Modeling complex systems by Generalized Factor Analysis

TL;DR

This paper introduces Generalized Factor Analysis (GFA), a new modeling approach for large stochastic systems that separates collective flocking behavior from uncorrelated noise, simplifying analysis of complex data.

Contribution

It presents a novel GFA framework that decomposes large stochastic systems into flocking and noise components, with rigorous characterization and methods for dynamic extraction.

Findings

GFA effectively separates collective motion from noise in large systems.

Static GFA components are rigorously characterized.

Dynamic GFA extraction methods are proposed for specific systems.

Abstract

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.