## 6 Experimental Results
### Comparison with Respect to the State-of-the-Art Techniques  
Here follows a comparison between ESCAPE and the main state-of-the-art techniques. **Joint-Approach. ** In order to assess how effectively ESCAPE is able to select the proper number of clusters, we compared the results obtained with those proposed by a state-of-the-art methodology designed for the same purpose. This method is known as the _elbow graph_ or the _knee_ approach [62]. In the following, we will refer to this method as \(k_{SSE}\). This method involves evaluating the evolution of the SSE (sum of squared errors) value as the value \(k_{cls}\) increases. The \(k_{cls}\) value identified as optimal is the one immediately preceding a negligible change in the SSE value (there is no great performance advantage in \begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset** & **Weight** & \(K_{CI}\) & **Perplexity** \\ \hline \multirow{4}{*}{D8} & BooL-IDF & 5 & 7.273681 \\ \cline{2-3}  & & 3 & 7.352020098 \\ \cline{2-3}  & LogTF-IDF & 5 & 7.263175195 \\ \cline{2-3}  & & **8** & **7.190609656** \\ \cline{2-3}  & TF-IDF & 5 & 7.270052194 \\ \hline \multirow{4}{*}{D9} & BooL-IDF & 2 & 7.588552184 \\ \cline{2-3}  & LogTF-IDF & 2 & 7.581219438 \\ \cline{1-1} \cline{2-3}  & TF-IDF & 2 & 7.583352794 \\ \hline \hline \end{tabular}
\end{table} 
Table 14: Experimental results for dataset D8 and D9 for the probabilistic approach. Figure 5: Boolean-IDF and LogTF-IDF weighting schemas’ results for the Luggage dataset. (**a**) Dataset D9. t-SNE representation. B-IDF weighting schema K = 3. (**b**) Dataset D9. t-SNE representation. LogTF-IDF weighting schema K = 4.  
adding another centroid). In the following, we will refer to the dataset \(D_{1}\) as representative, but similar trends have also occurred in other datasets. In order to compare the methods fairly, both ESCAPE and the \(k_{SSE}\) method receive as input the reduced matrix \(X_{K-LS1}\). This matrix is obtained by analyzing the trend of the singular values extracted by the decomposition of the original document-term matrix. In our proposed methodology, ESCAPE selects the possible good values at the points 10, 24, and 67. These three points are able to characterize the singular-value plot, analyzing different values which subsequently include a large number of dimensions in the reduction phase. However, the \(k_{SSE}\) method usually selects a lower number of optimal clusters than the one selected in ESCAPE. For example, in \(D_{1}\), the \(k_{SSE}\) method selects 5 clusters by exploiting TF-IDF, and 3 with LogTF-Entropy, against the 10 clusters selected by ESCAPE using TF-IDF and 6 clusters with LogTF-Entropy. To evaluate the best configuration between those identified by the two approaches, we evaluated the silhouette index for each clustered document in both methods. As shown in Figure 7, more than 83% of the documents obtain a higher index in the approach proposed by us than in that based on the analysis of the SSE curve. Thus, this result tells us that ESCAPE is able to discover a cluster set better than the knee approach. **Probabilistic Approach. ** Here, we offer a comparison between the results obtained by ESCAPE and those obtained with known state-of-the-art techniques, such as _RPC_ and _En-LDA_. RPC [50] is an heuristic algorithm that, in order to choose the proper number of topics, evaluates the average perplexity variation of the LDA models. Instead, EnLDA [63] chooses as the optimal \(K\) value the one that best reduces the total amount of entropy of the topic modeling. These two approaches will be discussed in more detail below. Table 15 shows a comparison between the results obtained by ESCAPE and those obtained by the RPC and en-LDA methods for the various weights considered. We can see that, using TF-IDF, these two approaches produce 3 and 19 as \(K\) values (with RPC  
Figure 6: The best partitioning t-sne maps for all the weighting strategies for the Luggage dataset are displayed above. **(a)** Dataset D8. t-SNE representation. Bool-IDF weighting schema K = 5. **(b)** Dataset D8.