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

2021 ◽  
pp. 1-1
Author(s):  
Cong Ye ◽  
Konstantinos Slavakis ◽  
Johan Nakuci ◽  
Sarah F. Muldoon ◽  
John Medaglia
Keyword(s):  
Time Series ◽  
Riemannian Manifolds ◽  
Multilayer Networks ◽  
Sequential Clustering

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

2020 ◽  
Author(s):  
Cong Ye ◽  
Konstantinos Slavakis ◽  
Johan Nakuci ◽  
Sarah F. Muldoon ◽  
John Medaglia
Keyword(s):  
Time Series ◽  
Riemannian Manifolds ◽  
Time Series Data ◽  
Moving Average ◽  
Point Clouds ◽  
Brain Network ◽  
Series Data ◽  
Network Clustering ◽  
Partial Correlations ◽  
Sequential Clustering

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 according to Riemannian multi-manifold modeling. A novel sequential-clustering scheme of Riemannian features is also established: feature points are first sampled in a non-random way to reveal the underlying geometric information, 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<br> (EEG) data.

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

2020 ◽  
Author(s):  
Cong Ye ◽  
Konstantinos Slavakis ◽  
Johan Nakuci ◽  
Sarah F. Muldoon ◽  
John Medaglia
Keyword(s):  
Time Series ◽  
Riemannian Manifolds ◽  
Time Series Data ◽  
Moving Average ◽  
Point Clouds ◽  
Brain Network ◽  
Series Data ◽  
Network Clustering ◽  
Partial Correlations ◽  
Sequential Clustering

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 according to Riemannian multi-manifold modeling. A novel sequential-clustering scheme of Riemannian features is also established: feature points are first sampled in a non-random way to reveal the underlying geometric information, 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<br> (EEG) data.

scholarly journals ONLINE CLASSIFICATION OF DYNAMIC MULTILAYER-NETWORK TIME SERIES IN RIEMANNIAN MANIFOLDS

2021 ◽  
Author(s):  
Cong Ye ◽  
Konstantinos Slavakis ◽  
Johan Nakuci ◽  
Sarah F. Muldoon ◽  
John Medaglia
Keyword(s):  
Time Series ◽  
Riemannian Manifolds ◽  
Moving Average ◽  
Brain Network ◽  
Training Data ◽  
Multilayer Network ◽  
Geometric Framework ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model

<div>This work exploits Riemannian manifolds to introduce a geometric framework for online state and community classification in dynamic multilayer networks where nodes are annotated with time series. A bottom-up approach is followed, starting from the extraction of Riemannian features from nodal time series, and reaching up to online/sequential classification of features via geodesic distances and angular information in the tangent spaces of a Riemannian manifold. As a case study, features in the Grassmann manifold are generated by fitting a kernel autoregressive-moving-average model to the nodal time series of the multilayer network. The paper highlights also numerical tests on synthetic and real brain-network data, where it is shown that the proposed geometric framework outperforms state-of-the-art deep-learning models in classification accuracy, especially in cases where the number of training data is small with respect to the number of the testing ones.</div><div><br></div><div>-------</div><div><br></div><div>© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<br></div><div><br></div>

scholarly journals TimeNexus: A Novel Cytoscape App to Analyze Time-Series Data Using Temporal MultiLayer Networks (tMLNs)

2020 ◽  
Author(s):  
Michaël Pierrelée ◽  
Ana Reynders ◽  
Fabrice Lopez ◽  
Aziz Moqrich ◽  
Laurent Tichit ◽  
...  
Keyword(s):  
Cell Cycle ◽  
Time Series ◽  
Network Structure ◽  
Time Series Data ◽  
Series Data ◽  
Omics Data ◽  
Expression Data ◽  
Temporal Expression ◽  
Multilayer Networks ◽  
Multilayer Network

Abstract Integrating -omics data with biological networks such as protein-protein interaction networks is a popular and useful approach to interpret expression changes of genes in changing conditions, and to identify relevant cellular pathways, active subnetworks or network communities. Yet, most -omics data integration tools are restricted to static networks and therefore cannot easily be used for analyzing time-series data. Determining regulations or exploring the network structure over time requires time-dependent networks which incorporate time as one component in their structure. Here, we present a method to project time-series data on sequential layers of a multilayer network, thus creating a temporal multilayer network (tMLN). We implemented this method as a Cytoscape app we named TimeNexus. TimeNexus allows to easily create, manage and visualize temporal multilayer networks starting from a combination of node and edge tables carrying the information on the temporal network structure. To allow further analysis of the tMLN, TimeNexus creates and passes on regular Cytoscape networks in form of static versions of the tMLN in three different ways: i) over the entire set of layers, ii) over two consecutive layers at a time, iii) or on one single layer at a time. We combined TimeNexus with the Cytoscape apps PathLinker and AnatApp/ANAT to extract active subnetworks from tMLNs. To test the usability of our app, we applied TimeNexus together with PathLinker or ANAT on temporal expression data of the yeast cell cycle and were able to identify active subnetworks relevant for different cell cycle phases. We furthermore used TimeNexus on our own temporal expression data from a mouse pain assay inducing hindpaw inflammation and detected active subnetworks relevant for an inflammatory response to injury, including immune response, cell stress response and regulation of apoptosis. TimeNexus is freely available from the Cytoscape app store at https://apps.cytoscape.org/apps/TimeNexus.

