47,488 research outputs found
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
Context-dependent random walk graph kernels and tree pattern graph matching kernels with applications to action recognition
Graphs are effective tools for modeling complex data. Setting out from two basic substructures, random walks and trees, we propose a new family of context-dependent random walk graph kernels and a new family of tree pattern graph matching kernels. In our context-dependent graph kernels, context information is incorporated into primary random walk groups. A multiple kernel learning algorithm with a proposed l12-norm regularization is applied to combine context-dependent graph kernels of different orders. This improves the similarity measurement between graphs. In our tree-pattern graph matching kernel, a quadratic optimization with a sparse constraint is proposed to select the correctly matched tree-pattern groups. This augments the discriminative power of the tree-pattern graph matching. We apply the proposed kernels to human action recognition, where each action is represented by two graphs which record the spatiotemporal relations between local feature vectors. Experimental comparisons with state-of-the-art algorithms on several benchmark datasets demonstrate the effectiveness of the proposed kernels for recognizing human actions. It is shown that our kernel based on tree pattern groups, which have more complex structures and exploit more local topologies of graphs than random walks, yields more accurate results but requires more runtime than the context-dependent walk graph kernel
Learning Structural Kernels for Natural Language Processing
Structural kernels are a flexible learning
paradigm that has been widely used in Natural
Language Processing. However, the problem
of model selection in kernel-based methods
is usually overlooked. Previous approaches
mostly rely on setting default values for kernel
hyperparameters or using grid search,
which is slow and coarse-grained. In contrast,
Bayesian methods allow efficient model
selection by maximizing the evidence on the
training data through gradient-based methods.
In this paper we show how to perform this
in the context of structural kernels by using
Gaussian Processes. Experimental results on
tree kernels show that this procedure results
in better prediction performance compared to
hyperparameter optimization via grid search.
The framework proposed in this paper can be
adapted to other structures besides trees, e.g.,
strings and graphs, thereby extending the utility
of kernel-based methods
Graph kernels based on tree patterns for molecules
Motivated by chemical applications, we revisit and extend a family of
positive definite kernels for graphs based on the detection of common subtrees,
initially proposed by Ramon et al. (2003). We propose new kernels with a
parameter to control the complexity of the subtrees used as features to
represent the graphs. This parameter allows to smoothly interpolate between
classical graph kernels based on the count of common walks, on the one hand,
and kernels that emphasize the detection of large common subtrees, on the other
hand. We also propose two modular extensions to this formulation. The first
extension increases the number of subtrees that define the feature space, and
the second one removes noisy features from the graph representations. We
validate experimentally these new kernels on binary classification tasks
consisting in discriminating toxic and non-toxic molecules with support vector
machines
Network Infusion to Infer Information Sources in Networks
Several models exist for diffusion of signals across biological, social, or engineered networks. However, the inverse problem of identifying the source of such propagated information appears more difficult even in the presence of multiple network snapshots, and especially for the single-snapshot case, given the many alternative, often similar, progression of diffusion that may lead to the same observed snapshots. Mathematically, this problem can be undertaken using a diffusion kernel that represents diffusion processes in a given network, but computing this kernel is computationally challenging in general. Here, we propose a path-based network diffusion kernel which considers edge-disjoint shortest paths among pairs of nodes in the network and can be computed efficiently for both homogeneous and heterogeneous continuous-time diffusion models. We use this network diffusion kernel to solve the inverse diffusion problem, which we term Network Infusion (NI), using both likelihood maximization and error minimization. The minimum error NI algorithm is based on an asymmetric Hamming premetric function and can balance between false positive and false negative error types. We apply this framework for both single-source and multi-source diffusion, for both single-snapshot and multi-snapshot observations, and using both uninformative and informative prior probabilities for candidate source nodes. We also provide proofs that under a standard susceptible-infected diffusion model, (1) the maximum-likelihood NI is mean-field optimal for tree structures or sufficiently sparse Erdos-Renyi graphs, (2) the minimum-error algorithm is mean-field optimal for regular tree structures, and (3) for sufficiently-distant sources, the multi-source solution is mean-field optimal in the regular tree structure. Moreover, we provide techniques to learn diffusion model parameters such as observation times. We apply NI to several synthetic networks and compare its performance to centrality-based and distance-based methods for Erdos-Renyi graphs, power-law networks, symmetric and asymmetric grids. Moreover, we use NI in two real-world applications. First, we identify the news sources for 3,553 stories in the Digg social news network, and validate our results based on annotated information, that was not provided to our algorithm. Second, we use NI to identify infusion hubs of human diseases, defined as gene candidates that can explain the connectivity pattern of disease-related genes in the human regulatory network. NI identifies infusion hubs of several human diseases including T1D, Parkinson, MS, SLE, Psoriasis and Schizophrenia. We show that, the inferred infusion hubs are biologically relevant and often not identifiable using the raw p-values
Graph kernels between point clouds
Point clouds are sets of points in two or three dimensions. Most kernel
methods for learning on sets of points have not yet dealt with the specific
geometrical invariances and practical constraints associated with point clouds
in computer vision and graphics. In this paper, we present extensions of graph
kernels for point clouds, which allow to use kernel methods for such ob jects
as shapes, line drawings, or any three-dimensional point clouds. In order to
design rich and numerically efficient kernels with as few free parameters as
possible, we use kernels between covariance matrices and their factorizations
on graphical models. We derive polynomial time dynamic programming recursions
and present applications to recognition of handwritten digits and Chinese
characters from few training examples
Extending local features with contextual information in graph kernels
Graph kernels are usually defined in terms of simpler kernels over local
substructures of the original graphs. Different kernels consider different
types of substructures. However, in some cases they have similar predictive
performances, probably because the substructures can be interpreted as
approximations of the subgraphs they induce. In this paper, we propose to
associate to each feature a piece of information about the context in which the
feature appears in the graph. A substructure appearing in two different graphs
will match only if it appears with the same context in both graphs. We propose
a kernel based on this idea that considers trees as substructures, and where
the contexts are features too. The kernel is inspired from the framework in
[6], even if it is not part of it. We give an efficient algorithm for computing
the kernel and show promising results on real-world graph classification
datasets.Comment: To appear in ICONIP 201
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