Longitudinal data are widely used information for repeated observations of the same units over a period of time in order to investigate developmental trends across life span of units. Each object depicts, in the space of the features and of time, a trajectory describing its changes over time. Here trajectories are modeled according to three features: trend, velocity and acceleration. Clustering trajectories of a longitudinal data set is an important issue to assess similarities in the histories of the observed units that we fully discuss in this chapter. Starting from the Tucker model, widely used in psychometrics, we consider the optimal partition of trajectories that minimizes a distance accounting for trend, for velocity and for acceleration of trajectories. A Sequential Quadratic Programming algorithm is proposed to solve the clustering problem and its performance is evaluated by simulation
