Authors:
H. R. Sachin Prabhu
and
Hua-Liang Wei
Affiliation:
The University of Sheffield, United Kingdom
Keyword(s):
Bipartite Graphs, Reduced Graphs, Ordered Matching, Rank, Subnetworks.
Related
Ontology
Subjects/Areas/Topics:
Informatics in Control, Automation and Robotics
;
Information-Based Models for Control
;
Modeling, Analysis and Control of Discrete-event Systems
;
Signal Processing, Sensors, Systems Modeling and Control
;
Signal Reconstruction
;
System Modeling
Abstract:
The problem of network inference can be solved as a constrained matrix factorization problem where some sparsity constraints are imposed on one of the matrix factors. The solution is unique up to a scaling factor when certain rank conditions are imposed on both the matrix factors. Two key issues in factorising a matrix of data from some netwrok are that of establishing simple identifiability conditions and decomposing a network into identifiable subnetworks. This paper solves both the problems by introducing the notion of an ordered matching in a bipartite graphs. Novel and simple graph theoretical conditions are developed which can replace the aforementioned computationally intensive rank conditions. A simple algorithm to reduce a bipartite graph and a graph preprocessing algorithm to decompose a network into a set of identifiable subsystems is proposed.