Horst Bunke’s research while affiliated with University of Bern and other places

The concept of graph edit distance constitutes one of the most flexible graph matching paradigms available. The major drawback of graph edit distance, viz. the exponential time complexity, has been recently overcome by means of a reformulation of the edit distance problem to a linear sum assignment problem. However, the substantial speed up of the matching is also accompanied by an approximation error on the distances. Major contribution of this paper is the introduction of a transformation process in order to convert the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on five benchmark graph sets with respect to the accuracy and run time of a distance based classifier.

This compendium is a completely revised version of an earlier book, Data Mining in Time Series Databases, by the same editors. It provides a unique collection of new articles written by leading experts that account for the latest developments in the field of time series and data stream mining. The emerging topics covered by the book include weightless neural modeling for mining data streams, using ensemble classifiers for imbalanced and evolving data streams, document stream mining with active learning, and many more. In particular, it addresses the domain of streaming data, which has recently become one of the emerging topics in Data Science, Big Data, and related areas. Existing titles do not provide sufficient information on this topic. © 2018 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.

The present paper is concerned with graph edit distance, which is widely accepted as one of the most flexible graph dissimilarity measures available. A recent algorithmic framework for approximating the graph edit distance overcomes the major drawback of this distance model, viz. its exponential time complexity. Yet, this particular approximation suffers from an overestimation of the true edit distance in general. Overall aim of the present paper is to improve the distance quality of this approximation by means of a post-processing search procedure. The employed search procedure is based on the idea of simulated annealing, which turns out to be particularly suitable for complex optimization problems. In an experimental evaluation on several graph data sets the benefit of this extension is empirically confirmed.

Many algorithms formulate graph matching as an optimization of an objective function of pairwise quantification of nodes and edges of two graphs to be matched. Pairwise measurements usually consider local attributes but disregard contextual information involved in graph structures. We address this issue by proposing contextual similarities between pairs of nodes. This is done by considering the tensor product graph (TPG) of two graphs to be matched, where each node is an ordered pair of nodes of the operand graphs. Contextual similarities between a pair of nodes are computed by accumulating weighted walks (normalized pairwise similarities) terminating at the corresponding paired node in TPG. Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG. We use contextual similarities to construct an objective function and optimize it with a linear programming approach. Since random walk formulation through TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities and better discrimination among the nodes and edges. Experimental results shown on synthetic as well as real benchmarks illustrate that higher order contextual similarities add discriminating power and allow one to find approximate solutions to the subgraph matching problem.

Many algorithms formulate graph matching as an optimization of an objective function of pairwise quantification of nodes and edges of two graphs to be matched. Pairwise measurements usually consider local attributes but disregard contextual information involved in graph structures. We address this issue by proposing contextual similarities between pairs of nodes. This is done by considering the tensor product graph (TPG) of two graphs to be matched, where each node is an ordered pair of nodes of the operand graphs. Contextual similarities between a pair of nodes are computed by accumulating weighted walks (normalized pairwise similarities) terminating at the corresponding paired node in TPG. Once the contextual similarities are obtained, we formulate subgraph matching as a node and edge selection problem in TPG. We use contextual similarities to construct an objective function and optimize it with a linear programming approach. Since random walk formulation through TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities and better discrimination among the nodes and edges. Experimental results shown on synthetic as well as real benchmarks illustrate that higher order contextual similarities add discriminating power and allow one to find approximate solutions to the subgraph matching problem.

Graph edit distance is one of the most popular graph matching paradigms available. By means of a reformulation of graph edit distance to an instance of a linear sum assignment problem, the major drawback of this dissimilarity model, viz. the exponential time complexity, has been invalidated recently. Yet, the substantial decrease of the computation time is at the expense of an approximation error. The present paper introduces a novel transformation that processes the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on three standard graph data sets. That is, we show that the accuracy of a distance based classifier can be improved with the proposed transformation while the run time remains nearly unaffected.

Approximation of graph edit distance in polynomial time enables us to compare large, arbitrarily labeled graphs for structural pattern recognition. In a recent approximation framework, bipartite graph matching (BP) has been proposed to reduce the problem of edit distance to a cubic-time linear sum assignment problem (LSAP) between local substructures. Following the same line of research, first attempts towards quadratic-time approximation have been made recently, including a lower bound based on Hausdorff matching (Hausdorff Edit Distance) and an upper bound based on greedy assignment (Greedy Edit Distance). In this paper, we compare the two approaches and derive a novel upper bound (BP2) which combines advantages of both. In an experimental evaluation on the IAM graph database repository, we demonstrate that the proposed quadratic-time methods perform equally well or, quite surprisingly, in some cases even better than the cubic-time method.

Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.