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

XML Matchers: approaches and challenges

Schema Matching, i.e. the process of discovering semantic correspondences between concepts adopted in different data source schemas, has been a key topic in Database and Artificial Intelligence research areas for many years. In the past, it was largely investigated especially for classical database models (e.g., E/R schemas, relational databases, etc.). However, in the latest years, the widespread adoption of XML in the most disparate application fields pushed a growing number of researchers to design XML-specific Schema Matching approaches, called XML Matchers, aiming at finding semantic matchings between concepts defined in DTDs and XSDs. XML Matchers do not just take well-known techniques originally designed for other data models and apply them on DTDs/XSDs, but they exploit specific XML features (e.g., the hierarchical structure of a DTD/XSD) to improve the performance of the Schema Matching process. The design of XML Matchers is currently a well-established research area. The main goal of this paper is to provide a detailed description and classification of XML Matchers. We first describe to what extent the specificities of DTDs/XSDs impact on the Schema Matching task. Then we introduce a template, called XML Matcher Template, that describes the main components of an XML Matcher, their role and behavior. We illustrate how each of these components has been implemented in some popular XML Matchers. We consider our XML Matcher Template as the baseline for objectively comparing approaches that, at first glance, might appear as unrelated. The introduction of this template can be useful in the design of future XML Matchers. Finally, we analyze commercial tools implementing XML Matchers and introduce two challenging issues strictly related to this topic, namely XML source clustering and uncertainty management in XML Matchers.Comment: 34 pages, 8 tables, 7 figure

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

Structural Data Recognition with Graph Model Boosting

This paper presents a novel method for structural data recognition using a large number of graph models. In general, prevalent methods for structural data recognition have two shortcomings: 1) Only a single model is used to capture structural variation. 2) Naive recognition methods are used, such as the nearest neighbor method. In this paper, we propose strengthening the recognition performance of these models as well as their ability to capture structural variation. The proposed method constructs a large number of graph models and trains decision trees using the models. This paper makes two main contributions. The first is a novel graph model that can quickly perform calculations, which allows us to construct several models in a feasible amount of time. The second contribution is a novel approach to structural data recognition: graph model boosting. Comprehensive structural variations can be captured with a large number of graph models constructed in a boosting framework, and a sophisticated classifier can be formed by aggregating the decision trees. Consequently, we can carry out structural data recognition with powerful recognition capability in the face of comprehensive structural variation. The experiments shows that the proposed method achieves impressive results and outperforms existing methods on datasets of IAM graph database repository.Comment: 8 page