多尺度网络约简方法：3,000+ U之间人类迁移流的双随机和差异过滤。S.县
Multiscale Network Reduction Methodologies: Bistochastic and Disparity Filtering of Human Migration Flows between 3,000+ U. S. Counties
摘要：
为了控制网络中的多尺度效应，可以使用迭代比例拟合（Sinkhorn-Knopp）程序将（一般）加权的有向节点间流矩阵转换为双随机（双随机）形式，该程序交替缩放行和列和，使其全部等于1。在bistochasticized表中的主要条目，然后可以用于网络约简，使用强分量层次聚类。我们说明了这个完善的，广泛应用的两阶段算法的各个方面与3107 × 3107（不对称）1995-2000年美国县际移民流量表。我们比较所获得的结果与使用视差过滤器，为“提取“多尺度骨干的复杂加权网络”，最近提出的塞拉诺，博古纳和Vespignani（SBV）（美国国家科学院院刊）。Acad. Sci. 106 [2009]，6483），对此我们已经简要地进行了评论（Proc. Natl. Acad. Sci. 106 [2009]，E66）。双随机滤波器的性能似乎是优越的-至少在这个特定的情况下-在两个方面：（1）它需要少得多的链接，以完成一个强连接的网络骨干;和（2）它“贬低”小流量和节点少-SBV的主要需求-在这个意义上，非零原始流量与相应的双随机链接的相关性要比与显著性的相关性弱得多由视差过滤器产生的水平。额外的比较研究-要求SBV-这两个过滤程序，特别是关于它们的拓扑性质，应该是相当大的兴趣。与此相关的是，在其许多地理应用中，两阶段程序-除极少数例外-将毗连区分组，往往重建传统区域（例如岛屿），尽管事先根本没有任何毗连限制。
英文摘要：
To control for multiscale effects in networks, one can transform the matrix of (in general) weighted, directed internodal flows to bistochastic (doubly-stochastic) form, using the iterative proportional fitting (Sinkhorn-Knopp) procedure, which alternatively scales row and column sums to all equal 1. The dominant entries in the bistochasticized table can then be employed for network reduction, using strong component hierarchical clustering. We illustrate various facets of this well-established, widely-applied two-stage algorithm with the 3, 107 x 3, 107 (asymmetric) 1995-2000 intercounty migration flow table for the United States. We compare the results obtained with ones using the disparity filter, for "extracting the "multiscale backbone of complex weighted networks", recently put forth by Serrano, Boguna and Vespignani (SBV) (Proc. Natl. Acad. Sci. 106 [2009], 6483), upon which we have briefly commented (Proc. Natl. Acad. Sci. 106 [2009], E66). The performance of the bistochastic filter appears to be superior-at least in this specific case-in two respects: (1) it requires far fewer links to complete a stongly-connected network backbone; and (2) it "belittles" small flows and nodes less-a principal desideratum of SBV-in the sense that the correlations of the nonzero raw flows are considerably weaker with the corresponding bistochastized links than with the significance levels yielded by the disparity filter. Additional comparative studies--as called for by SBV-of these two filtering procedures, in particular as regards their topological properties, should be of considerable interest. Relatedly, in its many geographic applications, the two-stage procedure has--with rare exceptions-clustered contiguous areas, often reconstructing traditional regions (islands, for example), even though no contiguity constraints, at all, are imposed beforehand.
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