Limits...
Graph reconstruction using covariance-based methods

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.


Related in: MedlinePlus

Illustration of the four different graphs that have been used in our study. Shown are the adjacency matrices of the graphs and their corresponding graph topologies. a Chain graph with maximum degree of 2. b Cluster graph which consists of three disjoint subgraphs. c Scale-free graph (Barabasi-Albert graph). d Hub graph, also known as a star graph
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5121191&req=5

Fig5: Illustration of the four different graphs that have been used in our study. Shown are the adjacency matrices of the graphs and their corresponding graph topologies. a Chain graph with maximum degree of 2. b Cluster graph which consists of three disjoint subgraphs. c Scale-free graph (Barabasi-Albert graph). d Hub graph, also known as a star graph

Mentions: In this section, we compare the correlation- and partial correlation-based methods on different graph topologies based on synthetic data. For this purpose, we have generated the synthetic data and a workflow of data generation is illustrated in Fig. 4. In the following, we shortly describe several graphs used in the comparison which are illustrated in Fig. 5:Fig. 4


Graph reconstruction using covariance-based methods
Illustration of the four different graphs that have been used in our study. Shown are the adjacency matrices of the graphs and their corresponding graph topologies. a Chain graph with maximum degree of 2. b Cluster graph which consists of three disjoint subgraphs. c Scale-free graph (Barabasi-Albert graph). d Hub graph, also known as a star graph
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig5: Illustration of the four different graphs that have been used in our study. Shown are the adjacency matrices of the graphs and their corresponding graph topologies. a Chain graph with maximum degree of 2. b Cluster graph which consists of three disjoint subgraphs. c Scale-free graph (Barabasi-Albert graph). d Hub graph, also known as a star graph
Mentions: In this section, we compare the correlation- and partial correlation-based methods on different graph topologies based on synthetic data. For this purpose, we have generated the synthetic data and a workflow of data generation is illustrated in Fig. 4. In the following, we shortly describe several graphs used in the comparison which are illustrated in Fig. 5:Fig. 4

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.


Related in: MedlinePlus