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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

Clustering coefficient (upper) and average pathlength (lower) for the four networks and estimation methods.
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pone.0129074.g005: Clustering coefficient (upper) and average pathlength (lower) for the four networks and estimation methods.

Mentions: As mentioned above, small-world networks are characterized by short average pathlengths and high clustering. This implies a high connectivity in each neighborhood of nodes [7, 35, 51]. Formally, the small-worldness index can be defined by the ratio of the clustering coefficient and the average pathlength relative to a random network of the same dimensions [35]. The small-worldness index of a network depends heavily on the number of triangles, since the clustering coefficient is the percentage of triangles out of the number of triplets (three nodes with two edges) [34, 35]. It is known that triangles are often erroneously obtained using pairwise correlations [11]. In the simulations, this problem can be observed in each of the four network topologies (see Fig 4). When using pairwise correlations to determine the connections in the network (red curve), the small-worldness index is much higher than the true value for each of the networks (dashed line), whether they are small-worlds or not. It even appears that, for pairwise correlations, the index increases as the numbers of observations increases. The shrinkage (blue curve) and lasso (green curve) estimates appear to be the most accurate in general. Thus, as expected, due to overestimation of the prevalence of triangles, the pairwise correlation method clearly inflates the clustering coefficient (Fig 5). When considering only pairs of regions, the number of triangles will be high when the correlations in the indirect connection are high [52]. Fig 4 also shows that obtaining too many connections (20%) results in lower estimates of small-worldness, but this is mainly due to the ensuing underestimation of the average pathlength (Fig 5), since the clustering coefficient hardly changes (Fig 5).


Making Large-Scale Networks from fMRI Data.

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

Clustering coefficient (upper) and average pathlength (lower) for the four networks and estimation methods.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0129074.g005: Clustering coefficient (upper) and average pathlength (lower) for the four networks and estimation methods.
Mentions: As mentioned above, small-world networks are characterized by short average pathlengths and high clustering. This implies a high connectivity in each neighborhood of nodes [7, 35, 51]. Formally, the small-worldness index can be defined by the ratio of the clustering coefficient and the average pathlength relative to a random network of the same dimensions [35]. The small-worldness index of a network depends heavily on the number of triangles, since the clustering coefficient is the percentage of triangles out of the number of triplets (three nodes with two edges) [34, 35]. It is known that triangles are often erroneously obtained using pairwise correlations [11]. In the simulations, this problem can be observed in each of the four network topologies (see Fig 4). When using pairwise correlations to determine the connections in the network (red curve), the small-worldness index is much higher than the true value for each of the networks (dashed line), whether they are small-worlds or not. It even appears that, for pairwise correlations, the index increases as the numbers of observations increases. The shrinkage (blue curve) and lasso (green curve) estimates appear to be the most accurate in general. Thus, as expected, due to overestimation of the prevalence of triangles, the pairwise correlation method clearly inflates the clustering coefficient (Fig 5). When considering only pairs of regions, the number of triangles will be high when the correlations in the indirect connection are high [52]. Fig 4 also shows that obtaining too many connections (20%) results in lower estimates of small-worldness, but this is mainly due to the ensuing underestimation of the average pathlength (Fig 5), since the clustering coefficient hardly changes (Fig 5).

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