# Many-Objective Optimization for Anomaly Detection on Multi-Layer Complex Interaction Networks
## 4 Results
### Case Study V: Real-World Multi-Layer Social Media Network--FriendFeed, Twitter, Youtube (FFTWYT)  
For the experiments in this final case study, we focused on a multi-layer network in the context of social media--considering networks on FriendFeed, Twitter, and Youtube (FFTWYT). The respective anonymized dataset [1, 3, 69] was obtained starting from FriendFeed, i.e., a social media aggregator. In the following, we summarize the data collection and aggregation according to [1, 3, 69]: In the FriendFeed system, the users can directly post messages and comment on other messages; in addition, they can also register their accounts on other systems. For constructing the dataset, the FriendFeed social media aggregator was used to align users also registered on the respective other platforms ([[http://multilayer.it.uu.se/](http://multilayer.it.uu.se/)]([http://multilayer.it.uu.se/](http://multilayer.it.uu.se/))  
Using the FriendFeed information about users who registered exactly one Twitter account that was associated to exactly one FriendFeed account, two layers can be inferred (ff-tw); in addition, an additional YouTube layer (ff-tw-yt) could be constructed using the respective links to YouTube, c.f., [1; 3; 69]. This results in three layers in total. The real network data applied features a total number of 6407 nodes and 74,862 edges. Table 12 shows a statistical characterization and network metrics of the different layers. From the Pareto Front of the social media network data, we obtained 7 nodes, i.e., nodes 143, 1101, 1102, 2551, 3418, 4391, and 4497, as shown in Table 13. While the many-objective optimization approach works fine on the dataset, it is easy to see that layer 1 (Youtube) does not contribute much regarding the findings, since the centralities are mostly zero due to the sparseness (low density) of the network. Therefore, we consider the ACE score only with the layer of high edge density edge, i.e., focusing on the FriendFeed and Twitter layers (layer 2 and layer 3). Due to the very large number of nodes, we show a summary of the detailed results in Table 14. As the result, from layer 2, we can observe that nodes in the Pareto Front with high ACE scores are nodes 143, 1101, and 1102. In addition, when we compute the ACE score in layer 3, we can see that the nodes in the Pareto Front with high ACE score are the nodes 1101, 1102, and 2551. Therefore, taking both these layers into account, we determined the final set of anomalous candidate nodes from this social media multiplex network as the nodes 143, 1101, 1102, and 2551, in total. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**NO** & **L1:Youtube** & **L2:FriendFeed** & **L3:Twitter** & **Node** & **Level** \\ \hline \hline
**1** & **0** & 3:15E-19 & **1.77E-06** & **143** & **1** \\ \hline \hline
**2** & 6.28E-06 & 3:53E-19 & 5.61E-19 & **1101** & **1** \\ \hline \hline
**3** & **0** & 3:19E-19 & 6.93E-19 & **1102** & **1** \\ \hline \hline
**4** & **0** & 3:32E-19 & 6.67E-19 & **2551** & **1** \\ \hline \hline
**5** & **0** & 3:87E-19 & **0** & **3418** & **1** \\ \hline \hline
**6** & **0** & 3:02E-19 & 0.0005862 & **4391** & **1** \\ \hline \hline
**7** & **0** & 3:76E-19 & **5.64E-19** & **4497** & **1** \\ \hline \hline
**8** & **0** & 3:35E-19 & 4.96E-08 & **2468** & **2** \\ \hline
**9** & **0** & 4.29E-19 & 2.59E-19 & **1306** & **2** \\ \hline
**10** & **0** & 4.14E-19 & 6.14E-19 & **2218** & **2** \\ \hline
**11** & **0** & 4.22E-19 & 5.79E-19 & **2219** & **2** \\ \hline
**12** & **0** & 4.43E-19 & **0** & **2995** & **2** \\ \hline
**13** & **0** & 3.19E-19 & 5.30E-05 & **4208** & **2** \\ \hline
**14** & **0** & 3.82E-19 & 6.43E-19 & **2919** & **2** \\ \hline
**15** & **0** & 3.35E-19 & 6.93E-19 & **5915** & **2** \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistical characterization: social media multiplex network (ff-tw-yt). \(\mu\) is the mean centrality of the layer, \(\sigma\) is the standard deviation of the centrality, and \(D\) is the density of the layer.