A Fuzzy Order for Graphs Based on the Continuous Entropy of Gaussian Markov Random Fields

DOI

10.2991/asum.k.210827.067How to use a DOI?

Keywords

Gaussian Markov Random Fields, Uniform correlation, Continuous Entropy, Fuzzy order of graphs

Abstract

Gaussian Markov Random Fields over graphs have been widely used in the context of both theoretical and applied Statistics. In this paper, we study the influence of the graph on the continuous entropy of the distribution. In particular, since the continuous entropy is highly dependant on the correlations between adjacent nodes in the graph, we consider the particular case of Gaussian Markov Random Fields with uniform correlation, i.e., Gaussian Markov Random Fields in which such correlations are equal. We define a partial order relation on the set of graphs that orders the graphs according to their contribution to the continuous entropy. We also present a graded version of this order relation that allows to compare incomparable graphs with respect to the original order relation. Finally, an example for the illustration of the graded order relation is provided.

Copyright

© 2021, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Juan Baz
AU  - Irene Díaz
AU  - Susana Montes
AU  - Raúl Pérez-Fernández
PY  - 2021
DA  - 2021/08/30
TI  - A Fuzzy Order for Graphs Based on the Continuous Entropy of Gaussian Markov Random Fields
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 509
EP  - 516
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.067
DO  - 10.2991/asum.k.210827.067
ID  - Baz2021
ER  -