Title: Dynamic matrix-variate clustering of sport activities
Authors: Mattia Stival - University of Padova-Dipartimento di Scienze Statistiche (Italy) [presenting]
Mauro Bernardi - University of Padova (Italy)
Abstract: A Bayesian matrix-variate state-space model is proposed which able to classify the trajectories of a large number (N) of P variate time series. The matrix state-space formulation allows us to consider both longitudinal and cross-sectional dependence, accounting also for missing values. Indeed, the matrix autoregressive process described by the state equation captures the time series dependence, and the use of matrix-variate normal distributions for both the measurement errors and state disturbances allows to consider cross-sectional dependence within variables (P) and between time series (N), and within states and between groups, respectively. A fully conjugate approach is adopted, and the relative Gibbs sampler is provided; to speed up the computations, Kalman recursions are performed on a vectorized and reduced form of the model. Further achievements can be derived by considering Metropolis-Hasting step to estimate in one-shot an unknown selection matrix, storing the time series cluster allocations. In the application part, we analyze the running activities of one athlete collected by his smartwatch, to say whether his performances are improving over time. In this context, data are collected as a sequence of activities, where each activity is represented by a multivariate time series, characterized by complex behavior and the presence of missing values.