Time series generation by multilayer networks

1998 ◽  
Vol 57 (6) ◽  
pp. 6564-6572 ◽  
Author(s):  
Liat Ein-Dor ◽  
Ido Kanter
Keyword(s):  
Time Series ◽  
Multilayer Networks

scholarly journals Introducing the novel Cytoscape app TimeNexus to analyze time-series data using temporal MultiLayer Networks (tMLNs)

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Michaël Pierrelée ◽  
Ana Reynders ◽  
Fabrice Lopez ◽  
Aziz Moqrich ◽  
Laurent Tichit ◽  
...  
Keyword(s):  
Cell Cycle ◽  
Time Series ◽  
Network Structure ◽  
Time Series Data ◽  
Series Data ◽  
Omics Data ◽  
Expression Data ◽  
Temporal Expression ◽  
Multilayer Networks ◽  
Multilayer Network

AbstractIntegrating -omics data with biological networks such as protein–protein interaction networks is a popular and useful approach to interpret expression changes of genes in changing conditions, and to identify relevant cellular pathways, active subnetworks or network communities. Yet, most -omics data integration tools are restricted to static networks and therefore cannot easily be used for analyzing time-series data. Determining regulations or exploring the network structure over time requires time-dependent networks which incorporate time as one component in their structure. Here, we present a method to project time-series data on sequential layers of a multilayer network, thus creating a temporal multilayer network (tMLN). We implemented this method as a Cytoscape app we named TimeNexus. TimeNexus allows to easily create, manage and visualize temporal multilayer networks starting from a combination of node and edge tables carrying the information on the temporal network structure. To allow further analysis of the tMLN, TimeNexus creates and passes on regular Cytoscape networks in form of static versions of the tMLN in three different ways: (i) over the entire set of layers, (ii) over two consecutive layers at a time, (iii) or on one single layer at a time. We combined TimeNexus with the Cytoscape apps PathLinker and AnatApp/ANAT to extract active subnetworks from tMLNs. To test the usability of our app, we applied TimeNexus together with PathLinker or ANAT on temporal expression data of the yeast cell cycle and were able to identify active subnetworks relevant for different cell cycle phases. We furthermore used TimeNexus on our own temporal expression data from a mouse pain assay inducing hindpaw inflammation and detected active subnetworks relevant for an inflammatory response to injury, including immune response, cell stress response and regulation of apoptosis. TimeNexus is freely available from the Cytoscape app store at https://apps.cytoscape.org/apps/TimeNexus.

scholarly journals Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

2020 ◽  
Author(s):  
Cong Ye ◽  
Konstantinos Slavakis ◽  
Johan Nakuci ◽  
Sarah F. Muldoon ◽  
John Medaglia
Keyword(s):  
Time Series ◽  
Riemannian Manifolds ◽  
Moving Average ◽  
Brain Network ◽  
Training Data ◽  
Multilayer Network ◽  
Geometric Framework ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model

<div>This work exploits Riemannian manifolds to introduce a geometric framework for online state and community classification in dynamic multilayer networks where nodes are annotated with time series. A bottom-up approach is followed, starting from the extraction of Riemannian features from nodal time series, and reaching up to online/sequential classification of features via geodesic distances and angular information in the tangent spaces of a Riemannian manifold. As a case study, features in the Grassmann manifold are generated by fitting a kernel autoregressive-moving-average model to the nodal time series of the multilayer network. The paper highlights also numerical tests on synthetic and real brain-network data, where it is shown that the proposed geometric framework outperforms state-of-the-art deep-learning models in classification accuracy, especially in cases where the number of training data is small with respect to the number of the testing ones.</div><div><br></div><div>-------</div><div><br></div><div>© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<br></div><div><br></div>

Online Classification of Dynamic Multilayer-Network Time Series in Riemannian Manifolds

2020 ◽  
Author(s):  
Cong Ye ◽  
Konstantinos Slavakis ◽  
Johan Nakuci ◽  
Sarah F. Muldoon ◽  
John Medaglia
Keyword(s):  
Time Series ◽  
Riemannian Manifolds ◽  
Moving Average ◽  
Brain Network ◽  
Training Data ◽  
Multilayer Network ◽  
Geometric Framework ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model

<div>This work exploits Riemannian manifolds to introduce a geometric framework for online state and community classification in dynamic multilayer networks where nodes are annotated with time series. A bottom-up approach is followed, starting from the extraction of Riemannian features from nodal time series, and reaching up to online/sequential classification of features via geodesic distances and angular information in the tangent spaces of a Riemannian manifold. As a case study, features in the Grassmann manifold are generated by fitting a kernel autoregressive-moving-average model to the nodal time series of the multilayer network. The paper highlights also numerical tests on synthetic and real brain-network data, where it is shown that the proposed geometric framework outperforms state-of-the-art deep-learning models in classification accuracy, especially in cases where the number of training data is small with respect to the number of the testing ones.</div><div><br></div><div>-------</div><div><br></div><div>© 20XX IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.<br></div><div><br></div>

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

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