sort	Cong Ye
title	Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks
title_short	Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks
title_full	Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks
title_fullStr	Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks
title_full_unstemmed	Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks
title_sort	fast sequential clustering in riemannian manifolds for dynamic and time-series-annotated multilayer networks
publisher	IEEE
publishDate	2021
url	https://doaj.org/article/8f51f7bb7a254092b4f80807399cb5a5
work_keys_str_mv	AT congye fastsequentialclusteringinriemannianmanifoldsfordynamicandtimeseriesannotatedmultilayernetworks AT konstantinosslavakis fastsequentialclusteringinriemannianmanifoldsfordynamicandtimeseriesannotatedmultilayernetworks AT johannakuci fastsequentialclusteringinriemannianmanifoldsfordynamicandtimeseriesannotatedmultilayernetworks AT sarahfmuldoon fastsequentialclusteringinriemannianmanifoldsfordynamicandtimeseriesannotatedmultilayernetworks AT johnmedaglia fastsequentialclusteringinriemannianmanifoldsfordynamicandtimeseriesannotatedmultilayernetworks
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Fast Sequential Clustering in Riemannian Manifolds for Dynamic and Time-Series-Annotated Multilayer Networks

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