Copyright notice:
The material is presented to ensure timely dissemination
of scholarly and technical work. Copyright and all rights
therein are retained by authors or by other copyright holders.
All persons copying this information are expected to
adhere to the terms and constraints invoked by each
copyright. In most cases, these works may not be
reposted without the explicit permission of the
copyright holder.
If you want a paper that is not available here,
or if you have any problems accessing these documents,
e-mail me.
Pyramid Quantized Weisfeiler-Lehman Graph Representation
The Pyramid Quantized Weisfeiler-Lehman Graph Representation
(WLpyramid) is an efficient graph representation and comparison
scheme for large graphs with continuous vector labels. Our
algorithm considers statistics of subtree patterns with discrete
labels based on the Weisfeiler-Lehman algorithm. The key advantage
of these subtree statistics, which are tree structures
constructed recursively from each node in the graph up to a
predefined depth h, is their linear complexity to the number
of edges in the graph under investigation. Moreover, they make
use of an efficient hashing scheme enumerating the relevant
dimensions of an exponentially sized feature space. To take
advantage of this efficient scheme when working on continuous vector
labeled graphs, we use a pyramid quantization strategy to
determine a logarithmic number of discrete labelings that
results in a representation that guarantees a multiplicative
error bound on an approximation to the optimal partial
matching. As a result, we approximate a graph representation
with continuous or vector valued labels as a sequence of
graphs discrete labels with increasingly granular discrete
labels. WLpyramid was evaluated on two different tasks with
real datasets, on a fMRI analysis task and on the generic
problem of 3D shape classification.
Publications
-
The Pyramid Quantized Weisfeiler-Lehman Graph Representation.
Gkirtzou K., and Blaschko M.
Neurocomputing, 2016
[pdf] [bibtex] [doi] -
Sparsity regularization and graph-based representation in medical imaging
Gkirtzou Katerina
PhD Thesis, Ecole Centrale de Paris, 2013.
[pdf] [bibtex] [presentation] -
fMRI Analysis with Sparse Weisfeiler-Lehman Graph Statistics.
Gkirtzou Katerina, Honorio Jean, Samaras Dimitris, Goldstein Rita and Blaschko B. Matthew
4th International Workshop on Machine Learning in Medical Imaging (MLMI), 2013.
[pdf] [bibtex] [doi]