Spatial clustering of time series via mixture of autoregressions models and Markov random fields

Time series data arise in many medical and biological imaging scenarios. In such images, a time series is obtained at each of a large number of spatially dependent data units. It is interesting to organize these data into model‐based clusters. A two‐stage procedure is proposed. In stage 1, a mixture of autoregressions (MoAR) model is used to marginally cluster the data. The MoAR model is fitted using maximum marginal likelihood (MMaL) estimation via a minorization–maximization (MM) algorithm. In stage 2, a Markov random field (MRF) model induces a spatial structure onto the stage 1 clustering. The MRF model is fitted using maximum pseudolikelihood (MPL) estimation via an MM algorithm. Both the MMaL and MPL estimators are proved to be consistent. Numerical properties are established for both MM algorithms. A simulation study demonstrates the performance of the two‐stage procedure. An application to the segmentation of a zebrafish brain calcium image is presented.