|
Published Articles >> Table of Contents >> Abstract
Digital Image Computing: Techniques and Applications (DICTA'05)
p. 11
A Thermodynamics Approach to Graph Similarity
Antonio Robles-Kelly, National ICT Australia and Australian National University
Full Article Text:
 
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/DICTA.2005.9
Send link to a friend
| Abstract |
|
In this paper, we describe the use of concepts from the
areas of spectral-graph theory, kernel methods and differential
geometry for the purposes of recovering a measure of
similarity between pairs of graphical structures. To do this,
we commence by relating each of the graphs under study to
a Riemannian manifold through the use of the graph Laplacian
and the heat operator. We do this by making use of
the heat kernel and the set of initial conditions for the space
of functions associated to the Laplace-Beltrami operator.
With these ingredients, we make use of the first law of thermodynamics
to recover the thermal energy associated to the
conduction of heat through the graph. Thus, the problem of
recovering a measure of similarity between pairs of graphs
becomes that of computing the difference in their thermal
energies. We illustrate the utility of the similarity metric
recovered in this way for purposes of content-based image
database indexing and retrieval.
|
 Additional Information
|
Citation:
Antonio Robles-Kelly,
"A Thermodynamics Approach to Graph Similarity,"
dicta,
p. 11,
Digital Image Computing: Techniques and Applications (DICTA'05),
2005
|
|
