# Analysis and Evaluation of Clustering Techniques Applied to Wireless Acoustics Sensor Network Data
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & \\
**Algor. 1** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **11** & **12** \\ \hline \multicolumn{10}{c}{BCN 1\({}^{\mathrm{s}}\) WASN data} \\ \hline HC 1 & 0.294 & 0.353 & 0.317 & 0.386 & 0.368 & 0.358 & 0.327 & 0.308 & 0.318 & 0.312 \\ KM 1 & 0.376 & 0.431 & 0.356 & 0.404 & 0.395 & 0.392 & 0.362 & 0.376 & 0.369 & 0.377 \\ DIANA & 0.138 & 0.308 & 0.299 & 0.310 & 0.324 & 0.319 & 0.318 & 0.321 & 0.338 & 0.318 \\ PAM & 0.368 & 0.415 & 0.358 & 0.350 & 0.334 & 0.344 & 0.350 & 0.362 & 0.335 & 0.345 \\ CLARA & 0.368 & 0.418 & 0.361 & 0.350 & 0.339 & 0.343 & 0.346 & 0.353 & 0.338 & 0.338 \\ SOM & 0.376 & 0.431 & 0.356 & 0.348 & 0.323 & 0.297 & 0.293 & 0.342 & 0.257 & 0.197 \\ GAUSS & 0.147 & 0.041 & 0.268 & 0.255 & 0.315 & 0.338 & 0.361 & NA 2 & 0.022 & 0.240 \\ SOTA & 0.336 & 0.245 & 0.284 & 0.264 & 0.280 & 0.277 & 0.243 & 0.238 & 0.257 & 0.226 \\ \hline \multicolumn{10}{c}{MAD 1\({}^{\mathrm{s}}\) WASN data} \\ \hline HC 1 & 0.376 & 0.301 & 0.307 & 0.287 & 0.317 & 0.291 & 0.294 & 0.291 & 0.272 & 0.230 \\ KM 1 & **0.396** & 0.382 & 0.341 & 0.320 & 0.319 & 0.290 & 0.292 & 0.294 & 0.275 & 0.261 \\ DIANA & 0.395 & 0.320 & 0.341 & 0.320 & 0.270 & 0.252 & 0.258 & 0.251 & 0.245 & 0.261 \\ PAM & 0.306 & 0.375 & 0.365 & 0.329 & 0.307 & 0.290 & 0.243 & 0.228 & 0.223 & 0.211 \\ CLARA & 0.306 & 0.375 & 0.365 & 0.329 & 0.303 & 0.287 & 0.250 & 0.235 & 0.231 & 0.218 \\ SOM & 0.354 & 0.382 & 0.287 & 0.192 & 0.246 & 0.222 & 0.187 & 0.162 & 0.182 & 0.156 \\ GAUSS & 0.239 & 0.023 & 0.167 & 0.171 & 0.072 & 0.195 & 0.174 & 0.112 & 0.144 & 0.127 \\ SOTA & 0.361 & 0.294 & 0.259 & 0.282 & 0.263 & 0.250 & 0.261 & 0.246 & 0.275 & NA 2 \\ \hline \multicolumn{10}{c}{Federated MAD 1 and BCN 1 joined WASN data} \\ \hline HC 1 & 0.399 & **0.415** & 0.359 & 0.309 & 0.397 & 0.347 & 0.355 & 0.388 & 0.396 & 0.385 \\ KM 1 & 0.303 & 0.371 & 0.380 & 0.389 & 0.371 & 0.378 & 0.394 & 0.391 & 0.406 & 0.385 \\ DIANA & 0.382 & 0.395 & 0.335 & 0.326 & 0.349 & 0.335 & 0.345 & 0.341 & 0.341 & 0.331 \\ PAM & 0.411 & 0.379 & 0.379 & 0.383 & 0.366 & 0.339 & 0.315 & 0.330 & 0.337 & 0.341 \\ CLARA & 0.310 & 0.379 & 0.366 & 0.374 & 0.356 & 0.379 & 0.382 & 0.346 & 0.280 & 0.359 \\ SOM & 0.411 & 0.380 & 0.380 & 0.383 & 0.366 & 0.330 & 0.341 & 0.317 & 0.305 & 0.293 \\ GAUSS & 0.192 & 0.187 & 0.086 & 0.028 & 0.077 & 0.099 & 0.205 & 0.209 & 0.232 & 0.213 \\ SOTA & 0.230 & 0.298 & 0.279 & 0.282 & 0.251 & 0.249 & 0.241 & 0.239 & 0.286 & 0.280 \\ \hline \multicolumn{10}{c}{} \\ \hline \end{tabular} \({}^{1}\) Abbreviations: Algor.: Algorithm, HC: Hierarchical Agglomeration and KM: K-means, MAD Madrid, BCN Barcelona. 2 No convergence.  
\end{table} 
Table 5: Evaluation and comparison of clustering techniques over WASN data based on the Silhouette Width. Figure 2: Nodes distribution within clusters by distance for \(k\) = 3 Hierarchical Agglomeration clustering. abbreviations: \(MAD_{\mathrm{X}}\) Madrid Stations, \(BCN_{\mathrm{X}}\) Barcelona Stations. Clusters groups are colored as presented in Table 6.  
A summary of the three discovered clusters obtained with federated data is presented in Table 6 in which the number of nodes per city is broken down together with the centroid of each acoustics parameter. It is remarkable that, as can be seen in Table 6, cluster number 2 only contains nodes belonging to Barcelona city, suggesting that this type of behavior is specific to this city. Moreover, the relative proportion of Madrid's nodes in cluster number 1 is lower than in cluster number 3, showing that Madrid has nodes with lower sound pressure levels on average than Barcelona. Now, Hierarchical Agglomeration is applied for \(k=4\) clusters. Figure 4 shows that previous cluster 1 (blue) with 42 nodes, obtained with \(k=3\), is split into two groups with 21 nodes each (blue and magenta).