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Making Large-Scale Networks from fMRI Data.

Schmittmann VD, Jahfari S, Borsboom D, Savi AO, Waldorp LJ - PLoS ONE (2015)

Bottom Line: However, this approach generally results in a poor representation of the true underlying network.As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not.We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Methodology and Statistics/Social and Behavioral Sciences, Tilburg University, Tilburg, the Netherlands.

ABSTRACT
Pairwise correlations are currently a popular way to estimate a large-scale network (> 1000 nodes) from functional magnetic resonance imaging data. However, this approach generally results in a poor representation of the true underlying network. The reason is that pairwise correlations cannot distinguish between direct and indirect connectivity. As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not. In a simulation study and an application to resting-state fMRI data, we compare the performance of pairwise correlations in large-scale networks (2000 nodes) against three other methods that are designed to filter out indirect connections. Recovery methods are evaluated in four simulated network topologies (small world or not, scale-free or not) in scenarios where the number of observations is very small compared to the number of nodes. Simulations clearly show that pairwise correlation networks are fragmented into separate unconnected components with excessive connectedness within components. This often leads to erroneous estimates of network metrics, like small-world structures or low betweenness centrality, and produces too many low-degree nodes. We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks. However, even with these methods, the presence of hubs in the generating network can be problematic if the number of observations is too small. Additionally, we show for resting-state fMRI that partial correlations are more robust than correlations to different parcellation sets and to different lengths of time-series.

No MeSH data available.


Related in: MedlinePlus

Exemplary network with path from node 1 to 5, showing partial covariances γij.
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pone.0129074.g002: Exemplary network with path from node 1 to 5, showing partial covariances γij.

Mentions: The correlation (or the unscaled version, the covariance) can be considered as a function of the partial correlations (partial covariances). Consider the network in Fig 2 and suppose that this is the true underlying network. Here is a path from 1 to 5 as 1 − 2 − 3 − 4 − 5. For Gaussian variables the covariance is a function of the product of partial covariances γ12γ23γ34γ45 [12, 13]. Because of this the correlation between nodes 1 and 5 is nonzero. It also follows that partialling out (i.e., conditioning on) any or all of the nodes in the path is sufficient to obtain the correct interpretation that there is no direct connection between nodes 1 and 5. In general, there is no knowledge of which paths there are, and so it seems best to condition on all other nodes.


Making Large-Scale Networks from fMRI Data.

Schmittmann VD, Jahfari S, Borsboom D, Savi AO, Waldorp LJ - PLoS ONE (2015)

Exemplary network with path from node 1 to 5, showing partial covariances γij.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556712&req=5

pone.0129074.g002: Exemplary network with path from node 1 to 5, showing partial covariances γij.
Mentions: The correlation (or the unscaled version, the covariance) can be considered as a function of the partial correlations (partial covariances). Consider the network in Fig 2 and suppose that this is the true underlying network. Here is a path from 1 to 5 as 1 − 2 − 3 − 4 − 5. For Gaussian variables the covariance is a function of the product of partial covariances γ12γ23γ34γ45 [12, 13]. Because of this the correlation between nodes 1 and 5 is nonzero. It also follows that partialling out (i.e., conditioning on) any or all of the nodes in the path is sufficient to obtain the correct interpretation that there is no direct connection between nodes 1 and 5. In general, there is no knowledge of which paths there are, and so it seems best to condition on all other nodes.

Bottom Line: However, this approach generally results in a poor representation of the true underlying network.As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not.We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks.

View Article: PubMed Central - PubMed

Affiliation: Department of Methodology and Statistics/Social and Behavioral Sciences, Tilburg University, Tilburg, the Netherlands.

ABSTRACT
Pairwise correlations are currently a popular way to estimate a large-scale network (> 1000 nodes) from functional magnetic resonance imaging data. However, this approach generally results in a poor representation of the true underlying network. The reason is that pairwise correlations cannot distinguish between direct and indirect connectivity. As a result, pairwise correlation networks can lead to fallacious conclusions; for example, one may conclude that a network is a small-world when it is not. In a simulation study and an application to resting-state fMRI data, we compare the performance of pairwise correlations in large-scale networks (2000 nodes) against three other methods that are designed to filter out indirect connections. Recovery methods are evaluated in four simulated network topologies (small world or not, scale-free or not) in scenarios where the number of observations is very small compared to the number of nodes. Simulations clearly show that pairwise correlation networks are fragmented into separate unconnected components with excessive connectedness within components. This often leads to erroneous estimates of network metrics, like small-world structures or low betweenness centrality, and produces too many low-degree nodes. We conclude that using partial correlations, informed by a sparseness penalty, results in more accurate networks and corresponding metrics than pairwise correlation networks. However, even with these methods, the presence of hubs in the generating network can be problematic if the number of observations is too small. Additionally, we show for resting-state fMRI that partial correlations are more robust than correlations to different parcellation sets and to different lengths of time-series.

No MeSH data available.


Related in: MedlinePlus