Learning edit cost estimation models for graph edit distance

Abstract

One of the most popular distance measures between a pair of graphs is the Graph Edit Distance. This approach consists of finding a set of edit operations that completely transforms a graph into another. Edit costs are introduced in order to penalize the distortion that each edit operation introduces. Then, one basic requirement when we design a Graph Edit Distance algorithm, is to define the appropriate edit cost functions. On the other hand, Machine Learning algorithms has been applied in many contexts showing impressive results, due, among other things, its ability to find correlations between input and output values. The aim of this paper is to bring the potentialities of Machine Learning to the Graph Edit Distance problem presenting a general framework in which this kind of algorithms are used to estimate the edit costs values for node substitutions.

Graphs in pattern recognition: successes, shortcomings, and perspectives

“…In Ref. 19, the authors show that, given a fixed dataset in which some graph correspondences are known, learning costs provide better results than using some fixed edit costs.…”

A Metric Learning Approach to Graph Edit Costs for Regression

“…Another set of methods that address the problem of learning edit costs for GED is proposed in [13,14]. These methods propose to optimize edit costs to maximize a ground truth mapping between nodes of graphs.…”

Interactive online learning for graph matching using active strategies

“…This information is embedded into a vector because we want to use a common supervised learning algorithm, such as neural network or a support vector machine. Several embedding methods have been presented in the literature, for instance, there is one in [57] or two more recent proposals in [58,59]. In our case, we present a simple one defined by the attribute nodes (semantic information) and the number of edges adjacent to the node (structural information) as we show in Figure 3.…”

“…In general, when we apply some of the proposed strategies, our method reaches the best results. Even when the performance is similar, as in [59], our model has the crucial advantage of using an online learning paradigm. This means that, as described above, it has the capacity to learn in each interaction, significantly minimizing the number of node-to-node impositions necessary to obtain the best results.…”