Ginestet, Cedric E., Nichols, Thomas E., Bullmore, Edward T. and Simmons, Andrew. (2011) Brain network analysis : separating cost from topology using cost-integration. PLoS ONE, Vol.6 (No.7). Article: e21570. ISSN 1932-6203

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry T Technology > TK Electrical engineering. Electronics Nuclear engineering
Divisions:	Faculty of Science > Statistics Faculty of Science > WMG (Formerly the Warwick Manufacturing Group)
Library of Congress Subject Headings (LCSH):	Graph theory, System analysis, Brain -- Mathematical models
Journal or Publication Title:	PLoS ONE
Publisher:	Public Library of Science
ISSN:	1932-6203
Date:	28 July 2011
Volume:	Vol.6
Number:	No.7
Number of Pages:	17
Page Range:	Article: e21570
Identification Number:	10.1371/journal.pone.0021570
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	National Institute for Health Research (Great Britain) (NIHR), Guy's & St. Thomas' Hospital Trust. Charitable Foundation, South London and Maudsley NHS Trust
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URI:	http://wrap.warwick.ac.uk/id/eprint/36875

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