State-Space Models for Clustering of Compositional Trajectories

Compositional data are drawing increasing interest for their ability to depict interdependent and constrained observations. While time series analysis has sometimes been employed for the study of individual compositional trajectories, little attention has been given to finding and modeling groups of trajectories. Driven by a sustainable mobility motivation, we propose a model-based approach, relying on a state space model representation and an Expectation-Maximization algorithm, for clustering compositional trajectories according to their evolution in the simplex. Trajectory covariates, not captured by the compositional representation, can be included in the component weights in a mixture of experts fashion. The method is applied to urban movement data, where people’s movements are represented in the simplex by the proportions of road types in their surroundings.