1,019 research outputs found
Improving Graph Neural Network Expressivity via Subgraph Isomorphism Counting
While Graph Neural Networks (GNNs) have achieved remarkable results in a
variety of applications, recent studies exposed important shortcomings in their
ability to capture the structure of the underlying graph. It has been shown
that the expressive power of standard GNNs is bounded by the Weisfeiler-Leman
(WL) graph isomorphism test, from which they inherit proven limitations such as
the inability to detect and count graph substructures. On the other hand, there
is significant empirical evidence, e.g. in network science and bioinformatics,
that substructures are often intimately related to downstream tasks. To this
end, we propose "Graph Substructure Networks" (GSN), a topologically-aware
message passing scheme based on substructure encoding. We theoretically analyse
the expressive power of our architecture, showing that it is strictly more
expressive than the WL test, and provide sufficient conditions for
universality. Importantly, we do not attempt to adhere to the WL hierarchy;
this allows us to retain multiple attractive properties of standard GNNs such
as locality and linear network complexity, while being able to disambiguate
even hard instances of graph isomorphism. We perform an extensive experimental
evaluation on graph classification and regression tasks and obtain
state-of-the-art results in diverse real-world settings including molecular
graphs and social networks. The code is publicly available at
https://github.com/gbouritsas/graph-substructure-networks
Learning to Count Isomorphisms with Graph Neural Networks
Subgraph isomorphism counting is an important problem on graphs, as many
graph-based tasks exploit recurring subgraph patterns. Classical methods
usually boil down to a backtracking framework that needs to navigate a huge
search space with prohibitive computational costs. Some recent studies resort
to graph neural networks (GNNs) to learn a low-dimensional representation for
both the query and input graphs, in order to predict the number of subgraph
isomorphisms on the input graph. However, typical GNNs employ a node-centric
message passing scheme that receives and aggregates messages on nodes, which is
inadequate in complex structure matching for isomorphism counting. Moreover, on
an input graph, the space of possible query graphs is enormous, and different
parts of the input graph will be triggered to match different queries. Thus,
expecting a fixed representation of the input graph to match diversely
structured query graphs is unrealistic. In this paper, we propose a novel GNN
called Count-GNN for subgraph isomorphism counting, to deal with the above
challenges. At the edge level, given that an edge is an atomic unit of encoding
graph structures, we propose an edge-centric message passing scheme, where
messages on edges are propagated and aggregated based on the edge adjacency to
preserve fine-grained structural information. At the graph level, we modulate
the input graph representation conditioned on the query, so that the input
graph can be adapted to each query individually to improve their matching.
Finally, we conduct extensive experiments on a number of benchmark datasets to
demonstrate the superior performance of Count-GNN.Comment: AAAI-23 main trac
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
Mining Frequent Graph Patterns with Differential Privacy
Discovering frequent graph patterns in a graph database offers valuable
information in a variety of applications. However, if the graph dataset
contains sensitive data of individuals such as mobile phone-call graphs and
web-click graphs, releasing discovered frequent patterns may present a threat
to the privacy of individuals. {\em Differential privacy} has recently emerged
as the {\em de facto} standard for private data analysis due to its provable
privacy guarantee. In this paper we propose the first differentially private
algorithm for mining frequent graph patterns.
We first show that previous techniques on differentially private discovery of
frequent {\em itemsets} cannot apply in mining frequent graph patterns due to
the inherent complexity of handling structural information in graphs. We then
address this challenge by proposing a Markov Chain Monte Carlo (MCMC) sampling
based algorithm. Unlike previous work on frequent itemset mining, our
techniques do not rely on the output of a non-private mining algorithm.
Instead, we observe that both frequent graph pattern mining and the guarantee
of differential privacy can be unified into an MCMC sampling framework. In
addition, we establish the privacy and utility guarantee of our algorithm and
propose an efficient neighboring pattern counting technique as well.
Experimental results show that the proposed algorithm is able to output
frequent patterns with good precision
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