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Statistical and Machine Learning Approaches for Network Analysis by Subhash C. Basak, Matthias Dehmer

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5.2 Methods

5.2.1 C3NET

5.2.1.1 C3NET (Conservative Causal Core)

C3NET consists of three main steps [12]. The first step is for estimating mutual information for all gene pairs. In the second step, the most significant link for each gene is selected. In the third step nonsignificant links, according to a chosen significance level α, between gene pairs are eliminated. The inferred link in a C3NET gene regulatory network correspond to the highest MI value among the neighbor edges for each gene. This implies that the highest possible number of edges that can be inferred by C3NET is equal to the number of genes under consideration. This number can decrease for several reasons. For example, when two genes have the same edge with maximum MI value. In this case, the same edge would be chosen by both genes to be included in the network. However, if an edge is already present another inclusion does not lead to an additional edge. Another case corresponds to the situation when a gene does not have significant edges at all. In this case, apparently, no edge can be included in the network. Since C3NET employs MI values as test statistics among genes, there is no directional information that can be inferred thereof. Hence, the resulting network is undirected and unweighted. Figure 5.1 shows the principle working mechanism of C3NET. The maximum mutual information value between gene 7 and 5 (dashed line) is not significant. All other genes have significant MI values. This results in a total of ...

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