Stefan Wrobel

On Graph Kernels: Hardness Results and Efficient Alternatives

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.

An Algorithm for Multi-relational Discovery of Subgroups

We consider the problem of finding statistically unusual subgroups in a multi-relation database, and extend previous work on single-relation subgroup discovery. We give a precise definition of the multi-relation 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.

Geovisual analytics for spatial decision support: Setting the research agenda

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.

Cyclic pattern kernels for predictive graph mining

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.

Visual analytics tools for analysis of movement data

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.

Efficient co-regularised least squares regression

In many applications, unlabelled examples are inexpensive and easy to obtain. Semi-supervised approaches try to utilise such examples to reduce the predictive error. In this paper, we investigate a semi-supervised least squares regression algorithm based on the co-learning approach. Similar to other semi-supervised algorithms, our base algorithm has cubic runtime complexity in the number of unlabelled examples. To be able to handle larger sets of unlabelled examples, we devise a semi-parametric variant that scales linearly in the number of unlabelled examples. Experiments show a significant error reduction by co-regularisation and a large runtime improvement for the semi-parametric approximation. Last but not least, we propose a distributed procedure that can be applied without collecting all data at a single site.

Comparative Evaluation of Approaches to Propositionalization

Propositionalization has already been shown to be a promising approach for robustly and effectively handling relational data sets for knowledge discovery. In this paper, we compare up-to-date methods for propositionalization from two main groups: logic-oriented and database-oriented techniques. Experiments using several learning tasks – both ILP benchmarks and tasks from recent international data mining competitions – show that both groups have their specific advantages. While logic-oriented methods can handle complex background knowledge and provide expressive first-order models, database-oriented methods can be more efficient especially on larger data sets. Obtained accuracies vary such that a combination of the features produced by both groups seems a further valuable venture.

A conceptual framework and taxonomy of techniques for analyzing movement

Movement data link together space, time, and objects positioned in space and time. They hold valuable and multifaceted information about moving objects, properties of space and time as well as events and processes occurring in space and time. We present a conceptual framework that describes in a systematic and comprehensive way the possible types of information that can be extracted from movement data and on this basis defines the respective types of analytical tasks. Tasks are distinguished according to the type of information they target and according to the level of analysis, which may be elementary (i.e. addressing specific elements of a set) or synoptic (i.e. addressing a set or subsets). We also present a taxonomy of generic analytic techniques, in which the types of tasks are linked to the corresponding classes of techniques that can support fulfilling them. We include techniques from several research fields: visualization and visual analytics, geographic information science, database technology, and data mining. We expect the taxonomy to be valuable for analysts and researchers. Analysts will receive guidance in choosing suitable analytic techniques for their data and tasks. Researchers will learn what approaches exist in different fields and compare or relate them to the approaches they are going to undertake.

Frequent subgraph mining in outerplanar graphs

In recent years there has been an increased interest in algorithms that can perform frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we define the class of so called tenuous outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for tenuous outerplanar graphs that works in incremental polynomial time, and evaluate the algorithm empirically on the NCI molecular graph dataset.

From movement tracks through events to places: Extracting and characterizing significant places from mobility data

We propose a visual analytics procedure for analyzing movement data, i.e., recorded tracks of moving objects. It is oriented to a class of problems where it is required to determine significant places on the basis of certain types of events occurring repeatedly in movement data. The procedure consists of four major steps: (1) event extraction from trajectories; (2) event clustering and extraction of relevant places; (3) spatio-temporal aggregation of events or trajectories; (4) analysis of the aggregated data. All steps are scalable with respect to the amount of the data under analysis. We demonstrate the use of the procedure by example of two real-world problems requiring analysis at different spatial scales.