噪声诱导子图检测的匹配滤波器
Matched Filters for Noisy Induced Subgraph Detection
摘要：
在两个顶点数不同的噪声图之间寻找顶点对应的问题在社交网络、神经科学和计算机视觉中有许多应用。我们提出了一个解决这个问题的方法，通过图匹配匹配滤波器：居中和填充较小的邻接矩阵，并应用图匹配方法将其对齐到较大的网络。居中和填充方案可以被合并到使用邻接矩阵进行匹配的任何算法中。在图的相关对的统计模型下，该模型在较大图内产生小图的噪声副本，由此产生的优化问题可以保证恢复网络之间的真实顶点对应。然而，目前还没有有效的算法来解决这个问题。为了说明这些问题的可能性和挑战，我们使用一种算法，可以利用部分已知的对应关系，并通过不同的模拟和应用程序{ \it果蝇}和人类连接体，这种方法可以实现良好的性能。
英文摘要：
The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to {\it Drosophila} and human connectomes that this approach can achieve good performance.
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。
