图表匹配：放松风险自担
Graph Matching: Relax at Your Own Risk
摘要：
图匹配--对齐一对图以最小化它们的边不一致--在过去的几十年里受到了理论和应用社区的广泛关注，包括组合学，计算机视觉和连接组学。它的关注可以部分归因于它的计算难度。虽然以前已经提出了许多算法来近似解决图匹配，但很少有理论支持它们的性能。一种常见的技术是将离散问题放松为连续问题，从而使从业者能够使用梯度下降型算法。我们证明了一个不定松弛（精确求解时）几乎总是发现最优置换，而一个共同的凸松弛几乎总是无法发现最优置换。这些理论结果表明，初始化的不确定算法与凸优化可能会产生改善的实际性能。事实上，实验结果照亮和证实了这些理论研究结果，证明了优秀的结果，在基准和实际数据的问题，合并这两种方法。
英文摘要：
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and connectomics. Its attention can be partially attributed to its computational difficulty. Although many heuristics have previously been proposed in the literature to approximately solve graph matching, very few have any theoretical support for their performance. A common technique is to relax the discrete problem to a continuous problem, therefore enabling practitioners to bring gradient-descent-type algorithms to bear. We prove that an indefinite relaxation (when solved exactly) almost always discovers the optimal permutation, while a common convex relaxation almost always fails to discover the optimal permutation. These theoretical results suggest that initializing the indefinite algorithm with the convex optimum might yield improved practical performance. Indeed, experimental results illuminate and corroborate these theoretical findings, demonstrating that excellent results are achieved in both benchmark and real data problems by amalgamating the two approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
