Modeling complex systems by Generalized Factor Analysis
This work offers a foundational framework for simplifying the analysis of complex stochastic systems, benefiting researchers in statistical modeling and machine learning.
The paper introduces Generalized Factor Analysis (GFA) as a new modeling paradigm for large-dimensional stochastic systems, decomposing data into a flocking component and an idiosyncratic component. It provides rigorous characterizations and discusses extraction methods for stationary linear systems and separable random fields.
We propose 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. We first discuss static GFA representations and characterize in a rigorous way the properties of the two components. The extraction of the dynamic flocking component is discussed for time-stationary linear systems and for a simple classes of separable random fields.