An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
On a cyclic string-to-string correction problem
Information Processing Letters
The String-to-String Correction Problem
Journal of the ACM (JACM)
Properties of Embedding Methods for Similarity Searching in Metric Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discovering Frequent Geometric Subgraphs
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
Graph Matching using Spectral Embedding and Alignment
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Prototype selection for dissimilarity-based classifiers
Pattern Recognition
Approximate graph edit distance computation by means of bipartite graph matching
Image and Vision Computing
A generative model for graph matching and embedding
Computer Vision and Image Understanding
Inexact Matching of Large and Sparse Graphs Using Laplacian Eigenvectors
GbRPR '09 Proceedings of the 7th IAPR-TC-15 International Workshop on Graph-Based Representations in Pattern Recognition
Comparing stars: on approximating graph edit distance
Proceedings of the VLDB Endowment
A survey of graph edit distance
Pattern Analysis & Applications
A graph matching method and a graph matching distance based on subgraph assignments
Pattern Recognition Letters
Graph Classification and Clustering Based on Vector Space Embedding
Graph Classification and Clustering Based on Vector Space Embedding
Reweighted random walks for graph matching
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
High efficiency and quality: large graphs matching
Proceedings of the 20th ACM international conference on Information and knowledge management
Towards the unification of structural and statistical pattern recognition
Pattern Recognition Letters
Progressive graph matching: Making a move of graphs via probabilistic voting
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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For many applications such as road network analysis and image processing, it is critical to study spatial properties of objects in addition to object relationships. Geometric graphs provide a suitable modeling framework for such applications, where vertices are located in some 2D space. For applications where the similarity between the structures of different graphs plays an important role, typically, inexact graph matching algorithms are employed. However, graph matching algorithms face many problems such as scalability with respect to graph size and less tolerance to changes in graph structure or labels. In this paper, we propose a solution to the problem of inexact graph matching for geometric graphs in the 2D space. Our approach allows to effectively answer subgraph and common subgraph queries for geometric graphs that differ in structure, spatial properties, and labels. Initially, a spatial feature is extracted from each vertex, and string edit distance is used to find the distance between pairs of vertices. To speed up graph matching, we propose vertex embedding into the Euclidean space. Based on this, the distance between two vertices can be computed using the Euclidean distance in constant time. To answer subgraph and common subgraph queries, we introduce an iterative matching algorithm that matches two graphs using their similarity in the Euclidean space. Such an algorithm merges highly similar vertices to create similar connected subgraphs. Using representative geometric graphs extracted from road networks, we show that our approach outperforms existing graph matching approaches in terms of matching quality and runtime.