19,865 research outputs found
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
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
Graph ambiguity
In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved
Positive Definite Kernels in Machine Learning
This survey is an introduction to positive definite kernels and the set of
methods they have inspired in the machine learning literature, namely kernel
methods. We first discuss some properties of positive definite kernels as well
as reproducing kernel Hibert spaces, the natural extension of the set of
functions associated with a kernel defined
on a space . We discuss at length the construction of kernel
functions that take advantage of well-known statistical models. We provide an
overview of numerous data-analysis methods which take advantage of reproducing
kernel Hilbert spaces and discuss the idea of combining several kernels to
improve the performance on certain tasks. We also provide a short cookbook of
different kernels which are particularly useful for certain data-types such as
images, graphs or speech segments.Comment: draft. corrected a typo in figure
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