Error-correcting Graph Matching Research Articles

A commentary on “Learning error-correcting graph matching with a multiclass neural network”, Pattern Recognition Letters, 2018

We analyze the learning graph-matching algorithm presented in M. Martineau, R. Raveaux, D. Conte, G.Venturini, Learning error-correcting graph matching with a multiclass neural network, Pattern Recognition Letters (2018). Authors propose a new definition of the graph edit distance and also a learning algorithm that deduces some weights on this new graph edit distance. In this commentary, we first show that this new definition of the graph edit distance cannot be considered a distance and then, we discuss how this fact influences on the application of their learning methodology.

Learning error-correcting graph matching with a multiclass neural network

Many tasks in computer vision and pattern recognition are formulated as graph matching problems. Despite the NP-hard nature of such problems, fast and accurate approximations have led to significant progress in a wide range of applications. However, learning graph matching from observed data, remains a challenging issue. In practice, the node correspondences ground truth is rarely available. This paper presents an effective scheme for optimizing the graph matching problem in a classification context. For this, we propose a representation that is based on a parametrized model graph, and optimize the associated parameters. The objective of the optimization problem is to increase the classification rate. Experimental results on seven public datasets demonstrate the effectiveness (in terms of accuracy and speed) of our approach compared to four reference graph classifiers.

Graph edit distance as a quadratic assignment problem

The Graph Edit Distance (GED) is a flexible measure of dissimilarity between graphs which arises in error-correcting graph matching. It is defined from an optimal sequence of edit operations (edit path) transforming one graph into another. Unfortunately, the exact computation of this measure is NP-hard. In the last decade, several approaches were proposed to approximate the GED in polynomial time, mainly by solving linear programming problems. Among them, the bipartite GED received much attention. It is deduced from a linear sum assignment of the nodes of the two graphs, which can be efficiently computed by Hungarian-type algorithms. However, edit operations on nodes and edges are not handled simultaneously, which limits the accuracy of the approximation. To overcome this limitation, we propose to extend the linear assignment model to a quadratic one. This is achieved through the definition of a family of edit paths induced by assignments between nodes. We formally show that the GED, restricted to the paths in this family, is equivalent to a quadratic assignment problem. Since this problem is NP-hard, we propose to compute an approximate solution by adapting two algorithms: Integer Projected Fixed Point method and Graduated Non Convexity and Concavity Procedure. Experiments show that the proposed approach is generally able to reach a more accurate approximation of the exact GED than the bipartite GED, with a computational cost that is still affordable for graphs of non trivial sizes.

A Review on: Automatic Movie Character Annotation by Robust Face-Name Graph Matching

a day's character Identification from films is a very challenging task due to the huge variation in the appearance of each & every character. It will lead significant research interests and may have many interesting applications in today's life. In this paper, we investigate the problem of identifying characters & annotating them with respective name using graph matching algorithm to get the most accurate identification result. The contribution of our work include: 1) the character-character relationship representation including a noise insensitive 2) Use an edit operation based error correcting graph matching algorithm.3) Graph partitioning and graph matching for more complex character changes to handle simultaneously. 4) The existing character identification approaches, also we are going to perform an in-depth sensitivity analysis which will introduce two types of simulated noises.

A graph distance metric combining maximum common subgraph and minimum common supergraph

The relationship between two important problems in pattern recognition using attributed relational graphs, the maximum common subgraph and the minimum common supergraph of two graphs, is established by means of simple constructions, which allow to obtain the maximum common subgraph from the minimum common supergraph, and vice versa. On this basis, a new graph distance metric is proposed for measuring similarities between objects represented by attributed relational graphs. The proposed metric can be computed by a straightforward extension of any algorithm that implements error-correcting graph matching, when run under an appropriate cost function, and the extension only takes time linear in the size of the graphs.

Error correcting graph matching: on the influence of the underlying cost function

Investigates the influence of the cost function on the optimal match between two graphs. It is shown that, for a given cost function, there are an infinite number of other cost functions that lead, for any given pair of graphs, to the same optimal error correcting matching. Furthermore, it is shown that well-known concepts from graph theory, such as graph isomorphism, subgraph isomorphism, and maximum common subgraph, are special cases of optimal error correcting graph matching under particular cost functions.

Recent Advances in Graph Matching

A powerful and universal data structure with applications invarious subfields of science and engineering is graphs. In computer vision and image analysis, graphs are often used for the representation of structured objects. For example, if the problem is to recognize instances of known objects in an image, then often models, or prototypes, of the known objects are represented by means of graphs and stored in a database. The unknown objects in the input image are extracted by means of suitable preprocessing and segmentation algorithms, and represented by graphs that are analogous to the model graphs. Thus, the problem of object recognition is transformed into a graph matching problem. In this paper, it is assumed that there is an input graph that is given on-line, and a number of model, or prototype, graphs that are known a priori. We present a new approach to subgraph isomorphism detection which is based on a compact representation of the model graphs that is computed off-line. Subgraphs that appear multiple times within the same or within different model graphs are represented only once, thus reducing the computational effort to detect them in an input graph. In the extreme case where all model graphs are highly similar, the run time of the new algorithm becomes independent of the number of model graphs. We also describe an extension of this method to error-correcting graph matching. Furthermore, an approach to subgraph isomorphism detection based on decision trees is proposed. A decision tree is generated from the models in an off-line phase. This decision tree can be used for subgraph isomorphism detection. The time needed for decision tree traversal is only polynomial in terms of the number of nodes of the input graph. Moreover, the time complexity of the decision tree traversal is completely independent on the number of model graphs, regardless of their similarity. However, the size of the decision tree is exponential in the number of nodes of the models. To cut down the space complexity of the decision tree, some pruning strategies are discussed.