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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

Recovery of node degrees based on 10000 observations.Scatter plots of true (x-axis) vs recovered (y-axis) node degrees of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).
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pone.0129074.g008: Recovery of node degrees based on 10000 observations.Scatter plots of true (x-axis) vs recovered (y-axis) node degrees of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).

Mentions: Correctly reproducing the underlying distribution of degrees does not necessarily imply that the nodes with low degrees indeed have low degrees and the nodes with high degrees indeed have high degrees, that is, that the degrees of the individual nodes are reproduced faithfully. Therefore, we compared the recovered degrees of the nodes to their true degrees. This comparison showed that pairwise correlation networks have a tendency to contain several nodes with much higher degree than the true network (Fig 8). In contrast, the partial correlation networks tend to underestimate the true degrees, but in general are closer to the degree distribution than the pairwise correlation network. Furthermore, the misfit between recovered and true degrees decreases for the partial correlation networks with longer time-series, but not so for the pairwise correlation networks (Fig 9). Weighted degrees (strengths) of the network nodes were in all conditions better estimated by partial correlation methods than by pairwise correlation (Fig 9).


Making Large-Scale Networks from fMRI Data.

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

Recovery of node degrees based on 10000 observations.Scatter plots of true (x-axis) vs recovered (y-axis) node degrees of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0129074.g008: Recovery of node degrees based on 10000 observations.Scatter plots of true (x-axis) vs recovered (y-axis) node degrees of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).
Mentions: Correctly reproducing the underlying distribution of degrees does not necessarily imply that the nodes with low degrees indeed have low degrees and the nodes with high degrees indeed have high degrees, that is, that the degrees of the individual nodes are reproduced faithfully. Therefore, we compared the recovered degrees of the nodes to their true degrees. This comparison showed that pairwise correlation networks have a tendency to contain several nodes with much higher degree than the true network (Fig 8). In contrast, the partial correlation networks tend to underestimate the true degrees, but in general are closer to the degree distribution than the pairwise correlation network. Furthermore, the misfit between recovered and true degrees decreases for the partial correlation networks with longer time-series, but not so for the pairwise correlation networks (Fig 9). Weighted degrees (strengths) of the network nodes were in all conditions better estimated by partial correlation methods than by pairwise correlation (Fig 9).

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