Kaspar Riesen

Approximate graph edit distance computation by means of bipartite graph matching

In recent years, the use of graph based object representation has gained popularity. Simultaneously, graph edit distance emerged as a powerful and flexible graph matching paradigm that can be used to address different tasks in pattern recognition, machine learning, and data mining. The key advantages of graph edit distance are its high degree of flexibility, which makes it applicable to any type of graph, and the fact that one can integrate domain specific knowledge about object similarity by means of specific edit cost functions. Its computational complexity, however, is exponential in the number of nodes of the involved graphs. Consequently, exact graph edit distance is feasible for graphs of rather small size only. In the present paper we introduce a novel algorithm which allows us to approximately, or suboptimally, compute edit distance in a substantially faster way. The proposed algorithm considers only local, rather than global, edge structure during the optimization process. In experiments on different datasets we demonstrate a substantial speed-up of our proposed method over two reference systems. Moreover, it is emprically verified that the accuracy of the suboptimal distance remains sufficiently accurate for various pattern recognition applications.

IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning

In recent years the use of graph based representation has gained popularity in pattern recognition and machine learning. As a matter of fact, object representation by means of graphs has a number of advantages over feature vectors. Therefore, various algorithms for graph based machine learning have been proposed in the literature. However, in contrast with the emerging interest in graph based representation, a lack of standardized graph data sets for benchmarking can be observed. Common practice is that researchers use their own data sets, and this behavior cumbers the objective evaluation of the proposed methods. In order to make the different approaches in graph based machine learning better comparable, the present paper aims at introducing a repository of graph data sets and corresponding benchmarks, covering a wide spectrum of different applications.

Fast suboptimal algorithms for the computation of graph edit distance

Graph edit distance is one of the most flexible mechanisms for error-tolerant graph matching. Its key advantage is that edit distance is applicable to unconstrained attributed graphs and can be tailored to a wide variety of applications by means of specific edit cost functions. Its computational complexity, however, is exponential in the number of vertices, which means that edit distance is feasible for small graphs only. In this paper, we propose two simple, but effective modifications of a standard edit distance algorithm that allow us to suboptimally compute edit distance in a faster way. In experiments on real data, we demonstrate the resulting speedup and show that classification accuracy is mostly not affected. The suboptimality of our methods mainly results in larger inter-class distances, while intra-class distances remain low, which makes the proposed methods very well applicable to distance-based graph classification.

Bipartite graph matching for computing the edit distance of graphs

In the field of structural pattern recognition graphs constitute a very common and powerful way of representing patterns. In contrast to string representations, graphs allow us to describe relational information in the patterns under consideration. One of the main drawbacks of graph representations is that the computation of standard graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for rather small graphs only. One of the most flexible error-tolerant graph similarity measures is based on graph edit distance. In this paper we propose an approach for the efficient compuation of edit distance based on bipartite graph matching by means of Munkres algorithm, sometimes referred to as the Hungarian algorithm. Our proposed algorithm runs in polynomial time, but provides only suboptimal edit distance results. The reason for its suboptimality is that implied edge operations are not considered during the process of finding the optimal node assignment. In experiments on semi-artificial and real data we demonstrate the speedup of our proposed method over a traditional tree search based algorithm for graph edit distance computation. Also we show that classification accuracy remains nearly unaffected.

Graph embedding in vector spaces by means of prototype selection

The field of statistical pattern recognition is characterized by the use of feature vectors for pattern representation, while strings or, more generally, graphs are prevailing in structural pattern recognition. In this paper we aim at bridging the gap between the domain of feature based and graph based object representation. We propose a general approach for transforming graphs into n-dimensional real vector spaces by means of prototype selection and graph edit distance computation. This method establishes the access to the wide range of procedures based on feature vectors without loosing the representational power of graphs. Through various experimental results we show that the proposed method, using graph embedding and classification in a vector space, outperforms the tradional approach based on k-nearest neighbor classification in the graph domain.

