Spatial Clustering of Time-Series via Mixture of Autoregressions Models and Markov Random Fields

摘要

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