22,283 research outputs found
Propagation Kernels
We introduce propagation kernels, a general graph-kernel framework for
efficiently measuring the similarity of structured data. Propagation kernels
are based on monitoring how information spreads through a set of given graphs.
They leverage early-stage distributions from propagation schemes such as random
walks to capture structural information encoded in node labels, attributes, and
edge information. This has two benefits. First, off-the-shelf propagation
schemes can be used to naturally construct kernels for many graph types,
including labeled, partially labeled, unlabeled, directed, and attributed
graphs. Second, by leveraging existing efficient and informative propagation
schemes, propagation kernels can be considerably faster than state-of-the-art
approaches without sacrificing predictive performance. We will also show that
if the graphs at hand have a regular structure, for instance when modeling
image or video data, one can exploit this regularity to scale the kernel
computation to large databases of graphs with thousands of nodes. We support
our contributions by exhaustive experiments on a number of real-world graphs
from a variety of application domains
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
A simple yet effective baseline for non-attributed graph classification
Graphs are complex objects that do not lend themselves easily to typical
learning tasks. Recently, a range of approaches based on graph kernels or graph
neural networks have been developed for graph classification and for
representation learning on graphs in general. As the developed methodologies
become more sophisticated, it is important to understand which components of
the increasingly complex methods are necessary or most effective.
As a first step, we develop a simple yet meaningful graph representation, and
explore its effectiveness in graph classification. We test our baseline
representation for the graph classification task on a range of graph datasets.
Interestingly, this simple representation achieves similar performance as the
state-of-the-art graph kernels and graph neural networks for non-attributed
graph classification. Its performance on classifying attributed graphs is
slightly weaker as it does not incorporate attributes. However, given its
simplicity and efficiency, we believe that it still serves as an effective
baseline for attributed graph classification. Our graph representation is
efficient (linear-time) to compute. We also provide a simple connection with
the graph neural networks.
Note that these observations are only for the task of graph classification
while existing methods are often designed for a broader scope including node
embedding and link prediction. The results are also likely biased due to the
limited amount of benchmark datasets available. Nevertheless, the good
performance of our simple baseline calls for the development of new, more
comprehensive benchmark datasets so as to better evaluate and analyze different
graph learning methods. Furthermore, given the computational efficiency of our
graph summary, we believe that it is a good candidate as a baseline method for
future graph classification (or even other graph learning) studies.Comment: 13 pages. Shorter version appears at 2019 ICLR Workshop:
Representation Learning on Graphs and Manifolds. arXiv admin note: text
overlap with arXiv:1810.00826 by other author
A tree-based kernel for graphs with continuous attributes
The availability of graph data with node attributes that can be either
discrete or real-valued is constantly increasing. While existing kernel methods
are effective techniques for dealing with graphs having discrete node labels,
their adaptation to non-discrete or continuous node attributes has been
limited, mainly for computational issues. Recently, a few kernels especially
tailored for this domain, and that trade predictive performance for
computational efficiency, have been proposed. In this paper, we propose a graph
kernel for complex and continuous nodes' attributes, whose features are tree
structures extracted from specific graph visits. The kernel manages to keep the
same complexity of state-of-the-art kernels while implicitly using a larger
feature space. We further present an approximated variant of the kernel which
reduces its complexity significantly. Experimental results obtained on six
real-world datasets show that the kernel is the best performing one on most of
them. Moreover, in most cases the approximated version reaches comparable
performances to current state-of-the-art kernels in terms of classification
accuracy while greatly shortening the running times.Comment: This work has been submitted to the IEEE Transactions on Neural
Networks and Learning Systems for possible publication. Copyright may be
transferred without notice, after which this version may no longer be
accessibl
Subgraph Matching Kernels for Attributed Graphs
We propose graph kernels based on subgraph matchings, i.e.
structure-preserving bijections between subgraphs. While recently proposed
kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al.,
2009) in general can not be applied to attributed graphs, our approach allows
to rate mappings of subgraphs by a flexible scoring scheme comparing vertex and
edge attributes by kernels. We show that subgraph matching kernels generalize
several known kernels. To compute the kernel we propose a graph-theoretical
algorithm inspired by a classical relation between common subgraphs of two
graphs and cliques in their product graph observed by Levi (1973). Encouraging
experimental results on a classification task of real-world graphs are
presented.Comment: Appears in Proceedings of the 29th International Conference on
Machine Learning (ICML 2012
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