## 6 Experimental Results
### ESCAPE Performances  
Here we report a summary of the experiments conducted on the six datasets using the joint-approach and the probabilistic approach. ESCAPE has been run several times, once for each weighting strategy and dataset. Dataset D1 has been chosen as the running example for a detailed comparison. **Joint-Approach. ** Table 4 reports the experimental results obtained for D1 and includes the metrics computed for evaluating the document partitions identified by our framework. For each weighting strategy, the top-three solutions (i.e., configurations) are reported to the analyst. The best solution is reported in bold. We observe that ESCAPE tends to select a partition with a low-medium number of dimensions as the optimal partition. The variability of the data distribution and the complexity of the cluster activity are directly proportional to the _K-LSA_ value. So, the silhouette indices usually decrease when considering a large number of terms with each document (columns of the dataset). For the weighting scheme TF-IDF, the 3 reduction factors for the SVD decomposition (\(K_{LSA}\)) are 26, 41, and 67. For each dimensionality-reduction parameter, ESCAPE selects the best value for the clustering phase. Given these numbers of dimensions, ESCAPE selects \(K_{Clustering=10}\) as the optimal partition. Since the silhouette-based metrics are quite stable, ESCAPE selects only the most-relevant terms in the building of the model, ignoring the less-relevant terms (dimensions). The TF local weight tends to differentiate the weighted terms, thus obtaining a larger number of clusters than that discovered by LogTF (because now several clusters are associated with different topics of the same category). This is also confirmed by the weight \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Weight** & \(\mathbf{K}_{LSA}\) & \(\mathbf{K}_{Clustering}\) & **GSI** & **ASI** & **Weighted** & **Execution** \\ \hline \multirow{4}{*}{TF-IDF} & 26 & 7 & 0.383 & 0.358 & 0.408 & \\ \cline{2-6}  & **41** & **10** & **0.419** & **0.339** & **0.391** & 22 m, 20 s \\ \cline{2-6}  & 67 & 10 & 0.361 & 0.297 & 0.352 & \\ \hline \multirow{4}{*}{TF-Entropy} & 29 & 11 & 0.334 & 0.350 & 0.401 & \\ \cline{2-6}  & **42** & **10** & **0.368** & **0.331** & **0.382** & 26 m, 18 s \\ \cline{2-6}  & 62 & 8 & 0.364 & 0.274 & 0.326 & \\ \hline \multirow{4}{*}{LogTF-IDF} & **19** & **5** & **0.437** & **0.431** & **0.480** & \\ \cline{2-6}  & 22 & 5 & 0.350 & 0.343 & 0.393 & 25 m, 23 s \\ \cline{2-6}  & 67 & 4 & 0.225 & 0.201 & 0.251 & \\ \hline \multirow{4}{*}{LogTF-Entropy} & **10** & **6** & **0.440** & **0.453** & **0.500** & \\ \cline{2-6}  & 24 & 5 & 0.323 & 0.318 & 0.367 & 27 m, 12 s \\ \cline{2-6}  & 67 & 7 & 0.268 & 0.218 & 0.267 & \\ \hline \multirow{4}{*}{Bool-IDF} & **8** & **5** & **0.445** & **0.444** & **0.494** & \\ \cline{2-6}  & 22 & 6 & 0.293 & 0.312 & 0.365 & 25 m, 3 3s \\ \cline{2-6}  & 65 & 6 & 0.226 & 0.233 & 0.286 & \\ \hline \multirow{4}{*}{Bool-Entropy} & **9** & **5** & **0.447** & **0.444** & **0.495** & \\ \cline{2-6}  & 23 & 5 & 0.354 & 0.348 & 0.400 & 28 m, 38 s \\ \cline{1-1} \cline{2-6}  & 65 & 4 & 0.280 & 0.234 & 0.285 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results for D1 through the joint-approach. definition. Indeed, the logarithmic function tends to decrease the very-high-frequency values. In fact, the more the frequency of the term increases, the more the function approaches the asymptote of the logarithm. This means that, from a certain frequency, the value of the local weight tends to flatten and the relevance of the most-frequent terms is reduced. With respect to the global weight, instead, we can observe that the entropy tends to find in average a large number of clusters. The TF-IDF and the TF-Entropy find a large number of topics with respect to the other solutions. The other weights instead are able to select the expected value of the category.