# Building Topic-Driven Virtual IoTs in a Multiple IoTs Scenario
## 6 Experiments
### Number and Size of Returned Virtual IoTs  
This last experiment makes sense only for the unsupervised approach. Through it we aimed at investigating how the number and the size of returned virtual IoTs (and, therefore, the number and the size of returned clusters) vary when the MIoT size increases. To make this experiment significant, we maintained constant all the parameters of the adopted clustering algorithm. We considered the MIoTs \(\mathcal{M}_{1}\cdots\mathcal{M}_{10}\) used in the previous experiments because, in this way, we had the possibility to investigate MIoT sizes ranging from 176 to 5024 nodes. We report the obtained results in Table 14.  
From the analysis of this table we can observe that the average size of virtual IoTs:  
* increases when the MIoT size ranges from 176 to 946;  
\begin{table}
\begin{tabular}{c c} \hline \hline
**MIoT (Size)** & **Average \(g_{st}\)** \\ \hline \(\mathcal{M}_{1}\) (176) & 1.341 \\ \(\mathcal{M}_{2}\) (301) & 1.269 \\ \(\mathcal{M}_{3}\) (485) & 1.211 \\ \(\mathcal{M}_{4}\) (778) & 1.177 \\ \(\mathcal{M}_{5}\) (946) & 1.173 \\ \(\mathcal{M}_{6}\) (1256) & 1.171 \\ \(\mathcal{M}_{7}\) (1725) & 1.194 \\ \(\mathcal{M}_{8}\) (2028) & 1.273 \\ \(\mathcal{M}_{9}\) (3544) & 1.281 \\ \(\mathcal{M}_{10}\) (5024) & 1.301 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Average values of \(g_{st}\) against the size of MIoTs (unsupervised approach).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**MIoT (Size)**} & \multicolumn{6}{c}{**Average \(g_{st}\)**} \\ \cline{2-7}  & \(|Q|=1\) & \(|Q|=2\) & \(|Q|=4\) & \(|Q|=6\) & \(|Q|=8\) & \(|Q|=10\) \\ \hline \(\mathcal{M}_{1}\) (176) & 4.018 & 2.792 & 2.223 & 1.918 & 1.331 & 1.321 \\ \(\mathcal{M}_{2}\) (301) & 3.563 & 2.619 & 2.445 & 2.009 & 1.683 & 1.664 \\ \(\mathcal{M}_{3}\) (485) & 3.269 & 2.370 & 1.426 & 1.528 & 1.626 & 1.674 \\ \(\mathcal{M}_{4}\) (778) & 3.130 & 2.168 & 2.367 & 1.916 & 1.494 & 1.325 \\ \(\mathcal{M}_{5}\) (946) & 3.232 & 2.102 & 1.864 & 1.712 & 1.461 & 1.391 \\ \(\mathcal{M}_{6}\) (1256) & 3.467 & 1.979 & 1.378 & 1.412 & 1.438 & 1.452 \\ \(\mathcal{M}_{7}\) (1725) & 3.476 & 2.224 & 1.414 & 1.444 & 1.494 & 1.492 \\ \(\mathcal{M}_{8}\) (2028) & 3.496 & 2.669 & 1.489 & 1.491 & 1.521 & 1.545 \\ \(\mathcal{M}_{9}\) (3544) & 3.507 & 2.712 & 1.612 & 1.624 & 1.631 & 1.632 \\ \(\mathcal{M}_{10}\) (5024) & 3.517 & 2.926 & 1.783 & 1.841 & 1.864 & 1.874 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Average values of \(g_{st}\) against the size of MIoTs and queries used to generate the virtual IoTs (supervised approach).  
* slightly increases when the MIoT size ranges from 946 to 2028;
* remains essentially constant when the MIoT size is higher than 2028.  
In the meantime, the number of clusters:
* slightly increases when the MIoT size ranges from 176 to 946;
* increases when the MIoT size ranges from 946 to 2028;
* highly increases when the MIoT size is higher than 2028.  
The obtained results are extremely interesting because they confirm the soundness of the reasoning made in Section 5.3. In particular, this experiment confirms the scalability of our approach. As a matter of fact, after the virtual IoTs have been constructed offline, their usage for querying and for the other tasks of interest for the user can be performed online. Now, we observed that the number of available virtual IoTs highly increases when the MIoT size increases. However, because the size of each virtual IoT is only slightly impacted by the growth of the corresponding MIoT, and because user tasks generally involve one or at most a few of available virtual IoTs, we can conclude that our approach is scalable with respect to the size variation of the MIoT.