Research On Graph Matching Algorithm Based On Graph Convolution Network

Graph matching is a basic problem in graph theory.With the development of artificial intelligence,graph matching has attracted more and more attention and is widely used in computer vision and pattern recognition fields.The graph matching problem refers to finding the corresponding relationship between a pair of nodes respectively belonging to two different graphs.It is essentially a combinatorial optimization problem that is difficult to find a global optimal solution.Therefore,most of existing algorithms focus on designing a model that can obtain the approximate solution with an acceptable cost of execution time and memory consumption at the expense of accuracy.In view of this,the focus of this article is to find a graph matching algorithm with higher matching accuracy and higher operating efficiency.In this paper,classic graph matching algorithms proposed domestically and abroad in recent years are categorized into two approaches,namely traditional machine learning based methods and deep learning based methods.After comparison and analysis,it can be found that most of the former rely on artificially designed similarity functions,which are relatively subjective and will bring certain errors,while the latter can more naturally reflect the relationship within the graph structure by using the learned similarity functions.In addition,factors such as graph size,noise,and outliers will also affect the accuracy of graph matching to a certain extent.In order to avoid the above-mentioned hidden errors and the interference of external factors,this article adopts graph neural network(GNN),a popular deep learning framework that is good at processing graph structure,to construct a graph matching model under the data driving with strong generalization ability and robust to external conditions.The main work of this paper includes the following two aspects:(1)A graph matching algorithm based on graph convolutional network is designed,and an end-to-end network channel is generated,which consists of graph building module,encoder module,graph convolution module,decoder module and loss function module.In the graph building module,the two graphs to be matched are constructed into a mapping graph through the newly created outer edges,and the graph matching problem is transformed into a problem of classifying the outer edges of the mapping graph.Compared with the composition method of the previous algorithm,In this paper,the node space complexity of the mapping graph is reduced from O(n~2)to O(n),and the edge space complexity is reduced from O(n~4)to O(n~2),which saves the memory overhead when the algorithm is running.In the graph convolution module,in order to make the process of aggregating information more efficient,according to the structure of the mapping graph,the operation method of the convolution function is improved,which also reduces the running time to a certain extent.(2)We explore the influence of the deformation noise,the number of inner points,the number of outer points and other scene changes on the performance of the graph matching algorithm.We uses the controlled variable method to do multiple experiments on multiple data sets such as Synthetic 2D Points,Pascal VOC,Willow,etc.The results show that the algorithm in this paper has the best comprehensive performance in matching accuracy and running time.