A fast MATLAB implementation of the one-dimensional Weisfeiler--Lehman graph transformation and associated kernel.
For more details about the fast hashing-based algorithm used, see the following paper:
Kersting, K., Mladenov, M., Garnett, R., and Grohe, M. Power Iterated Color Refinement. (2014). AAAI Conference on Artificial Intelligence (AAAI 2014).
For more details about the Weisfeiler--Lehman graph kernel, see the following paper:
Shervashidze, N., Schweitzer, P. van Leeuwen, E.J., Mehlhorn, K., and Borgward, K.M. Weisfeiler--Lehman graph kernels. (2010). Journal of Machine Learning Research 12(Sep):2539--2561.
This implementation uses a fast perfect hash for performing the
transformation. Consider a node , and let
and
represent the label of
and neighborhood of
,
respectively. Let
represent the ith prime. The hash for
is given by
It can be easily shown that, given two nodes ,
if and only if:
and
contain the same labels with the same cardinality,
that is, gives unique values to unique WL signatures. The
use of
is much faster than the typical string hashes used
for completing the WL transformation.
See the help for wl_transformation.m for usage information.