Segmental dynamic factor analysis for time series of curves

• Published in: Statistics and computing Vol. 27; no. 6; pp. 1617 - 1637
• Main Authors: Samé, Allou, Govaert, Gérard
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2017; Springer Nature B.V; Springer Verlag (Germany)
• Subjects: 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; 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
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-016-9707-5

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.