Segmental dynamic factor analysis for time series of curves
A new approach is introduced in this article for describing and visualizing time series of curves, where each curve has the particularity of being subject to changes in regime. For this purpose, the curves are represented by a regression model including a latent segmentation, and their temporal evol...
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| Published in | Statistics and computing Vol. 27; no. 6; pp. 1617 - 1637 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.11.2017
Springer Nature B.V Springer Verlag (Germany) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0960-3174 1573-1375 |
| DOI | 10.1007/s11222-016-9707-5 |
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| Abstract | A new approach is introduced in this article for describing and visualizing time series of curves, where each curve has the particularity of being subject to changes in regime. For this purpose, the curves are represented by a regression model including a latent segmentation, and their temporal evolution is modeled through a Gaussian random walk over low-dimensional factors of the regression coefficients. The resulting model is nothing else than a particular state-space model involving discrete and continuous latent variables, whose parameters are estimated across a sequence of curves through a dedicated variational Expectation-Maximization algorithm. The experimental study conducted on simulated data and real time series of curves has shown encouraging results in terms of visualization of their temporal evolution and forecasting. |
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| AbstractList | A new approach is introduced in this article for describing and visualizing time series of curves, where each curve has the particularity of being subject to changes in regime. For this purpose, the curves are represented by a regression model including a latent segmentation, and their temporal evolution is modeled through a Gaussian random walk over low-dimensional factors of the regression coefficients. The resulting model is nothing else than a particular state-space model involving discrete and continuous latent variables, whose parameters are estimated across a sequence of curves through a dedicated variational Expectation-Maximization algorithm. The experimental study conducted on simulated data and real time series of curves has shown encouraging results in terms of visualization of their temporal evolution and forecasting. A new approach is introduced in this article for describing and visualizing time series of curves, where each curve has the particularity of being subject to changes in regime. For this purpose, the curves are represented by a regression model including a latent segmentation, and their temporal evolution is modeled through a Gaussian random walk over low dimensional factors of the regression coefficients. The resulting model is neither else than a particular state-space model involving discrete and continuous latent variables, whose parameters are estimated across a sequence of curves through a dedicated variational Expectation-Maximization algorithm. The experimental study conducted on simulated data and real time series of curves has shown encouraging results in terms of visualization of their temporal evolution and forecasting. |
| Author | Govaert, Gérard Samé, Allou |
| Author_xml | – sequence: 1 givenname: Allou surname: Samé fullname: Samé, Allou email: allou.same@ifsttar.fr organization: Université Paris-Est, IFSTTAR, COSYS, GRETTIA – sequence: 2 givenname: Gérard surname: Govaert fullname: Govaert, Gérard organization: Laboratoire Heudiasyc, UMR CNRS 7253, Université de Technologie de Compiègne |
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| CitedBy_id | crossref_primary_10_1016_j_knosys_2021_106991 crossref_primary_10_1109_LSP_2022_3185958 crossref_primary_10_1214_22_AOAS1724 crossref_primary_10_1007_s10614_019_09952_5 crossref_primary_10_1109_JSEN_2024_3493893 |
| Cites_doi | 10.1214/12-AOAS551 10.1016/j.neunet.2009.06.040 10.1093/comjnl/bxq003 10.1111/j.1467-9892.1982.tb00349.x 10.1016/S0893-6080(99)00066-0 10.1016/j.jeconom.2005.03.005 10.1002/env.611 10.1109/TPAMI.2009.149 10.1111/1467-9469.00215 10.1002/9780470191613 10.1093/biomet/87.3.587 10.1007/978-1-4757-7107-7 10.1007/978-1-4419-7865-3 10.1016/S0167-9473(02)00183-4 10.1017/S037016460002006X 10.1090/S0025-5718-1972-0323087-4 10.1016/j.csda.2006.07.028 10.1115/1.3662552 10.1080/07350015.2014.941467 10.1023/A:1007665907178 10.1080/14786440109462720 10.1109/TAC.2008.2008348 10.1111/j.1467-9868.2007.00601.x 10.1111/j.2517-6161.1977.tb01600.x 10.1111/j.2517-6161.1984.tb01288.x 10.1109/IJCNN.2009.5178921 10.1007/BF02294246 10.1145/1143844.1143859 |
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| Keywords | Functional time series Condition monitoring Variational EM Visualization and forecasting Dynamic factor analysis Mixture of regressions RAILWAY CONDITION MONITORING SERIE TEMPORELLE MIXTURE OF REGRESSION DYNAMIC FACTOR ANALYSIS PREVISION VARIATIONAL ALGORITHM FUNCTIONAL DATA VISUALIZATION SEGMENTATION COURBE |
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| SubjectTerms | Artificial Intelligence Computer simulation Continuity (mathematics) Economic models Engineering Sciences Evolution Factor analysis Mathematics and Statistics Other Parameter estimation Probability and Statistics in Computer Science Random walk Regression analysis Regression coefficients State space models Statistical Theory and Methods Statistics Statistics and Computing/Statistics Programs Time series |
| Title | Segmental dynamic factor analysis for time series of curves |
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