## 3 LDA Application  
Before going into detail about the results obtained from the literature review, it is important to give a brief introduction to understand the LDA and its application. Following what is also shown by [17], this research applied the five steps for the application of LDA. The first four steps implement the essential text pre-processing stage: tokenization; sparse terms removal and stop-words removal; stemming and lemmatization; and N-grams tagging. At the end of these text pre-processing stages, there is a final stage, called text features extraction. Specifically, it is to underline that LDA has been applied to a new text generated by the merge of title, abstract and keywords. The LDA was proposed by [16], and is currently one of the most widely used techniques for document analysis and topic assignment. Given an analyzed text, \(D\), which is identified with the term corpus, with \(M\) documents, in which a specific document \(d\) has \(N_{d}\) words, for each document in \(D\) the LDA algorithm provides the following generative process [16]:  
1. Select a multinomial distribution \(\phi_{t}\) for topic \(t\) (\(t\in\){1,..., \(T\)}) from a Dirichlet distribution with parameter \(\beta\);
2. Select a multinomial distribution \(\theta_{d}\) for document \(d\) (\(d\in\){1,..., \(M\)}) from a Dirichlet distribution with parameter \(\alpha\);
3. For a word \(w_{n}\) (\(n\in\) {1,..., \(N_{d}\)}) in document \(d\), \(\circ\) Select a topic \(z_{n}\) from \(\theta_{d}\);  
Figure 5: Country analysis. \(\circ\) Select a word \(w_{n}\) from \(\varphi_{zn}\). The assumption behind the LDA technique is that a document is written by authors as a set of different topics and each document has its peculiar distribution of topics [17]. Two parameters characterize the LDA:  
* \(\alpha\), that represents, considering each of the topics identified in the document, the probability that the document under consideration belongs to each of the topics;
* \(\beta\), that represents, considering each of the tokens, what is the probability that the topic under consideration contains each of the tokens. In the process presented above, the only variables observed are the words in the documents. \(\varphi\) and \(\theta\) are latent variables and \(\alpha\) and \(\beta\) are hyperparameters [22]. The next step is to calculate and maximize the probability of the observed data \(D\), which following what has been proposed in the previous contribution [22], follows (1):  
\[p(D|\alpha,\beta)=\prod_{d=1}^{M}\int p(\theta_{d}|\alpha)(\sum_{n=1}^{N_{d}} p(z_{n}|\theta_{d})p(w_{d_{n}}\left|z_{d_{n},\varphi}\right)P(\varphi|\beta)) \mathrm{d}\theta_{d}d_{\varphi} \tag{1}\]  
An issue to be considered, if attention is drawn to (1), is that of exact inference in LDA, which turns out to be intractable due to the coupling between \(\theta\) and \(\varphi\)[22]. Some approximate algorithms are used in this respect, such as variational inference [16] or Markov chain Monte Carlo [23]. The optimum number of topics is chosen using a perplexity score, a statistical measure of how well a statistical model describes a dataset, with lower perplexity denoting a better probabilistic model [22], and a coherence score that represents the semantic similarity between high scoring words in the topic value [24]. To define perplexity, it evaluates how well the dataset is described by the statistical model. Perplexity is defined as (2) [16]:  
\[\mathrm{Perplexity}=\exp\left\{-\frac{\sum_{d=1}^{M}log\ p(w_{d})}{\sum_{d=1} ^{M}N_{d}}\right\} \tag{2}\]  
For the coherence score, higher values are sought, considering that the value moves between 0 and 1. In the specific case of this research, the analysis works on text strings of abstract, title, and keywords.