We present a novel approach for finding multiple noisily embedded template graphs in a very large background graph. Our method builds upon the graph-matching-matched-filter technique proposed in Sussman et al., with the discovery of multiple diverse matchings being achieved by iteratively penalizing a suitable node-pair similarity matrix in the matched filter algorithm. In addition, we propose algorithmic speed-ups that greatly enhance the scalability of our matched-filter approach. We present theoretical justification of our methodology in the setting of correlated Erdos-Renyi graphs, showing its ability to sequentially discover multiple templates under mild model conditions. We additionally demonstrate our method's utility via extensive experiments both using simulated models and real-world dataset, include human brain connectomes and a large transactional knowledge base.

翻译：我们提出了一种新颖的方法，用于在大型背景图中发现多个带有噪声嵌入的模板图。该方法基于Sussman等人提出的图匹配匹配滤波技术，通过迭代性地对匹配滤波器算法中合适的节点对相似性矩阵施加惩罚，实现多个多样化匹配的发现。此外，我们提出了算法加速策略，极大增强了匹配滤波器方法的可扩展性。在相关埃尔德什-雷尼图设定下，我们给出了方法论的理论依据，证明了其在温和模型条件下依次发现多个模板的能力。我们进一步通过大量实验展示了该方法的实用性，实验涵盖模拟模型和真实数据集，包括人类脑连接组和一个大规模交易知识库。