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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

True positive rate as a function of node degree (given 10000 observations) of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).For each network, nodes were divided into 6 bins according to degree: 5 equally-sized bins, and a 6th bin containing the 50 nodes with the highest degree (i.e., the hubs in the hub networks). TPR is shown for each pairing of degree bins (e.g., sixteenth pair  refers to edges between the nodes with lowest degrees and the nodes with highest degrees; rightmost pair  refers to edges between the nodes with highest degrees).
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pone.0129074.g013: True positive rate as a function of node degree (given 10000 observations) of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).For each network, nodes were divided into 6 bins according to degree: 5 equally-sized bins, and a 6th bin containing the 50 nodes with the highest degree (i.e., the hubs in the hub networks). TPR is shown for each pairing of degree bins (e.g., sixteenth pair refers to edges between the nodes with lowest degrees and the nodes with highest degrees; rightmost pair refers to edges between the nodes with highest degrees).

Mentions: We also examined whether the identification of a true connection depends on the degrees of the two nodes that are connected by it (e.g., are connections between nodes with two degrees more easily identified than connections between a hub node and a node with two degrees?). For this purpose, we calculated the TPR and the FPR as a function of the true degrees of each pair of connected nodes. Fig 13 shows that the TPR is higher in the partial correlation networks than in the pairwise correlation networks for almost all degree pairings. Pairwise correlation networks have a very low TPR for connections between lowest to larger degree nodes. Merely for connections involving largest and hub nodes does the TPR of pairwise correlation networks approach or exceed the TPRs of the partial correlation networks. However, in exactly these cases, the FPR of the pairwise correlation networks are inacceptably large (Fig 14). The graphical lasso networks have somewhat elevated FPRs and TPRs for connections between hub nodes. In contrast, the FPR of the other two partial correlation networks remains relatively small across low, medium, large degree and hub nodes, while their TPRs are in general the highest (> .75 for networks without hubs, and ranging between .25 and .5 for networks with hubs) and relatively stable across the whole range of lowest degree to hub nodes.


Making Large-Scale Networks from fMRI Data.

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

True positive rate as a function of node degree (given 10000 observations) of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).For each network, nodes were divided into 6 bins according to degree: 5 equally-sized bins, and a 6th bin containing the 50 nodes with the highest degree (i.e., the hubs in the hub networks). TPR is shown for each pairing of degree bins (e.g., sixteenth pair  refers to edges between the nodes with lowest degrees and the nodes with highest degrees; rightmost pair  refers to edges between the nodes with highest degrees).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0129074.g013: True positive rate as a function of node degree (given 10000 observations) of shrinkage (blue), ridge (orange), and lasso (green) estimated partial correlations, and of pairwise correlations (red).For each network, nodes were divided into 6 bins according to degree: 5 equally-sized bins, and a 6th bin containing the 50 nodes with the highest degree (i.e., the hubs in the hub networks). TPR is shown for each pairing of degree bins (e.g., sixteenth pair refers to edges between the nodes with lowest degrees and the nodes with highest degrees; rightmost pair refers to edges between the nodes with highest degrees).
Mentions: We also examined whether the identification of a true connection depends on the degrees of the two nodes that are connected by it (e.g., are connections between nodes with two degrees more easily identified than connections between a hub node and a node with two degrees?). For this purpose, we calculated the TPR and the FPR as a function of the true degrees of each pair of connected nodes. Fig 13 shows that the TPR is higher in the partial correlation networks than in the pairwise correlation networks for almost all degree pairings. Pairwise correlation networks have a very low TPR for connections between lowest to larger degree nodes. Merely for connections involving largest and hub nodes does the TPR of pairwise correlation networks approach or exceed the TPRs of the partial correlation networks. However, in exactly these cases, the FPR of the pairwise correlation networks are inacceptably large (Fig 14). The graphical lasso networks have somewhat elevated FPRs and TPRs for connections between hub nodes. In contrast, the FPR of the other two partial correlation networks remains relatively small across low, medium, large degree and hub nodes, while their TPRs are in general the highest (> .75 for networks without hubs, and ranging between .25 and .5 for networks with hubs) and relatively stable across the whole range of lowest degree to hub 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