Michel Neuhaus

Edit distance-based kernel functions for structural pattern classification

A common approach in structural pattern classification is to define a dissimilarity measure on patterns and apply a distance-based nearest-neighbor classifier. In this paper, we introduce an alternative method for classification using kernel functions based on edit distance. The proposed approach is applicable to both string and graph representations of patterns. By means of the kernel functions introduced in this paper, string and graph classification can be performed in an implicit vector space using powerful statistical algorithms. The validity of the kernel method cannot be established for edit distance in general. However, by evaluating theoretical criteria we show that the kernel functions are nevertheless suitable for classification, and experiments on various string and graph datasets clearly demonstrate that nearest-neighbor classifiers can be outperformed by support vector machines using the proposed kernel functions.

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.

Bridging the Gap Between Graph Edit Distance and Kernel Machines

In graph-based structural pattern recognition, the idea is to transform patterns into graphs and perform the analysis and recognition of patterns in the graph domain - commonly referred to as graph matching. A large number of methods for graph matching have been proposed. Graph edit distance, for instance, defines the dissimilarity of two graphs by the amount of distortion that is needed to transform one graph into the other and is considered one of the most flexible methods for error-tolerant graph matching.This book focuses on graph kernel functions that are highly tolerant towards structural errors. The basic idea is to incorporate concepts from graph edit distance into kernel functions, thus combining the flexibility of edit distance-based graph matching with the power of kernel machines for pattern recognition. The authors introduce a collection of novel graph kernels related to edit distance, including diffusion kernels, convolution kernels, and random walk kernels. From an experimental evaluation of a semi-artificial line drawing data set and four real-world data sets consisting of pictures, microscopic images, fingerprints, and molecules, the authors demonstrate that some of the kernel functions in conjunction with support vector machines significantly outperform traditional edit distance-based nearest-neighbor classifiers, both in terms of classification accuracy and running time.

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.

Automatic learning of cost functions for graph edit distance

Abstract Graph matching and graph edit distance have become important tools in structural pattern recognition. The graph edit distance concept allows us to measure the structural similarity of attributed graphs in an error-tolerant way. The key idea is to model graph variations by structural distortion operations. As one of its main constraints, however, the edit distance requires the adequate definition of edit cost functions, which eventually determine which graphs are considered similar. In the past, these cost functions were usually defined in a manual fashion, which is highly prone to errors. The present paper proposes a method to automatically learn cost functions from a labeled sample set of graphs. To this end, we formulate the graph edit process in a stochastic context and perform a maximum likelihood parameter estimation of the distribution of edit operations. The underlying distortion model is learned using an Expectation Maximization algorithm. From this model we finally derive the desired cost functions. In a series of experiments we demonstrate the learning effect of the proposed method and provide a performance comparison to other models.

An Error-Tolerant Approximate Matching Algorithm for Attributed Planar Graphs and Its Application to Fingerprint Classification

Graph edit distance is a powerful error-tolerant similarity measure for graphs. For pattern recognition problems involving large graphs, however, the high computational complexity makes it sometimes impossible to apply edit distance algorithms. In the present paper we propose an efficient algorithm for edit distance computation of planar graphs. Given graphs embedded in the plane, we iteratively match small subgraphs by locally optimizing structural correspondences. Eventually we obtain a valid edit path and hence an upper bound of the edit distance. To demonstrate the efficiency of our approach, we apply the proposed algorithm to the problem of fingerprint classification.

Transforming strings to vector spaces using prototype selection

A common way of expressing string similarity in structural pattern recognition is the edit distance. It allows one to apply the kNN rule in order to classify a set of strings. However, compared to the wide range of elaborated classifiers known from statistical pattern recognition, this is only a very basic method. In the present paper we propose a method for transforming strings into n-dimensional real vector spaces based on prototype selection. This allows us to subsequently classify the transformed strings with more sophisticated classifiers, such as support vector machine and other kernel based methods. In a number of experiments, we show that the recognition rate can be significantly improved by means of this procedure.

Self-organizing maps for learning the edit costs in graph matching

Although graph matching and graph edit distance computation have become areas of intensive research recently, the automatic inference of the cost of edit operations has remained an open problem. In the present paper, we address the issue of learning graph edit distance cost functions for numerically labeled graphs from a corpus of sample graphs. We propose a system of self-organizing maps (SOMs) that represent the distance measuring spaces of node and edge labels. Our learning process is based on the concept of self-organization. It adapts the edit costs in such a way that the similarity of graphs from the same class is increased, whereas the similarity of graphs from different classes decreases. The learning procedure is demonstrated on two different applications involving line drawing graphs and graphs representing diatoms, respectively.

A graph matching based approach to fingerprint classification using directional variance

In the present paper we address the fingerprint classification problem with a structural pattern recognition approach. Our main contribution is the definition of modified directional variance in orientation vector fields. The new directional variance allows us to extract regions from fingerprints that are relevant for the classification in the Henry scheme. After processing the regions of interest, the resulting structures are converted into attributed graphs. The classification is finally performed with an efficient graph edit distance algorithm. The performance of the proposed classification method is evaluated on the NIST-4 database of fingerprints.

A probabilistic approach to learning costs for graph edit distance

Graph edit distance provides an error-tolerant way to measure distances between attributed graphs. The effectiveness of edit distance based graph classification algorithms relies on the adequate definition of edit operation costs. We propose a cost inference method that is based on a distribution estimation of edit operations. For this purpose, we employ an expectation maximization algorithm to learn mixture densities from a labeled sample of graphs and derive edit costs that are subsequently applied in the context of a graph edit distance computation framework. We evaluate the performance of the proposed distance model in comparison to another recently introduced learning model for edit costs.