A Regression Mixture Model with Spatial Constraints for Clustering Spatiotemporal Data

We present a new approach for curve clustering designed for analysis of spatiotemporal data. Such data contains both spatial and temporal patterns that we desire to capture. The proposed methodology is based on regression and Gaussian mixture modeling. The novelty of the herein work is the incorporation of spatial smoothness constraints in the form of a prior for the data labels. This allows to take into account the property of spatiotemporal data according to which spatially adjacent data points have higher probability to belong to the same cluster. The proposed model can be formulated as a Maximum a Posteriori (MAP) problem, where the Expectation Maximization (EM) algorithm is used to estimate the model parameters. Several numerical experiments with both simulated data and real cardiac perfusion MRI data are used for evaluating the methodology. The results are promising and demonstrate the value of the proposed approach.