On reduction of graphs and Markov chain models

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper introduces a new method for reducing large directed graphs to simpler graphs with fewer nodes. The reduction is carried out through node and edge aggregation, where the simpler graph is representative of the original large graph. Representativeness is measured using a metric defined herein, which is motivated by thermodynamic free energy and vector quantization problems in the data compression literature. The resulting aggregation scheme is largely based on the maximum entropy principle. The proposed algorithm is general in the sense that it can accommodate a large class of functions for characterizing distance between the nodes. As a special case, we show that this method applies to the Markov chain model-reduction problem, providing a soft-clustering approach that enables better aggregation of state-transition matrices than existing methods. Simulation results are provided to illustrate the theoretical results.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages2317-2322
Number of pages6
DOIs
StatePublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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