Brain network analysis: separating cost from topology using cost-integration.
Brain network analysis: separating cost from topology using cost-integration.
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DOI：
10.1371/journal.pone.0021570
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发表时间：
2011
期刊：
影响因子：
3.7
通讯作者：
Simmons A
中科院分区：
文献类型：
--
作者：
Ginestet CE;Nichols TE;Bullmore ET;Simmons A
进行大脑网络分析的统计原则性方法仍然缺乏。比较不同群体的大脑网络是困难的，因为拓扑学本质上依赖于布线成本，其中成本被定义为未加权图中的边数。在这篇文章中，我们评估了使用集成成本的拓扑度量的好处和局限性。我们的重点是使用全局效率比较平均关联权不同的加权无向图的群体。我们的关键结果表明，过度成本积分等价于控制加权图的权集的任何单调变换。也就是说，当积分超过成本时，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的拓扑度量，以及在成本水平上的任何分布选择。因此，成本整合有助于将成本差异与拓扑差异分开。相反，我们表明，使用拓扑度量的加权版本通常不是解决这个问题的有效方法。事实上，我们证明了，在弱条件下，使用加权版本的全局效率等价于简单地比较加权成本。因此，我们建议报告(1)加权成本的差异和(2)关于成本域上不同分布的成本综合拓扑度量的差异。我们展示了这些技术在fMRI工作记忆任务的重新分析中的应用。我们还提供了一种蒙特卡罗方法来逼近成本积分的拓扑度。最后，我们讨论了集成拓扑而不是成本的局限性，当一些权重为零时，当权重的等级中存在多重性时，以及当人们期望微妙的依赖于成本的拓扑差异时，这可能会产生问题，这可能被成本整合所掩盖。
A statistically principled way of conducting brain network analysis is still lacking. Comparison of different populations of brain 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 that differ in mean association weight, using global efficiency. 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, and for any choice of distribution over cost levels. 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 is generally not a valid approach to this problem. Indeed, we prove that, under weak 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 with respect to different distributions over the cost domain. We demonstrate the application of these techniques in a re-analysis of an fMRI working memory task. We also provide a Monte Carlo method for approximating cost-integrated topological measures. 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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DOI：
10.1523/jneurosci.1929-08.2008
发表时间：
2008-09-10
期刊：
The Journal of neuroscience : the official journal of the Society for Neuroscience
影响因子：
--
作者：
Bassett DS;Bullmore E;Verchinski BA;Mattay VS;Weinberger DR;Meyer-Lindenberg A
通讯作者：
Meyer-Lindenberg A
影响因子：
5.3
作者：
Achard, S;Salvador, R;Bullmore, ET
通讯作者：
Bullmore, ET
影响因子：
4.3
作者：
Achard S;Bullmore E
通讯作者：
Bullmore E
影响因子：
5.7
作者：
Ginestet, Cedric E.;Simmons, Andrew
通讯作者：
Simmons, Andrew
DOI：
10.1111/j.2517-6161.1995.tb02031.x
发表时间：
1995-01-01
影响因子：
5.8
作者：
BENJAMINI, Y;HOCHBERG, Y
通讯作者：
HOCHBERG, Y