## 6 Experimental Results
### Comparison Between Joint-Approach and LDA
#### 6.7.2 Boolean Weight  
While analyzing the ARI between the two approaches for dataset D1, the highest value is computed for the Boolean weighting strategy. This highlights a great similarity between the two partitions. Moreover, the number of documents in each cluster is comparable. In the joint-approach, we have integrated two weighting strategies with respect to the local weight Boolean, which are Boolean-IDF and Boolean-Entropy. However, since the two partitions were really similar, we only consider the Boolean-IDF for comparison with respect to the Boolean-TF used for the LDA modeling.  
We have reported, in Figures 16 and 17, the word clouds of the two approaches, respectively. Specifically, Figure 16 is related to the five topics found using the algebraic approach, while Figure 17 is related to the probabilistic model. In detail, analyzing Figure 16, we can observe that, with respect to the TF-IDF local weight, the analysis is less precise. We can extract the main topic from each word cloud; however, the partitions present more common words used for more topics.  
For the probabilistic model, we can observe that when we consider the clustering obtained with \(K\) equal to five and its topic descriptions, when looking at the word clouds in Figure 17, many terms (such as _include_ or _first_) appear to be in all the groups of the most-significant words for each cluster. This happens because the Boolean-TF weighting scheme gave more relevance to words which appeared most in the whole corpus without penalizing them. However, it could mean that these words do not belong to any specific topic, or they just do not bring any additional information useful for the topic modeling description phase. To this end, we have included a post-processing phase for this particular weighting scheme.  
Figure 15: D1 t-SNE representation, TF-IDF weighting scheme, \(K=10\), joint-approach (**top**) and probabilistic approach (**bottom**).  
In order to not consider these terms and bring up the words characterising the topics identified by the LDA modeling process, we have decided to apply a further post-processing step to evaluate the results. Once the models have been created and the \(K\) values selected, we took into consideration more words to describe the topics, and then we removed all the words appearing at least in four topic representations from them.  
The results obtained by this post-processing operation are reported in Table 18. In this way, the most-common words that do not carry any specific information have been excluded from the descriptions, and the terms relevant for the meaning of the categories are visible to the analysts. As a matter of fact, the assigned labels to the clusters generated by the LDA model cover the following main topics: _sport_, _mathematics_, _music_, _cooking_, and _literature_. Using this post-processing approach, we are able to describe the macro-categories of this dataset perfectly.  
To better show the impact of removing words that appear at least in four topics, we reported the graph representation before and after this improvement. Figure 18 shows the graph representation analyzing the top-20 words for each topic. Specifically, on the left, the case without the post-processing is reported, while on the right, we report the case with the proposed post-processing. The first graph is more connected with respect to the second one; moreover, from the analysis of the graph after the post-processing, we can see the improvement of this phase, since the new graph is not connected at all. This means that the words that describe each topic are well-separated from cluster to cluster.  
Figure 16: D1 word cloud representation, Boolean-IDF weighting scheme, joint-approach.  
Figure 17: D1 word cloud representation, Boolean-TF weighting scheme, \(K=5\), probabilistic modeling.