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>

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 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>

Time series modelling — an integrated approach

1982 ◽  
Vol 19 (A) ◽  
pp. 413-425
Author(s):  
Don McNeil
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Integrated Approach ◽  
Autoregressive Moving Average ◽  
Linear Segment ◽  
Economic Data ◽  
Autoregressive Moving Average Model ◽  
Straight Line ◽  
Time Series Modelling ◽  
Moving Average Model

Some inadequacies of both the traditional (exponential smoothing) and Box-Jenkins approaches to time series forecasting of economic data are investigated. An approach is suggested which integrates these two methodologies. It is based on smoothing the data using straight line segments instead of differencing to obtain stationarity, and forecasting using an autoregressive-moving-average model for the residuals from the most recent linear segment. The efficiency of this approach is calculated theoretically using a series comprising integrated white noise.

scholarly journals Reliability Prediction of Ontology-Based Service Compositions Using Petri Net and Time Series Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Jia Li ◽  
Yunni Xia ◽  
Xin Luo
Keyword(s):  
Time Series ◽  
Petri Net ◽  
Response Times ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Firing Rates ◽  
Dynamic Framework ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model ◽  
Service Components

OWL-S, one of the most important Semantic Web service ontologies proposed to date, provides a core ontological framework and guidelines for describing the properties and capabilities of their web services in an unambiguous, computer interpretable form. Predicting the reliability of composite service processes specified in OWL-S allows service users to decide whether the process meets the quantitative quality requirement. In this study, we consider the runtime quality of services to be fluctuating and introduce a dynamic framework to predict the runtime reliability of services specified in OWL-S, employing the Non-Markovian stochastic Petri net (NMSPN) and the time series model. The framework includes the following steps: obtaining the historical response times series of individual service components; fitting these series with a autoregressive-moving-average-model (ARMA for short) and predicting the future firing rates of service components; mapping the OWL-S process into a NMSPN model; employing the predicted firing rates as the model input of NMSPN and calculating the normal completion probability as the reliability estimate. In the case study, a comparison between the static model and our approach based on experimental data is presented and it is shown that our approach achieves higher prediction accuracy.

Modeling and Forecasting Sales Data by Time Series Analysis

1981 ◽  
Vol 18 (1) ◽  
pp. 94-100 ◽  
Author(s):  
S. G. Kapoor ◽  
P. Madhok ◽  
S. M. Wu
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Time Series Modeling ◽  
Average Model ◽  
Sales Data ◽  
Autoregressive Moving Average Model ◽  
Deterministic Function ◽  
Modeling And Forecasting ◽  
Moving Average Model

Time series modeling technique is used to model a series of sales data in which seasonality causes distinct spike peaks. The analysis of actual sales data shows that the seasonality in the data can be approximated by a deterministic function and the stochastic component is a sixth-order autoregressive moving average model. Use of the combined deterministic and stochastic models to derive the minimum mean squared forecast yields reliable results.

Health Prognostic Method Based on the Time Series Analysis for Actuators

2013 ◽  
Vol 373-375 ◽  
pp. 329-332 ◽  
Author(s):  
Jing Kai Zhang ◽  
Juan Wang ◽  
Xiao Xiong Liu ◽  
Wei Guo Zhang
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Flight Control ◽  
Moving Average ◽  
Autoregressive Moving Average ◽  
Health State ◽  
Future Health ◽  
Series Analysis ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model

The purpose of health prognostic is to predict the future health status of system and determine the time from the current health state to functional failure completely. Application data time series analysis method often can get the expected prediction effect. Taking into account the failure characteristics of the actuators in flight control system, the autoregressive moving average model is introduced to health prognostic. The prognostic model is established. The simulation results show the effectiveness of the algorithm.

Time series modelling — an integrated approach

1982 ◽  
Vol 19 (A) ◽  
pp. 413-425
Author(s):  
Don McNeil
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Integrated Approach ◽  
Autoregressive Moving Average ◽  
Linear Segment ◽  
Economic Data ◽  
Autoregressive Moving Average Model ◽  
Straight Line ◽  
Time Series Modelling ◽  
Moving Average Model

Some inadequacies of both the traditional (exponential smoothing) and Box-Jenkins approaches to time series forecasting of economic data are investigated. An approach is suggested which integrates these two methodologies. It is based on smoothing the data using straight line segments instead of differencing to obtain stationarity, and forecasting using an autoregressive-moving-average model for the residuals from the most recent linear segment. The efficiency of this approach is calculated theoretically using a series comprising integrated white noise.

Estimation and Forecast Performance of a Multivariate Time Series Model of Sales

1980 ◽  
Vol 17 (4) ◽  
pp. 558-565 ◽  
Author(s):  
Mark Moriarty ◽  
Gerald Salamon
Keyword(s):  
Time Series ◽  
Moving Average ◽  
Multivariate Time Series ◽  
Substantial Improvement ◽  
Product Line ◽  
Time Series Model ◽  
Autoregressive Moving Average ◽  
Forecast Performance ◽  
Autoregressive Moving Average Model ◽  
Moving Average Model

A unique form of a multivariate time series model—a “seemingly unrelated autoregressive moving average” model (SURARMA)—is developed in the context of forecasting unit sales of a product in four states. Data from an anonymous firm are used to test the appropriateness of the model and are found to conform to the model's constraints. The model provides substantial improvement in parameter estimation efficiency and forecast performance in comparison with individual state univariate models. SURARMA is potentially relevant to many market forecasting problems involving multiple constituent time series subunits such as states, regions, or products from a product line.

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.

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