Model-based clustering and segmentation of time series with changes in regime

Abstract

Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the Expectation-Maximization (EM) algorithm. Within the context of a railway application, this paper introduces a novel mixture model for dealing with time series that are subject to changes in regime. The proposed approach, called ClustSeg, consists in modeling each cluster by a regression model in which the polynomial coefficients vary according to a discrete hidden process. In particular, this approach makes use of logistic functions to model the (smooth or abrupt) transitions between regimes. The model parameters are estimated by the maximum likelihood method solved by an Expectation-Maximization algorithm. This approach can also be regarded as a clustering approach which operates by finding groups of time series having common changes in regime. In addition to providing a time series partition, it therefore provides a time series segmentation. The problem of selecting the optimal numbers of clusters and segments is solved by means of the Bayesian Information Criterion (BIC). The ClustSeg approach is shown to be efficient using a variety of simulated time series and real-world time series of electrical power consumption from rail switching operations. Mixture model, Regression mixture, Hidden logistic proces

Laplace mixture of linear experts

“…For example, Wedel (2002) and Grun and Leisch (2008) considered MoLE densities for modeling concomitant variables; Ingrassia et al (2012) showed it to be related to cluster-weighted modeling; and Chamroukhi et al (2009Chamroukhi et al ( , 2010, and Same et al (2011) applied it to fit, classify, and cluster time-series data, respectively.…”

Model‐based clustering and classification of functional data

“…Each curve represents the consumed power by the switch motor during each switch operation and the aim is to predict the state of the switch given a new operation data, or to cluster the times series to discover possible defaults. These data were studied in Chamroukhi (), Chamroukhi, Samé, Govaert, and Aknin (), Chamroukhi et al (, ), and Samé, Chamroukhi, Govaert, and Aknin (). Figure e shows n = 120 curves where each curve consists of m = 564 observations and Figure f shows n = 146 curves where each curve consists of m = 511 observations.…”

Modeling and clustering water demand patterns from real-world smart meter data

“…Many functional clustering methods have been developed over the last decade. These methods can usually be separated into two categories: nonparametric methods using specific distances or dissimilarities between curves (Dabo-Niang et al, 2007), and mixture-model-based methods (Samé et al, 2011;Jacques and Preda, 2014). The collected curves can be multivariate, leading to a large representation space like in (Cheifetz et al, 2013) for change-point detection based on a specific curve modeling.…”