Edit distance is a fundamental measure of distance between strings, the extensive study of which has recently focused on computational problems such as nearest neighbor search, sketching and fast approximation. A very powerful paradigm is to map the metric space induced by the edit distance into a normed space (e. g., `1) with small distortion, and then use the rich algorithmic toolkit known fo...

Graph edit distance is a dissimilarity measure for arbitrarily structured and arbitrarily labeled graphs. In contrast with other approaches, it does not suffer from any restrictions and can be applied to any type of graph, including hypergraphs [1]. Graph edit distance can be used to address various graph classification problems with different methods, for instance, k-nearest-neighbor classifie...

This paper addresses 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 representing attribute distance spaces that encode edit operation costs. The selforganizing maps are iteratively adapted to minimize the edit distance of those graphs that are required to be similar. To demonstra...

The purpose of this paper is to study the definition of edit distances with convex gap weights for trees. In the special case of strings, this problem has yield to the definition of classical solutions: Galil and Giancarlo produced in [2] an algorithm in O(n log(n)), for example. For trees, standart edit distance algorithms – [7] or more recently [4] with a O(n log(n))) solution – are concerned...

Geometric trees can be formalized as unordered combinatorial trees whose edges are endowed with geometric information. Examples are skeleta of shapes from images; anatomical tree-structures such as blood vessels; or phylogenetic trees. An inter-tree distance measure is a basic prerequisite for many pattern recognition and machine learning methods to work on anatomical, phylogenetic or skeletal ...

The editing of a combinatorial object is the alteration of some of its elements such that the resulting object satisfies a certain fixed property. The edit problem for graphs, when the edges are added or deleted, was first studied independently by the authors and Kézdy [J. Graph Theory (2008) 58(2), 123–138] and by Alon and Stav [Random Structures Algorithms (2008) 33(1), 87–104]. In this paper...

Trees provide a suited structural representation to deal with complex tasks such as web information extraction, RNA secondary structure prediction, or conversion of tree structured documents. In this context, many applications require the calculation of similarities between tree pairs. The most studied distance is likely the tree edit distance (ED) for which improvements in terms of complexity ...

In many applications, it is necessary to determine the similarity of two strings. A widely-used notion of string similarity is the edit distance: the minimum number of insertions, deletions, and substitutions required to transform one string into the other. In this report, we provide a stochastic model for string edit distance. Our stochastic model allows us to learn a string edit distance func...