## 4 Methodology  
In this section, we present the methodological steps have been followed to collect and transform data and to generate the semantic space to perform the mobility analysis. * **Data Collection**: We collect all the abstracts and key-words from the papers published by the authors in the considered time interval and the relevant features about each scholar. This step aims to collect the raw dataset that is likely to contain relevant patterns;
* **Data Preprocessing**: The preprocessing phase increases the quality of the textual data and allows one to reach better results in the following steps, removing noise and incomplete data; In particular NLP techniques are applied to transform data in the necessary form required by the embedding algorithms (Tokenization, Stemming, Stop words removal). * **Generation of the Semantic Space**: in this step, the Word2 Vec algorithm and independently SBERT are used to create the respective semantic spaces;
* **Evaluation of Scholars' Locations**: for each author, the scientific production is used to compute the \"average topic\" in the semantic space for each year. Coordinates for each year work as locations in the time in the semantic space
* **Estimation of trajectories and mobility**: a dynamic analysis is conducted, measuring the Radius of Gyration as an index of the mobility volume of each researcher across scientific topics. We estimated the RoG using both the Word2 Vec space and the SBERT one. At an abstract level, these phases are organized according to Algorithm 1. Each phase is described in detail in one of the following subsections. ```
1:functionCalculatePath(\(\mathcal{A},\mathcal{W},\mathcal{T}\))
2:\(\mathcal{P}\leftarrow\varnothing\)\(\triangleright\) Map: time \(\rightarrow\) coordinates
3:for all\(time\in\mathcal{T}\)do
4:\(\mathcal{A}^{\prime}\leftarrow\{a\mid a\in\mathcal{A}\wedge a_{time}=time\}\)
5:\(\mathcal{Q}\leftarrow\varnothing\)
6:for all\(word\in Concatenate(\mathcal{A}^{\prime})\)do
7:\(coord\leftarrow\omega_{1}\mid w\in\mathcal{W}\wedge w_{0}=word\)\(\triangleright\) Get coordinates from embedding
8:\(\mathcal{Q}\leftarrow\mathcal{Q}\cup\{coord\}\)
9:endfor
10:\(\mathcal{P}\leftarrow\mathcal{P}\cup\{(time,Average(\mathcal{Q}))\}\)
11:endfor
12:return\(\mathcal{P}\)
13:endfunction
14:functionAnalyzeScholarsMobility(\(\mathcal{S},\mathcal{T}\))
15:\(\mathcal{C}\leftarrow\varnothing\)\(\triangleright\) Whole corpus
16:for all\(scholar\in\mathcal{S}\)do
17:\(\mathcal{C}\leftarrow\mathcal{C}\cup CollectArticles(scholar,\mathcal{T})\)
18:endfor
19:\(\mathcal{W}\leftarrow\textit{TrainWordEmbedding}(\mathcal{C})\)\(\triangleright\) Map: lemma \(\rightarrow\) coordinates
20:
21:\(\mathcal{M}\leftarrow\varnothing\)\(\triangleright\) Map: scholar \(\rightarrow\) mobility
22:\(\mathcal{H}\leftarrow\varnothing\)\(\triangleright\) Map: scholar \(\rightarrow\) hIndex
23:\(\mathcal{L}\leftarrow\varnothing\)\(\triangleright\) All scholars' pathswhere:

* \(\mathcal{A}\) is a scholar's set of articles,\(\mathcal{T}\) is a set of timepoints (samples) and \(\mathcal{S}\) is a set of scholars;
* \(\mathcal{W}\) is the semantic model obtained with the word embedding algorithm;
* \(\mathcal{C}\) is the whole corpus of texts (used both for training the word embedding model and for data mining);
* \(\mathcal{P}\) is a path, which associates each timepoint in \(\mathcal{T}\) with a point in the embedding space;
* \(\mathcal{Q}\) is a set of points in the embedding space, representing the words collected for a given timepoint;
* \(a_{time}\) is the publication date of the article \(a\);
* \(a_{authors}\) is the set of authors of the article \(a\). ### Data Collection

To investigate the correlation between the mobility in the topic space and the success in scientific research, 2998 authors were selected from the 3500 \"Highly Cited Researchers\" list provided by Clarivate Analytics ([[https://clarivate.com/](https://clarivate.com/)]([https://clarivate.com/](https://clarivate.com/)), accessed on 8 January 2022).