## 4 Methodology
To control this process, we have used a Python implementation of t-SNE (sklearn.manifold.TSNE ([[http://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html](http://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html)]([http://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html](http://scikit-learn.org/stable/modules/generated/sklearn.manifold.TSNE.html)), accessed on 8 January 2022)) to visualize the Word2 Vec model topics data in a 2D plot. The _window size_ parameter is set as the average number of words (132) contained in all the abstracts and keywords of the considered papers. With this choice, words coming from the same paper (words of abstracts and keywords) tend to be related to each other. After the creation of the model, the vocabulary contains 13187 unique words. After the training phase, the model can express a numerical distance between two vectors, which represent two words (topics). Some examples of distances expressed as cosine similarity values are shown in the following:

* care, health_care = 0.302976
* volume, distribution = 0.004110

### Evaluation of Scholars' Locations

The Word2 vec-obtained model holds a vocabulary of words. Each word is represented by a multi-dimensional vector of 600 coordinates. For each active year of an author, words that come from all preprocessed abstracts and keywords of their published papers are collected, if they belong to the model. Then, the geometric center (\(r_{i}\), for the i-th year) of the coordinates of the selected words is calculated. Figure 1 shows an example of mobility of anauthor during 3 years. For each of the 3 years, the geometric center (in red) of all the topics (words) of that year is computed (\(r_{i}\)). On the other hand, since SBERT returns directly the sentence embedding we did not have the need for averaging words and looking for the geometric center. For SBERT we merged all the documents of an author for each year in a separate document called \"year-document\" and we fine-tune SBERT to directly produce the embedding of these documents that represent the location of each author for each year in its semantic space. ### Estimation of Trajectories and Mobility

This phase aims to estimate the \"mobility\" of researchers in the semantic space created with the word embedding models (Section 3.2). The mobility volume can be estimated through the Radius of Gyration. In the present work, this metric is used to estimate semantic mobility across different research topics, measuring how the works of a researcher are distributed over different research topics. The geometric center (\(r_{gm}\)) of all geometric centers (\(r_{i}\)) of an author's active years is computed in the case of Word2 Vec (Figure 2). For SBERT the geometric center (\(r_{gm}\)) is computed among the embeddings of all the year-documents of an author during the years that are represented by (\(r_{i}\)). The Radius of Gyration corresponds to the mean squared error of the distances between each \(r_{i}\) and \(r_{gm}\), which is the geometric center of all geometric centers (in green). Figure 1: An example of mobility of an author during 3 years with Word2 Vec. For each year, the geometric center (in red) of all the topics (words) of that year is computed (\(r_{i}\)). Figure 2: Schematic representation of data used for tracing an author, including: topics, geometric centers by year and overall center. It is also interesting to investigate the possible different behaviors of researchers working in different countries and in different research areas. The extracted knowledge is described in detail in Section 5. ## 5 Results and Discussion

Once the semantic spaces where scholars move in are generated, we further analyzed them from different points of view with the aim of extracting latent knowledge from scholars' research trajectories. In particular, we aim to answer the following intriguing questions:

* Is it possible to predict a researcher's success just by observing their trajectory in terms of attitude to explore new research topics?