## 6 Experimental Results
### Comparison Between Joint-Approach and LDA
#### 6.7.1 TF-IDF Weight  
Here, we have analyzed the impact of the TF-IDF weighting function on both the methodologies integrated in ESCAPE. To this end, we have reported the word cloud comparison for the weighting scheme TF-IDF for both the methodologies. Specifically, in Figure 11, the 10 word clouds related to the joint-approach are reported, while in Figure 12, the 10 ones related to the LDA modeling are reported. By analyzing the most-likely words for each topic, we can extract the following considerations. In both the partitions found, we have 10 clusters; however, the partitions should not be the same, since the value of the ARI index is not 1. Moreover, we recall that the five a priori known categories are: _cooking_, _literature_, _mathematics_, _music_, and _sport_. We expect to find these themes in the 10 partitions. Firstly, we reported a summary of the found topic in Table 17. Although the partitions are equivalent in number (10 topics), the meaning of the topics found are different. In fact, the five macro-categories are correctly identified by both approaches, but the algebraic method finds subdivisions for the mathematics and sport categories, while the probabilistic method finds them for the literature and sports categories. Both the results are satisfactory. We have also included the correlation analysis of the discovered partitions. For the joint-approach, we have reported the correlation matrix in terms of hot-cold topics. In this way, the colors help the analyst to read the possible correlation between topics. We have used red to highlight correlations between partitions (see Figure 13). Meanwhile, in the probabilistic approach, we have reported the graph representation, which is able to help the end-user to analyze the possible intersection between words in the different topics (see \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Weighting Scheme**} \\ \hline
**Dataset** & **TF-IDF** & **LogTF-IDF** & **TF-Entropy** & **LogTF-Entropy** & **Boolean** \\ \hline D1 & 0.554 & 0.321 & 0.320 & 0.100 & 0.790 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Adjusted Rand index for Dataset D1. Figure 12: D1, word cloud representation, TF-IDF weighting scheme for LDA modeling. Figure 13: D1 Hot-topic correlation matrix representation, TF-IDF weighting scheme, \(K\) = 10, joint-approach. From Figure 13, we can notice a high correlation between clusters 4 and 5, which, by analyzing Table 17, (Topic--Joint-Approach column) are both related to sports. Moreover, there is another correlation between clusters 3 and 6, which, looking always at Table 17 or also the previously presented word clouds, are both related to the maths topic. Specifically, cluster 3 is related to several maths topics, while cluster 6 is inherent mainly to graph theory. Instead, Figure 14 reports the graph representation for the probabilistic LDA modeling. The most-relevant words for each topic, (i.e., the words which are most likely to belong to a particular topic) are well-separated, as can be deduced from the graph analysis. Considering both the top-20 (see Figure 14a) and the top-40 (see Figure 14b) words, the graph is still very disconnected, indicating that the analyzed partitions are well-separated. Another way to compare the found partitions with respect to the two approaches is the analysis of the t-SNE representations, which give the analyst the possibility to plot the high-dimensional data under analysis into a lower space (i.e., 2D in our framework). This representation is reported in Figure 15. We recall that the T-distributed sstochastic neighbor embedding (t-SNE) is a machine learning algorithm for visualization, which is based on a non-linear dimensionality-reduction technique well-suited for embedding high-dimensional data for visualization in a low-dimensional space.