二分网络和单分网络之间的图匹配：崩溃，还是不崩溃，这是一个问题
Graph matching between bipartite and unipartite networks: to collapse, or not to collapse, that is the question
摘要：
图匹配包括对齐两个未标记图的顶点，以最大化网络中的共享结构;当图是单部图时，这通常被公式化为最小化它们的边不一致。在本文中，我们解决了常见的设置，其中一个图匹配是一个二分网络和一个是unipartite。通常，二分网络被折叠或投影到一个单分图中，图匹配过程与经典设置相同。这可能导致噪声边缘估计和信息丢失。我们制定的二分图和单分图之间的图匹配问题，使用无向图形模型，并引入方法来找到与此模型的对齐，而不会崩溃。我们从理论上证明，我们的方法是一致的，并提供非渐近条件，确保精确恢复的匹配解决方案。在模拟和真实数据示例中，我们展示了我们的方法如何比将二分网络转换为单分网络的朴素方法更准确地匹配，并且我们展示了我们的方法在模拟和真实数据网络中实现的性能增益，包括合著-引用网络对，以及大脑结构和功能数据。
英文摘要：
Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this paper, we address the common setting in which one of the graphs to match is a bipartite network and one is unipartite. Commonly, the bipartite networks are collapsed or projected into a unipartite graph, and graph matching proceeds as in the classical setting. This potentially leads to noisy edge estimates and loss of information. We formulate the graph matching problem between a bipartite and a unipartite graph using an undirected graphical model, and introduce methods to find the alignment with this model without collapsing. We theoretically demonstrate that our methodology is consistent, and provide non-asymptotic conditions that ensure exact recovery of the matching solution. In simulations and real data examples, we show how our methods can result in a more accurate matching than the naive approach of transforming the bipartite networks into unipartite, and we demonstrate the performance gains achieved by our method in simulated and real data networks, including a co-authorship-citation network pair, and brain structural and functional data.
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。
