5 research outputs found
k-hop Graph Neural Networks
Graph neural networks (GNNs) have emerged recently as a powerful architecture
for learning node and graph representations. Standard GNNs have the same
expressive power as the Weisfeiler-Leman test of graph isomorphism in terms of
distinguishing non-isomorphic graphs. However, it was recently shown that this
test cannot identify fundamental graph properties such as connectivity and
triangle freeness. We show that GNNs also suffer from the same limitation. To
address this limitation, we propose a more expressive architecture, k-hop GNNs,
which updates a node's representation by aggregating information not only from
its direct neighbors, but from its k-hop neighborhood. We show that the
proposed architecture can identify fundamental graph properties. We evaluate
the proposed architecture on standard node classification and graph
classification datasets. Our experimental evaluation confirms our theoretical
findings since the proposed model achieves performance better or comparable to
standard GNNs and to state-of-the-art algorithms.Comment: Accepted at Neural Network
A Survey on Graph Kernels
Graph kernels have become an established and widely-used technique for
solving classification tasks on graphs. This survey gives a comprehensive
overview of techniques for kernel-based graph classification developed in the
past 15 years. We describe and categorize graph kernels based on properties
inherent to their design, such as the nature of their extracted graph features,
their method of computation and their applicability to problems in practice. In
an extensive experimental evaluation, we study the classification accuracy of a
large suite of graph kernels on established benchmarks as well as new datasets.
We compare the performance of popular kernels with several baseline methods and
study the effect of applying a Gaussian RBF kernel to the metric induced by a
graph kernel. In doing so, we find that simple baselines become competitive
after this transformation on some datasets. Moreover, we study the extent to
which existing graph kernels agree in their predictions (and prediction errors)
and obtain a data-driven categorization of kernels as result. Finally, based on
our experimental results, we derive a practitioner's guide to kernel-based
graph classification