Neural Information Processing Systems http://nips.cc/

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are obtained from an optimal bijection between parts, which can provide a more valid notion of similarity. In general however, optimal assignments yield indefinite functions, which complicates their use in kernel methods. We characterize a class of base kernels used to compare parts that guarantees positive semidefinite optimal assignment kernels. These base kernels give rise to hierarchies from which the optimal assignment kernels are computed in linear time by histogram intersection. We apply these results by developing the Weisfeiler-Lehman optimal assignment kernel for graphs. It provides high classification accuracy on widely-used benchmark data sets improving over the original Weisfeiler-Lehman kernel.

We describe the design of a reproducing kernel suitable for attributed graphs, in which the similarity between the two graphs is defined based on the neighborhood information of the graph nodes with the aid of a product graph formulation. We represent the proposed kernel as the weighted sum of two other kernels of which one is an R-convolution kernel that processes the attribute information of the graph and the other is an optimal assignment kernel that processes label information. They are formulated in such a way that the edges processed as part of the kernel computation have the same neighborhood properties and hence the kernel proposed makes a well-defined correspondence between regions processed in graphs. These concepts are also extended to the case of the shortest paths. We identified the state-of-the-art kernels that can be mapped to such a neighborhood preserving framework. We found that the kernel value of the argument graphs in each iteration of the Weisfeiler-Lehman color refinement algorithm can be obtained recursively from the product graph formulated in our method. By incorporating the proposed kernel on support vector machines we analyzed the real-world data sets and it has shown superior performance in comparison with that of the other state-of-the-art graph kernels.

Kernels for structured data are commonly obtained by decomposing objects into their parts and adding up the similarities between all pairs of parts measured by a base kernel. Assignment kernels are based on an optimal bijection between the parts and have proven to be an effective alternative to the established convolution kernels. We explore how the base kernel can be learned as part of the classification problem. We build on the theory of valid assignment kernels derived from hierarchies defined on the parts. We show that the weights of this hierarchy can be optimized via multiple kernel learning. We apply this result to learn vertex similarities for the Weisfeiler-Lehman optimal assignment kernel for graph classification. We present first experimental results which demonstrate the feasibility and effectiveness of the approach.

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.

Graph kernels have recently emerged as a promising approach for tackling the graph similarity and learning tasks at the same time. In this paper, we propose a general framework for designing graph kernels. The proposed framework capitalizes on the well-known message passing scheme on graphs. The kernels derived from the framework consist of two components. The first component is a kernel between vertices, while the second component is a kernel between graphs. The main idea behind the proposed framework is that the representations of the vertices are implicitly updated using an iterative procedure. Then, these representations serve as the building blocks of a kernel that compares pairs of graphs. We derive four instances of the proposed framework, and show through extensive experiments that these instances are competitive with state-of-the-art methods in various tasks.

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are obtained from an optimal bijection between parts, which can provide a more valid notion of similarity. In general however, optimal assignments yield indefinite functions, which complicates their use in kernel methods. We characterize a class of base kernels used to compare parts that guarantees positive semidefinite optimal assignment kernels. These base kernels give rise to hierarchies from which the optimal assignment kernels are computed in linear time by histogram intersection. We apply these results by developing the Weisfeiler-Lehman optimal assignment kernel for graphs. It provides high classification accuracy on widely-used benchmark data sets improving over the original Weisfeiler-Lehman kernel.

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their parts and sums over all pairs of parts. Assignment kernels, in contrast, are obtained from an optimal bijection between parts, which can provide a more valid notion of similarity. In general however, optimal assignments yield indefinite functions, which complicates their use in kernel methods. We characterize a class of base kernels used to compare parts that guarantees positive semidefinite optimal assignment kernels. These base kernels give rise to hierarchies from which the optimal assignment kernels are computed in linear time by histogram intersection. We apply these results by developing the Weisfeiler-Lehman optimal assignment kernel for graphs. It provides high classification accuracy on widely-used benchmark data sets improving over the original Weisfeiler-Lehman kernel.