Graph Matching and Similarity in Pattern Recognition

Graph matching and similarity constitute foundational operations in pattern recognition, underpinning tasks from image analysis to bioinformatics. A graph models data as nodes representing entities and edges capturing relationships. Matching seeks to establish correspondences between graph elements, while similarity quantifies structural resemblance. Techniques range from exact solutions such as subgraph isomorphism to approximate strategies including edit distance measures, spectral methods, kernel-based comparisons and embedding approaches. Advances in optimisation algorithms and machine learning have substantially enhanced scalability, enabling the analysis of large-scale networks and complex relational data. In particular, graph neural networks have emerged to learn structural features end to end, facilitating applications in chemistry, social-network analysis and computer vision. This field’s global significance lies in its versatility for modelling diverse phenomena and its capacity to reveal hidden patterns within interconnected data.

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Graph Matching and Similarity in Pattern Recognition publication trend

The graph below shows the total number of articles in graph matching and similarity in pattern recognition across all publications each year (not limited to Nature Index journals).

Technical terms

Graph: A data structure comprising nodes (vertices) and edges (links) representing relationships.

Graph matching: The process of finding correspondences between nodes and edges of two graphs to align their structures.

Graph similarity: A quantitative measure of how alike two graphs are in terms of structure and attributes.

Graph edit distance: A metric defined by the minimum cost sequence of edit operations (insertions, deletions, substitutions) to transform one graph into another.

Spectral clustering: A technique using the eigenvalues and eigenvectors of graph Laplacian matrices to partition nodes into clusters.

Graph kernel: A function that computes similarity by comparing substructures of graphs in a reproducing kernel Hilbert space.

Graph embedding: The mapping of graph elements or entire graphs into a vector space to enable standard machine learning methods.

Contrastive learning: An unsupervised approach that trains models by distinguishing similar and dissimilar samples via a specialised loss function.

Graph convolutional network (GCN): A neural network architecture that generalises convolution operations to graph-structured data, aggregating local neighbourhood features.

References

1. Graph-based pattern recognition on spectral reduced graphs. Pattern Recognition (2023).
2. Neural Graph Similarity Computation with Contrastive Learning. Applied Sciences (2022).
3. Efficient Top-k Graph Similarity Search With GED Constraints. IEEE Access (2022).