7,954 research outputs found
Generalized Shortest Path Kernel on Graphs
We consider the problem of classifying graphs using graph kernels. We define
a new graph kernel, called the generalized shortest path kernel, based on the
number and length of shortest paths between nodes. For our example
classification problem, we consider the task of classifying random graphs from
two well-known families, by the number of clusters they contain. We verify
empirically that the generalized shortest path kernel outperforms the original
shortest path kernel on a number of datasets. We give a theoretical analysis
for explaining our experimental results. In particular, we estimate
distributions of the expected feature vectors for the shortest path kernel and
the generalized shortest path kernel, and we show some evidence explaining why
our graph kernel outperforms the shortest path kernel for our graph
classification problem.Comment: Short version presented at Discovery Science 2015 in Banf
Scalable kernels for graphs with continuous attributes
While graphs with continuous node attributes arise in many applications, state-of-the-art graph kernels for comparing continuous-attributed graphs suffer from a high runtime complexity. For instance, the popular shortest path kernel scales as O(n4), where n is the number of nodes. In this paper, we present a class of graph kernels with computational complexity O(n 2(m+log n+δ2 +d)), where is the graph diameter, m is the number of edges, and d is the dimension of the node attributes. Due to the sparsity and small diameter of real-world graphs, these kernels typically scale comfortably to large graphs. In our experiments, the presented kernels outperform state-of-the-art kernels in terms of speed and accuracy on classification benchmark datasets
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
Learning from graphs with structural variation
We study the effect of structural variation in graph data on the predictive
performance of graph kernels. To this end, we introduce a novel, noise-robust
adaptation of the GraphHopper kernel and validate it on benchmark data,
obtaining modestly improved predictive performance on a range of datasets.
Next, we investigate the performance of the state-of-the-art Weisfeiler-Lehman
graph kernel under increasing synthetic structural errors and find that the
effect of introducing errors depends strongly on the dataset.Comment: Presented at the NIPS 2017 workshop "Learning on Distributions,
Functions, Graphs and Groups
A Labeled Graph Kernel for Relationship Extraction
In this paper, we propose an approach for Relationship Extraction (RE) based
on labeled graph kernels. The kernel we propose is a particularization of a
random walk kernel that exploits two properties previously studied in the RE
literature: (i) the words between the candidate entities or connecting them in
a syntactic representation are particularly likely to carry information
regarding the relationship; and (ii) combining information from distinct
sources in a kernel may help the RE system make better decisions. We performed
experiments on a dataset of protein-protein interactions and the results show
that our approach obtains effectiveness values that are comparable with the
state-of-the art kernel methods. Moreover, our approach is able to outperform
the state-of-the-art kernels when combined with other kernel methods
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
Graph Kernels via Functional Embedding
We propose a representation of graph as a functional object derived from the
power iteration of the underlying adjacency matrix. The proposed functional
representation is a graph invariant, i.e., the functional remains unchanged
under any reordering of the vertices. This property eliminates the difficulty
of handling exponentially many isomorphic forms. Bhattacharyya kernel
constructed between these functionals significantly outperforms the
state-of-the-art graph kernels on 3 out of the 4 standard benchmark graph
classification datasets, demonstrating the superiority of our approach. The
proposed methodology is simple and runs in time linear in the number of edges,
which makes our kernel more efficient and scalable compared to many widely
adopted graph kernels with running time cubic in the number of vertices
- …