An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems

Abstract

International audienceGraph edit distance is an error tolerant matching technique 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; it represents the minimum-cost sequence of basic edit operations to transform one graph into another by means of insertion, deletion and substitution of vertices and/or edges. A widely used method for exact graph edit distance computation is based on the A* algorithm. To overcome its high memory load while traversing the search tree for storing pending solutions to be explored, we propose a depth-first graph edit distance algorithm which requires less memory and searching time. An evaluation of all possible solutions is performed without explicitly enumerating them all. Candidates are discarded using an upper and lower bounds strategy. A solid experimental study is proposed; experiments on a publicly available database empirically demonstrated that our approach is better than the A* graph edit distance computation in terms of speed, accuracy and classification rate

Autoregressive Models for Sequences of Graphs

“…The comparative analysis of the tested methods is performed by considering a graph edit distance (GED) [11] d(g t+1 ,ĝ t+1 )…”

Efficient k-nearest neighbors search in graph space

“…To overcome the bottleneck of the best rst BnB algorithm referred to as A * in (Neuhaus et al, 2006a), a recent GED algorithm, referred to as DF, was put forward in (Abu-Aisheh et al, 2015) to reduce the memory consumption and also the computation time. This was done using a dierent exploration strategy (i.e., depth-rst instead of best-rst).…”

“…Finding the exact kNN can be done through the calculation of an exact GED (such as in Abu-Aisheh et al (2015); Neuhaus et al (2006a)). This approach has an exponential complexity in function of the size of compared graphs and a linear complexity in function of the number of training graphs.…”

“…During the classication of a test graph, all the GED computations whose objective is to classify an unknown graph G i are merged to obtain a more global problem. As a rst algorithm to solve the MGED problem, we take advantage of a recent exact branch-and-bound (BnB) GED approach, called DF in (Abu-Aisheh et al, 2015). The knowledge about the global MGED problem can be considered as the merging of the search spaces to prune the global search space associated to all sub-GED problems.…”

Anytime graph matching

“…At present, two main families of error-tolerant GM methods can be found in the literature: exact and approximate. Few exact methods have been found in the literature (Justice and Hero (2006); Riesen et al (2007); Abu-Aisheh et al (2015a)). On the other hand, a number of approximate GM methods have been proposed with reduced computational time and accuracy.…”