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. Related in: MedlinePlus |
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Mentions: We associate to G and G∗ their weighted adjacency matrices denoted A and A∗, respectively. Observe that G∗ contains self-loops or cycles (e.g., for a node i with at least one edge, i is connected to i by a path of length two through i→j→i), and hence, A∗ will have non-zero diagonal entries. The transitive closure of the graph is depicted in Fig. 1a for illustration.Fig. 1 |
View Article: PubMed Central - PubMed
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.