A Deep Neural Network Architecture to Estimate Node Assignment Costs for the Graph Edit Distance

Abstract

The problem of finding a distance and a correspondence between a pair of graphs is commonly referred to as the Error-tolerant Graph matching problem. The Graph Edit Distance is one of the most popular approaches to solve this problem. This method needs to define a set of parameters and the cost functions aprioristically. On the other hand, in recent years, Deep Neural Networks have shown very good performance in a wide variety of domains due to their robustness and ability to solve non-linear problems. The aim of this paper is to present a model to compute the assignments costs for the Graph Edit Distance by means of a Deep Neural Network previously trained with a set of pairs of graphs properly matched. We empirically show a major improvement using our method with respect to the state-of-the-art results.

Sub-optimal Graph Matching by Node-to-Node Assignment Classification

“…Recently, two new papers assume the cost matrix could filled as the output of a supervised machine learning model. In [7], the authors use a Neural Network to learn only the substitution costs (no insertion nor deletion operations are allowed). And in [6], a general framework is presented to learn and define this costs.…”

“…Inspired by methods such as the ones in [7,6], we propose a supervised machine learning model that splits the node-to-node assignments in two classes, depending whether the learning database considers that they have to be mapped in f or not. Note that in [7,6], the learning algorithms deduce edit costs instead of discerning between two classes. The key idea of our model is to decide if a node in G is mapped to a node in G using a classifier.…”

“…), however, in any case we need to transform each node-to-node mapping into a vector that becomes the input of the classifier. Thus, we propose to embed each matching into a vector, similar as proposed in [7]. In this case, the embedded representation of a mapping between two nodes v i and v a of G and G , is…”

“…In the first two methods, the cost function is defined as an edit cost based on the Euclidean distance between the node attributes plus the difference of the degree of these attributes, as it was done in [14,15]. In the other two, the cost function is defined as the output of a Neural Network previously trained as in [7]. Figure 2 (top) shows the matching accuracy versus the number of frames of separation using the Hotel-House database.…”

“…Note that a proper definition of these cost functions is crucial to achieve good classification or recognition results. For this reason, several methods have been presented to learn these edit costs [6,7]. Moreover, the Graph Edit Distance has been demonstrated to be an NP-hard problem.…”