6533b835fe1ef96bd129f6fc

RESEARCH PRODUCT

Model Identification of a Network as Compressing Sensing

Donatello MaterassiGiacomo InnocentiMurti V. SalapakaLaura Giarre

subject

IdentificationReduced modelTheoretical computer scienceGeneral Computer ScienceDynamical systems theoryComputer scienceNetworkTopology (electrical circuits)Dynamical Systems (math.DS)Systems and Control (eess.SY)Set (abstract data type)symbols.namesakeFOS: MathematicsFOS: Electrical engineering electronic engineering information engineeringElectrical and Electronic EngineeringMathematics - Dynamical SystemsMathematics - Optimization and ControlMathematics - General TopologySparsificationMechanical EngineeringWiener filterSystem identificationGeneral Topology (math.GN)Function (mathematics)Compressive sensingIdentification (information)Compressed sensingControl and Systems EngineeringOptimization and Control (math.OC)symbolsIdentification; Sparsification; Reduced models; Networks; Compressive sensingComputer Science - Systems and Control

description

In many applications, it is important to derive information about the topology and the internal connections of dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology, and unveiling an unknown structure as the estimate of a "sparse Wiener filter". A geometric interpretation of the problem in a pre-Hilbert space for wide-sense stochastic processes is provided. We cast the problem as the optimization of a cost function where a set of parameters are used to operate a trade-off between accuracy and complexity in the final model. The problem of reducing the complexity is addressed by fixing a certain degree of sparsity and finding the solution that "better" satisfies the constraints according to the criterion of approximation. Applications starting from real data and numerical simulations are provided.

yearjournalcountryeditionlanguage
2013-01-01
https://dx.doi.org/10.48550/arxiv.1103.0744