利用图拓扑的感知不确定性高效子图同构
Uncertainty-aware Efficient Subgraph Isomorphism using Graph Topology
AI总结：
提出一种基于图拓扑的两步子图同构方法，通过提取最小唯一拓扑子集和共识算法实现不精确匹配，具有亚线性效率和噪声鲁棒性。
摘要：
子图同构，也称为子图匹配，通常被视为一个NP完全问题。在实际应用中，当边权为实数值且可能受到测量噪声和潜在数据缺失的影响时，这一复杂性进一步加剧。这种图匹配在图像匹配和地图匹配等应用中经常出现。大多数子图匹配方法在存在此类损坏的情况下无法执行节点到节点的匹配。我们提出了一种方法，用于在无节点标签的不精确情况下识别子图与完整图之间的节点对应关系，分为两步：(a) 从子图中提取最小唯一拓扑保持子集，并在完整图中找到其可行匹配；(b) 实现一种基于共识的算法，通过基于边界交换性的唯一路径配对来扩展匹配节点集。为了证明所提出方法的有效性，在Erdos-Renyi随机图上进行了模拟，并分别在基于图像仿射协变特征数据集和KITTI立体数据集上进行了两项案例研究。超越现有的子图匹配方法，所提出的方法被证明具有实际上的亚线性计算效率、对随机测量噪声的鲁棒性以及良好的统计特性。我们的方法也无需损失一般性即可直接应用于精确匹配情况。
英文摘要：
Subgraph isomorphism, also known as subgraph matching, is typically regarded as an NP-complete problem. This complexity is further compounded in practical applications where edge weights are real-valued and may be affected by measurement noise and potential missing data. Such graph matching routinely arises in applications such as image matching and map matching. Most subgraph matching methods fail to perform node-to-node matching under presence of such corruptions. We propose a method for identifying the node correspondence between a subgraph and a full graph in the inexact case without node labels in two steps - (a) extract the minimal unique topology preserving subset from the subgraph and find its feasible matching in the full graph, and (b) implement a consensus-based algorithm to expand the matched node set by pairing unique paths based on boundary commutativity. To demonstrate the effectiveness of the proposed method, a simulation is performed on the Erdos-Renyi random graphs and two case studies are performed on the image-based affine covariant features dataset and KITTI stereo dataset respectively. Going beyond the existing subgraph matching approaches, the proposed method is shown to have realistically sub-linear computational efficiency, robustness to random measurement noise, and good statistical properties. Our method is also readily applicable to the exact matching case without loss of generality.
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