Brain network analysis: separating cost from topology using cost-integration.

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...

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Autores principales:	Cedric E Ginestet, Thomas E Nichols, Ed T Bullmore, Andrew Simmons
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2011
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/21852b70a1e646d49e246b21378fd131
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spelling	oai:doaj.org-article:21852b70a1e646d49e246b21378fd1312021-11-18T06:49:12ZBrain network analysis: separating cost from topology using cost-integration.1932-620310.1371/journal.pone.0021570https://doaj.org/article/21852b70a1e646d49e246b21378fd1312011-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/21829437/?tool=EBIhttps://doaj.org/toc/1932-6203A 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.Cedric E GinestetThomas E NicholsEd T BullmoreAndrew SimmonsPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 6, Iss 7, p e21570 (2011)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Cedric E Ginestet Thomas E Nichols Ed T Bullmore Andrew Simmons Brain network analysis: separating cost from topology using cost-integration.
description	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.
format	article
author	Cedric E Ginestet Thomas E Nichols Ed T Bullmore Andrew Simmons
author_facet	Cedric E Ginestet Thomas E Nichols Ed T Bullmore Andrew Simmons
author_sort	Cedric E Ginestet
title	Brain network analysis: separating cost from topology using cost-integration.
title_short	Brain network analysis: separating cost from topology using cost-integration.
title_full	Brain network analysis: separating cost from topology using cost-integration.
title_fullStr	Brain network analysis: separating cost from topology using cost-integration.
title_full_unstemmed	Brain network analysis: separating cost from topology using cost-integration.
title_sort	brain network analysis: separating cost from topology using cost-integration.
publisher	Public Library of Science (PLoS)
publishDate	2011
url	https://doaj.org/article/21852b70a1e646d49e246b21378fd131
work_keys_str_mv	AT cedriceginestet brainnetworkanalysisseparatingcostfromtopologyusingcostintegration AT thomasenichols brainnetworkanalysisseparatingcostfromtopologyusingcostintegration AT edtbullmore brainnetworkanalysisseparatingcostfromtopologyusingcostintegration AT andrewsimmons brainnetworkanalysisseparatingcostfromtopologyusingcostintegration
_version_	1718424339972358144

Brain network analysis: separating cost from topology using cost-integration.

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