To achieve greater accuracy, hypergraph matching algorithms require exponential increases in computational resources. Recent kd-tree-based approximate nearest neighbor (ANN) methods, despite the sparsity of their compatibility tensor, still require exhaustive calculations for large-scale graph matching. This work utilizes CUR tensor decomposition and introduces a novel cascaded second and third-order hypergraph matching framework (CURSOR) for efficient hypergraph matching. A CUR-based second-order graph matching algorithm is used to provide a rough match, and then the core of CURSOR, a fiber-CUR-based tensor generation method, directly calculates entries of the compatibility tensor by leveraging the initial second-order match result. This significantly decreases the time complexity and tensor density. A probability relaxation labeling (PRL)-based matching algorithm, specifically suitable for sparse tensors, is developed. Experiment results on large-scale synthetic datasets and widely-adopted benchmark sets demonstrate the superiority of CURSOR over existing methods. The tensor generation method in CURSOR can be integrated seamlessly into existing hypergraph matching methods to improve their performance and lower their computational costs.

本文介绍了一种基于CUR张量分解的超图匹配方法（CURSOR），通过CUR基于第二阶图匹配算法提供初步匹配，然后利用基于纤维的CUR张量生成方法直接计算兼容张量的条目，从而显著降低时间复杂度和张量的密度，最后利用基于概率松弛标记的匹配算法进一步提高匹配效果，实验证明CURSOR方法在大规模合成数据集和广泛采用的基准集上优于现有方法并降低计算成本。

CUR分解在可扩展的混合高阶超图匹配中的应用