Abstract. As most 'real-world' data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered. This paper investigates kernels on labeled directed graphs with general structure. It is shown that computing a strictly positive definite graph kernel is at least as hard as solving the graph isomorphism problem. It is also shown that computing an inner product in a feature space indexed by all possible graphs, where each feature counts the number of subgraphs isomorphic to that graph, is NP-hard. On the other hand, inner products in an alternative feature space, based on walks in the graph, can be computed in polynomial time. Such kernels are defined in this paper.

We consider the problem of finding statistically unusual subgroups in a multi-relation database, and extend previous work on singlerelation subgroup discovery. We give a precise definition of the multirelation subgroup discovery task, propose a specific form of declarative bias based on foreign links as a means of specifying the hypothesis space, and show how propositional evaluation functions can be adapted to the multi-relation setting. We then describe an algorithm for this problem setting that uses optimistic estimate and minimal support pruning, an optimal refinement operator and sampling to ensure efficiency and can easily be parallelized.

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This article summarizes the results of the workshop on Visualization, Analytics & Spatial Decision Support, which took place at the GIScience conference in September 2006. The discussions at the workshop and analysis of the state of the art have revealed a need in concerted cross-disciplinary efforts to achieve substantial progress in supporting space-related decision making. The size and complexity of real-life problems together with their ill-defined nature call for a true synergy between the power of computational techniques and the human capabilities to analyze, envision, reason, and deliberate. Existing methods and tools are yet far from enabling this synergy. Appropriate methods can only appear as a result of a focused research based on the achievements in the fields of geovisualization and information visualization, human-computer interaction, geographic information science, operations research, data mining and machine learning, decision science, cognitive science, and other disciplines. The name 'Geovisual Analytics for Spatial Decision Support' suggested for this new research direction emphasizes the importance of visualization and interactive visual interfaces and the link with the emerging research discipline of Visual Analytics. This article, as well as the whole special issue, is meant to attract the attention of scientists with relevant expertise and interests to the major challenges requiring multidisciplinary efforts and to promote the establishment of a dedicated research community where an appropriate range of competences is combined with an appropriate breadth of thinking

With applications in biology, the world-wide web, and several other areas, mining of graph-structured objects has received significant interest recently. One of the major research directions in this field is concerned with predictive data mining in graph databases where each instance is represented by a graph. Some of the proposed approaches for this task rely on the excellent classification performance of support vector machines. To control the computational cost of these approaches, the underlying kernel functions are based on frequent patterns. In contrast to these approaches, we propose a kernel function based on a natural set of cyclic and tree patterns independent of their frequency, and discuss its computational aspects. To practically demonstrate the effectiveness of our approach, we use the popular NCI-HIV molecule dataset. Our experimental results show that cyclic pattern kernels can be computed quickly and offer predictive performance superior to recent graph kernels based on frequent patterns. Keywordsgraph mining, kernel methods, computational chemistry * This work was supported in part by the DFG project (WR 40/2-1) Hybride Methoden und Systemarchitekturen für heterogene Informationsräume.

With widespread availability of low cost GPS devices, it is becoming possible to record data about the movement of people and objects at a large scale. While these data hide important knowledge for the optimization of location and mobility oriented infrastructures and services, by themselves they lack the necessary semantic embedding which would make fully automatic algorithmic analysis possible. At the same time, making the semantic link is easy for humans who however cannot deal well with massive amounts of data. In this paper, we argue that by using the right visual analytics tools for the analysis of massive collections of movement data, it is possible to effectively support human analysts in understanding movement behaviors and mobility patterns. We suggest a framework for analysis combining interactive visual displays, which are essential for supporting human perception, cognition, and reasoning, with database operations and computational methods, which are necessary for handling large amounts of data. We demonstrate the synergistic use of these techniques in case studies of two real datasets

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