Model-based clustering with Hidden Markov Model regression for time series with regime changes
This addresses clustering for time series with regime changes, such as in railway diagnosis, but it is incremental as it builds on existing model-based clustering and HMM techniques.
The paper tackles clustering time series with regime changes by introducing a mixture of polynomial regressions governed by hidden Markov chains, and it demonstrates effectiveness through comparisons with existing methods like EM for Gaussian mixtures and K-means.
This paper introduces a novel model-based clustering approach for clustering time series which present changes in regime. It consists of a mixture of polynomial regressions governed by hidden Markov chains. The underlying hidden process for each cluster activates successively several polynomial regimes during time. The parameter estimation is performed by the maximum likelihood method through a dedicated Expectation-Maximization (EM) algorithm. The proposed approach is evaluated using simulated time series and real-world time series issued from a railway diagnosis application. Comparisons with existing approaches for time series clustering, including the stand EM for Gaussian mixtures, $K$-means clustering, the standard mixture of regression models and mixture of Hidden Markov Models, demonstrate the effectiveness of the proposed approach.