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Graph reconstruction using covariance-based methods

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ABSTRACT

Methods based on correlation and partial correlation are today employed in the reconstruction of a statistical interaction graph from high-throughput omics data. These dedicated methods work well even for the case when the number of variables exceeds the number of samples. In this study, we investigate how the graphs extracted from covariance and concentration matrix estimates are related by using Neumann series and transitive closure and through discussing concrete small examples. Considering the ideal case where the true graph is available, we also compare correlation and partial correlation methods for large realistic graphs. In particular, we perform the comparisons with optimally selected parameters based on the true underlying graph and with data-driven approaches where the parameters are directly estimated from the data.

Electronic supplementary material: The online version of this article (doi:10.1186/s13637-016-0052-y) contains supplementary material, which is available to authorized users.

No MeSH data available.


Selecting a hard-threshold based on the R2 and the mean degree values which are plotted versus hard-thresholding values. The hard-thresholded values starting from 0.3 give rise to scale-free topology except 0.7 and higher. The corresponding mean degree values are relatively low indicating a sparsity of the underlying graph. The numbers in the plot represent different thresholds which are plotted for illustration purposes
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Fig3: Selecting a hard-threshold based on the R2 and the mean degree values which are plotted versus hard-thresholding values. The hard-thresholded values starting from 0.3 give rise to scale-free topology except 0.7 and higher. The corresponding mean degree values are relatively low indicating a sparsity of the underlying graph. The numbers in the plot represent different thresholds which are plotted for illustration purposes

Mentions: The simplest way to reconstruct the covariance graph is based on the sample covariance matrix which is easy to compute. However, the graph resulting from the sample covariance matrix is fully connected. One way to reconstruct a sparse covariance graph is to threshold the sample covariance matrix. This method is popular in applications; for instance, it is at the core of WGCNA package [6]. One study showed that the connected components of the concentration graph can be completely described by the covariance graph obtained by thresholding the sample covariance matrix [12] (Fig. 3).Fig. 3


Graph reconstruction using covariance-based methods
Selecting a hard-threshold based on the R2 and the mean degree values which are plotted versus hard-thresholding values. The hard-thresholded values starting from 0.3 give rise to scale-free topology except 0.7 and higher. The corresponding mean degree values are relatively low indicating a sparsity of the underlying graph. The numbers in the plot represent different thresholds which are plotted for illustration purposes
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5121191&req=5

Fig3: Selecting a hard-threshold based on the R2 and the mean degree values which are plotted versus hard-thresholding values. The hard-thresholded values starting from 0.3 give rise to scale-free topology except 0.7 and higher. The corresponding mean degree values are relatively low indicating a sparsity of the underlying graph. The numbers in the plot represent different thresholds which are plotted for illustration purposes
Mentions: The simplest way to reconstruct the covariance graph is based on the sample covariance matrix which is easy to compute. However, the graph resulting from the sample covariance matrix is fully connected. One way to reconstruct a sparse covariance graph is to threshold the sample covariance matrix. This method is popular in applications; for instance, it is at the core of WGCNA package [6]. One study showed that the connected components of the concentration graph can be completely described by the covariance graph obtained by thresholding the sample covariance matrix [12] (Fig. 3).Fig. 3

View Article: PubMed Central - PubMed

ABSTRACT

Methods based on correlation and partial correlation are today employed in the reconstruction of a statistical interaction graph from high-throughput omics data. These dedicated methods work well even for the case when the number of variables exceeds the number of samples. In this study, we investigate how the graphs extracted from covariance and concentration matrix estimates are related by using Neumann series and transitive closure and through discussing concrete small examples. Considering the ideal case where the true graph is available, we also compare correlation and partial correlation methods for large realistic graphs. In particular, we perform the comparisons with optimally selected parameters based on the true underlying graph and with data-driven approaches where the parameters are directly estimated from the data.

Electronic supplementary material: The online version of this article (doi:10.1186/s13637-016-0052-y) contains supplementary material, which is available to authorized users.

No MeSH data available.