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：我们提出了一种在大型背景图中寻找多个噪声嵌入模板图的新方法。该方法基于Sussman等人提出的图匹配匹配滤波器技术，通过在匹配滤波器算法中迭代惩罚合适的节点对相似度矩阵，实现多个多样化匹配的发现。此外，我们提出了算法加速方案，显著提升了匹配滤波器方法的可扩展性。我们在相关Erdos-Renyi图设置下提供了理论证明，表明该方法在温和模型条件下能够顺序发现多个模板。通过模拟模型和真实数据集的广泛实验（包括人类脑连接组和大型事务知识库），我们进一步验证了该方法的实用性。