PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Entropy versus Heterogeneity for Graphs.
Lin Han, Edwin Hancock and Richard Wilson
In: Graph-Based Representations in Pattern Recognition - 8th IAPR-TC-15 International Workshop, GbRPR 2011, May 18-20, 2011., Munster, Germany.


In this paper we explore and compare two contrasting graph characterizations. The first of these is Estrada’s heterogeneity index, which measures the heterogeneity of the node degree across a graph. Our second measure is the the von Neumann entropy associated with the Laplacian eigenspectrum of graphs. Here we show how to approximate the von Neumann entropy by replacing the Shannon entropy by its quadratic counterpart. This quadratic entropy can be expressed in terms of a series of permutation invariant traces, which can be computed from the node degrees in quadratic time. We compare experimentally the effectiveness of the approximate expression for the entropy with the heterogeneity index.

EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Machine Vision
ID Code:8557
Deposited By:Edwin Hancock
Deposited On:13 February 2012