Information-based measure for influence characterization in dynamical systems with applications

In this paper, we introduce novel measure based on information to define influence in a dynamical system. The objective is to determine how a particular state (or a linear combination of states) in dynamical system influence or participate in the dynamics of another state (or a linear combination of states). An important parameter in determining the influence is the definition of the influence. We propose information or entropy-based measure for influence characterization. In particular, state x is said to influence or participate in the dynamics of state y, if the evolution of state x results in change in entropy or information content of state y. This work builds on our prior work on formalism for information transfer in dynamical network [1]. We discuss the applications of the developed framework for influence characterization in power system and social network. For power system, the proposed influence measure is used for the computation of participation factor of individual generator to the inter-area oscillation mode of the power system. For social network application, we use a Twitter network for influence characterization. The influence measure is used to understand the distribution of influential nodes and for influence-based clustering of the Twitter network.

[1]  Markus Siegel,et al.  Cortical information flow during flexible sensorimotor decisions , 2015, Science.

[2]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[3]  Alan M. Frieze,et al.  Clustering Large Graphs via the Singular Value Decomposition , 2004, Machine Learning.

[4]  J. Massey.  CAUSALITY, FEEDBACK AND DIRECTED INFORMATION , 1990 .

[5]  Umesh Vaidya,et al.  On information transfer in discrete dynamical systems , 2017, 2017 Indian Control Conference (ICC).

[6]  José Ignacio Pérez Arriaga,et al.  Selective modal analysis with applications to electric power systems , 1981 .

[7]  G. Verghese,et al.  Selective Modal Analysis With Applications to Electric Power Systems, Part II: The Dynamic Stability Problem , 1982, IEEE Transactions on Power Apparatus and Systems.

[8]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[9]  C. Sims.  Money, Income, and Causality , 1972 .

[10]  Alfred O. Hero,et al.  Motif Discovery in Tissue-Specific Regulatory Sequences Using Directed Information , 2007, EURASIP J. Bioinform. Syst. Biol..

[11]  O. Sporns.  Networks of the Brain , 2010 .

[12]  Umesh Vaidya,et al.  Formalism for information transfer in dynamical network , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[13]  Pramod P. Khargonekar,et al.  Introduction to wide-area control of power systems , 2013, 2013 American Control Conference.

[14]  Mathukumalli Vidyasagar,et al.  Probabilistic Methods in Cancer Biology , 2011, Eur. J. Control.

[15]  C. Granger.  Investigating Causal Relations by Econometric Models and Cross-Spectral Methods , 1969 .

[16]  M. Lam,et al.  All Friends are Not Equal : Using Weights in Social Graphs to Improve Search , 2010 .