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，用于在非常大的背景图中寻找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，通过对匹配滤波器算法中合适的节点对相似性矩阵进行迭代惩罚，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，极大地提升了匹配滤波方法的可扩展性。我们在相关Erdos-Renyi图设置下提供了理论论证，表明该方法能在温和模型条件下顺序发现多个模板。通过模拟模型和真实世界数据集（包括人脑连接组和大型事务知识库）的大量实验，我们进一步证明了该方法的实用性。