双分网络中自一致度量的收敛性准则
Convergence criteria for self-consistent measures in bipartite networks
AI总结：
本文研究双分网络中自一致度量的收敛性准则，提出两种改进收敛性质的方法。
摘要：
许多用于表征网络元素的量是通过显式形式定义并直接从网络结构计算得出的；例如包括中心性度量如度数、接近度或介数。然而，也有一些隐式定义的定量指标，通常通过迭代方式以自一致的方式计算，如PageRank或国家的适应性/产品的复杂性关系。迭代算法涉及对整个网络的计算；因此，它们的收敛性质取决于网络的结构。在此，我们专注于研究双分网络中两个节点集的自一致度量，其中一组中的量由另一组中的量决定，反之亦然。我们推导了这些量迭代的显式收敛准则，并描述了两种不同的方法来改进收敛性质。第一种方法是识别
英文摘要：
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there are also implicitly defined quantitative measures, which are usually calculated iteratively, in a self-consistent manner, like PageRank or countries' fitness / products' complexity relations. The iteration algorithms involve calculations over the entire network; therefore, their convergence properties depend on the structure of the network. Here, we focus on investigating self-consistently defined quantities in bipartite networks of two sets of nodes where the quantities in one set are determined by the quantities in the other set and vice versa. We derive an explicit convergence criterion for iterations of these quantities and describe two different approaches to improve the convergence properties. In the first one, we identify "problematic nodes" that can be removed or merged while in the second one, we introduce a regularization scheme and show how to estimate the regularization parameter.
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