Analysis and identification of complex stochastic systems admitting a flocking structure

We discuss a new modeling paradigm for large dimensional aggregates of stochastic systems by Generalized Factor Analysis (GFA) models. These models describe the data as the sum of a flocking plus an uncorrelated idiosyncratic component. The flocking component describes a sort of collective orderly motion which admits a much simpler mathematical description than the whole ensemble while the idiosyncratic component describes weakly correlated noise. The extraction of the dynamic flocking component is discussed for timestationary systems and for a simple class of separable random fields.