TY - GEN

T1 - Network edge entropy from maxwell-boltzmann statistics

AU - Wang, Jianjia

AU - Wilson, Richard C.

AU - Hancock, Edwin R.

N1 - Publisher Copyright:
© Springer International Publishing AG 2017.

PY - 2017

Y1 - 2017

N2 - In prior work, we have shown how to compute global network entropy using a heat bath analogy and Maxwell-Boltzmann statistics. In this work, we show how to project out edge-entropy components so that the detailed distribution of entropy across the edges of a network can be computed. This is particularly useful if the analysis of non-homogeneous networks with a strong community as hub structure is being attempted. To commence, we view the normalized Laplacian matrix as the network Hamiltonian operator which specifies a set of energy states with the Laplacian eigenvalues. The network is assumed to be in thermodynamic equilibrium with a heat bath. According to this heat bath analogy, particles can populate the energy levels according to the classical Maxwell-Boltzmann distribution, and this distribution together with the energy states determines thermodynamic variables of the network such as entropy and average energy. We show how the entropy can be decomposed into components arising from individual edges using the eigenvectors of the normalized Laplacian. Compared to previous work based on the von Neumann entropy, this thermodynamic analysis is more effective in characterizing changes of network structure since it better represents the edge entropy variance associated with edges connecting nodes of large degree. Numerical experiments on real-world datasets are presented to evaluate the qualitative and quantitative differences in performance.

AB - In prior work, we have shown how to compute global network entropy using a heat bath analogy and Maxwell-Boltzmann statistics. In this work, we show how to project out edge-entropy components so that the detailed distribution of entropy across the edges of a network can be computed. This is particularly useful if the analysis of non-homogeneous networks with a strong community as hub structure is being attempted. To commence, we view the normalized Laplacian matrix as the network Hamiltonian operator which specifies a set of energy states with the Laplacian eigenvalues. The network is assumed to be in thermodynamic equilibrium with a heat bath. According to this heat bath analogy, particles can populate the energy levels according to the classical Maxwell-Boltzmann distribution, and this distribution together with the energy states determines thermodynamic variables of the network such as entropy and average energy. We show how the entropy can be decomposed into components arising from individual edges using the eigenvectors of the normalized Laplacian. Compared to previous work based on the von Neumann entropy, this thermodynamic analysis is more effective in characterizing changes of network structure since it better represents the edge entropy variance associated with edges connecting nodes of large degree. Numerical experiments on real-world datasets are presented to evaluate the qualitative and quantitative differences in performance.

KW - Maxwell-Boltzmann statistics

KW - Network edge entropy

UR - http://www.scopus.com/inward/record.url?scp=85032480461&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-68560-1_23

DO - 10.1007/978-3-319-68560-1_23

M3 - Conference Proceeding

AN - SCOPUS:85032480461

SN - 9783319685595

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 254

EP - 264

BT - Image Analysis and Processing - ICIAP 2017 - 19th International Conference, Proceedings

A2 - Schettini, Raimondo

A2 - Battiato, Sebastiano

A2 - Gallo, Giovanni

A2 - Stanco, Filippo

PB - Springer Verlag

T2 - 19th International Conference on Image Analysis and Processing, ICIAP 2017

Y2 - 11 September 2017 through 15 September 2017

ER -