脑网络分析：使用成本整合将成本与拓扑分离
Brain Network Analysis: Separating Cost from Topology using Cost-integration
摘要：
一个统计原则的方式进行加权网络分析仍然缺乏。不同群体的加权网络的比较是困难的，因为拓扑结构固有地依赖于布线成本，其中成本被定义为未加权图中的边的数量。在本文中，我们评估的好处和限制与使用成本集成拓扑度量。我们的重点是比较人口的加权无向图使用全局效率。我们评估不同的方法来比较加权网络，不同的平均关联权重。我们的关键结果表明，集成成本是等价于控制的加权图的重量集的任何单调变换。也就是说，当对成本进行积分时，我们消除了可能由于权重集的单调变换而导致的拓扑差异。我们的结果适用于任何未加权拓扑测度。因此，成本整合有助于将成本差异与拓扑结构差异分开。相比之下，我们表明，使用的加权版本的拓扑度量不构成一个有效的方法来解决这个问题。事实上，我们证明，在温和的条件下，使用加权版本的整体效率是等同于简单地比较加权成本。因此，我们建议报告（一）加权成本的差异和（二）成本综合拓扑测量的差异。我们展示了这些技术在功能磁共振工作记忆任务的重新分析中的应用。最后，我们讨论了集成拓扑成本的限制，这可能会造成问题时，一些权重为零，当多重性存在于权重的行列中，当人们期望微妙的成本依赖的拓扑差异，这可能会被掩盖的成本集成。
英文摘要：
A statistically principled way of conducting weighted network analysis is still lacking. Comparison of different populations of weighted networks is hard because topology is inherently dependent on wiring cost, where cost is defined as the number of edges in an unweighted graph. In this paper, we evaluate the benefits and limitations associated with using cost-integrated topological metrics. Our focus is on comparing populations of weighted undirected graphs using global efficiency. We evaluate different approaches to the comparison of weighted networks that differ in mean association weight. Our key result shows that integrating over cost is equivalent to controlling for any monotonic transformation of the weight set of a weighted graph. That is, when integrating over cost, we eliminate the differences in topology that may be due to a monotonic transformation of the weight set. Our result holds for any unweighted topological measure. Cost-integration is therefore helpful in disentangling differences in cost from differences in topology. By contrast, we show that the use of the weighted version of a topological metric does not constitute a valid approach to this problem. Indeed, we prove that, under mild conditions, the use of the weighted version of global efficiency is equivalent to simply comparing weighted costs. Thus, we recommend the reporting of (i) differences in weighted costs and (ii) differences in cost-integrated topological measures. We demonstrate the application of these techniques in a re-analysis of an fMRI working memory task. Finally, we discuss the limitations of integrating topology over cost, which may pose problems when some weights are zero, when multiplicities exist in the ranks of the weights, and when one expects subtle cost-dependent topological differences, which could be masked by cost-integration.
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