# Detecting Composite Functional Module in miRNA Regulation and mRNA Interaction Network
## 4 Experiments and Results
### Structural Significance and Functional Coherence of CMFMs  
CMFMs are the units that represent consistency between CRs and PPIs in the integrated network. We herein carry on comparative analysis on density for each module to exhibit the connection between miRNAs and mRNAs. As illustrated in Figure 3A, the densities of modules from MBCFM are clearly larger than SNMNMF and Mirsynergy, which indicates that modules identified by MBCFM are significantly more densely connected than SNMNMF and Mirsynergy. It is also observed that the densities in modules from SNMNMF and Mirsynergy are generally small, which implies that many of the mRNAs in these modules are not regulated by miRNAs, which is not in agreement with the standpoint of miRNA cooperative regulation. In addition to evaluating the density values of modules, we also computed the averaged anti-correlation between miRNAs and mRNAs in the identified modules. As shown in Table 1, Mirsynergy and MBCFM exhibit negative average anti-correlations while SNMNMF shows a positive average anti-correlation. In detail, as illustrated in Figure 3B, MBCFM can collect lots of negative anti-correlation modules in which the correlation values are less than \(-1\), while the other two methods can only collect a few modules whose correlation values are between 0 and \(-1\). Due to the sparsity of connections in Mirsynergy and MBCFM modules, the miMEC  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Num** & **AmiRNA** & **AmRNA** & **Density** & **miMEC** & **Runtime(h)** \\ \hline MBCFM & 94 & 5.42 & 40.3 & 0.312 & \(-\)0.28 & \(\leq\)1 \\ Mirsynergy & 84 & 4.76 & 7.57 & 0.063 & \(-\)0.06 & \(\geq\)14 \\ SNMNMF & 49 & 4.12 & 81.37 & 0.004 & 0.06 & \(\geq\)24 \\ \hline \hline \end{tabular}  
* Num is the number of modules. AmiRNA and AmRNA are the average number of miRNAs and mRNAs per module respectively. Density is the averaged regulatory module density of identified modules; the larger is the density value, the stronger are the biological relationships. miMEC is the averaged miRNA-mRNA expression correlation across all modules; the more negative is miMEC, the stronger is the expression of miRNA-mRNA. Runtime is the number of hours of algorithm completion.  
\end{table}
Table 1: Performance summary of MBCFM, Mirsynergy and SNMNMF.  
values almost equal to zero in those two method modules, which further explains why the miRNAs and mRNAs in SNMNMF-modules and Mirsynergy-modules are not cooperatively regulated. All of the above results demonstrate that the modules identified by MBCFM are in agreement with the cooperative regulation between miRNAs and mRNAs.  
As illustrated in Figure 4, the distribution of MBCFM-modules between density and anti-correlation also outperforms than Mirsynergy and SNMNMF. The observations confirm that the densities from MBCFM modules are denser than Mirsynergy and SNMNMF, and corresponding anti-correlations are also more negative than theirs. Therefore, the modules identified by our method show stronger regulation between miRNAs and mRNAs than Mirsynergy and SNMNMF.  
Figure 4: The distributions between density and anti-correlation for modules detected by MBCFM, Mirsynergy and SNMNMF. Large number of anti-correlation values of the modules detected by Mirsynergy are close to zero. Lots of density values of the modules detected by SNMNMF are also close to zero.  
Figure 3: The cumulative distribution function (CDF) for the density and miMEC of modules identified by MBCFM, Mirsynergy and SNMNMF on ovarian dataset. (**A**) There are plenty of zero-density modules identified by Mirsynergy and SNMNMF; (**B**) MBCFM can collect lots of negative anti-correlation modules in which the correlation values are less than \(-1\), while other two methods only can collect a few of modules whose correlation values are between \(0\) and \(-1\).