Graph matching is a fundamental problem in theoretical computer science and artificial intelligence, and lays the foundation for many computer vision and machine learning tasks. Approximate algorithms are necessary for graph matching due to its NP-complete nature. Inspired by the usage in network-related tasks, random walk is generalized to graph matching as a type of approximate algorithm. However, it may be inappropriate for the previous random walk-based graph matching algorithms to utilize continuous techniques without considering the discrete property. In this paper, we propose a novel random walk-based graph matching algorithm by incorporating both continuous and discrete constraints in the optimization process. Specifically, after interpreting graph matching by random walk, the continuous constraints are directly embedded in the random walk constraint in each iteration. Further, both the assignment matrix (vector) and the pairwise similarity measure between graphs are iteratively updated according the discrete constraints, which automatically leads the continuous solution to the discrete domain. Comparisons on both synthetic and real-world data demonstrate the effectiveness of the proposed algorithm.

中文翻译：

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将离散约束纳入基于随机游走的图匹配

图匹配是理论计算机科学和人工智能中的一个基本问题，为许多计算机视觉和机器学习任务奠定了基础。由于其 NP 完全性质，近似算法对于图匹配是必要的。受网络相关任务中使用的启发，随机游走被推广到图匹配作为一种近似算法。然而，之前的基于随机游走的图匹配算法在不考虑离散特性的情况下利用连续技术可能是不合适的。在本文中，我们通过在优化过程中结合连续和离散约束，提出了一种新的基于随机游走的图匹配算法。具体来说，通过随机游走解释图匹配后，在每次迭代中，连续约束直接嵌入到随机游走约束中。此外，分配矩阵（向量）和图之间的成对相似性度量都根据离散约束迭代更新，这会自动将连续解引向离散域。对合成数据和真实世界数据的比较证明了所提出算法的有效性。