768 research outputs found
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
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
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
An Empirical Study on Budget-Aware Online Kernel Algorithms for Streams of Graphs
Kernel methods are considered an effective technique for on-line learning.
Many approaches have been developed for compactly representing the dual
solution of a kernel method when the problem imposes memory constraints.
However, in literature no work is specifically tailored to streams of graphs.
Motivated by the fact that the size of the feature space representation of many
state-of-the-art graph kernels is relatively small and thus it is explicitly
computable, we study whether executing kernel algorithms in the feature space
can be more effective than the classical dual approach. We study three
different algorithms and various strategies for managing the budget. Efficiency
and efficacy of the proposed approaches are experimentally assessed on
relatively large graph streams exhibiting concept drift. It turns out that,
when strict memory budget constraints have to be enforced, working in feature
space, given the current state of the art on graph kernels, is more than a
viable alternative to dual approaches, both in terms of speed and
classification performance.Comment: Author's version of the manuscript, to appear in Neurocomputing
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