Recent advances in graph-based pattern recognition with applications in document analysis

Graphs are a powerful and popular representation formalism in pattern recognition. Particularly in the field of document analysis they have found widespread application. From the formal point of view, however, graphs are quite limited in the sense that the majority of mathematical operations needed to build common algorithms, such as classifiers or clustering schemes, are not defined. Consequently, we observe a severe lack of algorithmic procedures that can directly be applied to graphs. There exists recent work, however, aimed at overcoming these limitations. The present paper first provides a review of the use of graph representations in document analysis. Then we discuss a number of novel approaches suitable for making tools from statistical pattern recognition available to graphs. These novel approaches include graph kernels and graph embedding. With several experiments, using different data sets from the field of document analysis, we show that the new methods have great potential to outperform traditional procedures applied to graph representations.

Graph Classification and Clustering Based on Vector Space Embedding

This book is concerned with a fundamentally novel approach to graph-based pattern recognition based on vector space embedding of graphs. It aims at condensing the high representational power of graphs into a computationally efficient and mathematically convenient feature vector. This volume utilizes the dissimilarity space representation originally proposed by Duin and Pekalska to embed graphs in real vector spaces. Such an embedding gives one access to all algorithms developed in the past for feature vectors, which has been the predominant representation formalism in pattern recognition and related areas for a long time.

Generalized median graph computation by means of graph embedding in vector spaces

The median graph has been presented as a useful tool to represent a set of graphs. Nevertheless its computation is very complex and the existing algorithms are restricted to use limited amount of data. In this paper we propose a new approach for the computation of the median graph based on graph embedding. Graphs are embedded into a vector space and the median is computed in the vector domain. We have designed a procedure based on the weighted mean of a pair of graphs to go from the vector domain back to the graph domain in order to obtain a final approximation of the median graph. Experiments on three different databases containing large graphs show that we succeed to compute good approximations of the median graph. We have also applied the median graph to perform some basic classification tasks achieving reasonable good results. These experiments on real data open the door to the application of the median graph to a number of more complex machine learning algorithms where a representative of a set of graphs is needed.

Speeding up graph edit distance computation through fast bipartite matching

In the field of structural pattern recognition graphs constitute a very common and powerful way of representing objects. The main drawback of graph representations is that the computation of various graph similarity measures is exponential in the number of involved nodes. Hence, such computations are feasible for rather small graphs only. One of the most flexible graph similarity measures is graph edit distance. In this paper we propose a novel approach for the efficient computation of graph edit distance based on bipartite graph matching by means of the Volgenant-Jonker assignment algorithm. Our proposed algorithm provides only suboptimal edit distances, but runs in polynomial time. The reason for its sub-optimality is that edge information is taken into account only in a limited fashion during the process of finding the optimal node assignment between two graphs. In experiments on diverse graph representations we demonstrate a high speed up of our proposed method over a traditional algorithm for graph edit distance computation and over two other sub-optimal approaches that use the Hungarian and Munkres algorithm. Also, we show that classification accuracy remains nearly unaffected by the suboptimal nature of the algorithm.

Towards the unification of structural and statistical pattern recognition

Highlights? The unification of statistical and structural pattern recognition has been a concern for a long time. ? We review attempts made towards bridging the gap between both approaches. ? The aim is to profit from the benefits of each approach and eliminate the drawbacks. ? In an experimental evaluation we show the novel procedures are more powerful than approaches from the early period. The field of pattern recognition is usually subdivided into the statistical and the structural approach. Structural pattern recognition allows one to use powerful and flexible representation formalisms but offers only a limited repertoire of algorithmic tools needed to solve classification and clustering problems. By contrast, the statistical approach is mathematically well founded and offers many tools, but provides a representation formalism that is limited in its power and flexibility. Hence, both subfields are complementary to each other. During the last three decades several efforts have been made towards bridging the gap between structural and statistical pattern recognition in order to profit from the benefits of each approach and eliminate the drawbacks. The present paper reviews some of these attempts made towards the unification of structural and statistical pattern recognition and analyzes the progress that has been achieved.