## 3 Methods and Materials
### Model Architecture
#### 3.1.3 Extracting, Linking, and Mapping
Algorithm A1 (Appendix A) illustrates the processes prior to calculating the similarity when computing the number of papers for each author (lines 4-10), the total number of author citations (lines 11-13), and the range of the publication years (lines 14-19). Furthermore, as a consequence of \(\mathrm{PNum}\big{(}x_{j}\big{)}\), \(\mathrm{Cite}\big{(}x_{j}\big{)}\), and \(\mathrm{Years}(x)\), they are converted to vectors. Before applying the cosine similarity equation to \(\mathrm{PCYnum}\), the vectors were normalized to unit length in order to be more suitable and accurate for similarity calculation by rescaling and subtracting the minimum value for each number in \(\mathrm{PCYnum}\) and then dividing the result by the range (the difference between the maximum and the minimum value) [37]. \[X_{\mathrm{norm}}=\frac{x\;-\;x_{\mathrm{min}}}{x_{\mathrm{max}}-\;x_{\mathrm{ min}}} \tag{7}\]  
Additionally, all of these explanations and calculations lead to the proposed enhanced authors' similarity measure, which can be written as follows:  
\[\mathrm{Author}_{\mathrm{sim}}\left(\overset{\rightarrow}{\mathrm{x}}, \overset{\rightarrow}{\mathrm{y}}\right)=\;\alpha\times\;\mathrm{Topic}_{ \mathrm{sim}}\left(\overset{\rightarrow}{\mathrm{x}},\overset{\rightarrow}{ \mathrm{y}}\right)+(1-\alpha)\times\left(\mathrm{Word}_{\mathrm{sim}}\left( \overset{\rightarrow}{\mathrm{x}},\overset{\rightarrow}{\mathrm{y}}\right)+ \mathrm{PCYnum}_{\mathrm{sim}}\left(\overset{\rightarrow}{\mathrm{x}}, \overset{\rightarrow}{\mathrm{y}}\right)\right) \tag{8}\]  
wherein \(\alpha\) is the weight parameter; \(\mathrm{Word}_{\mathrm{sim}}\) represents the keywords similarity; \(\mathrm{PCYnum}_{\mathrm{sim}}\) represents the paper, citation, and year similarities; and \(\mathrm{Topic}_{\mathrm{sim}}\) represents the topics similarity. Meanwhile, Algorithm A2 (Appendix A) illustrates the processes that were used to determine the similarity between authors using three factors: the author-selected keywords (lines 4-5), the authors' publication statistics (lines 6-9), and publication topic distributions (lines 10-14). Additionally, combining the computed similarities gives greater weight to the topics distribution due to the significant impact they have on the similarity (lines 15-18). Extracting Expertise  
In this phase, the expertise of an author in a specific topic is extracted by relying on the multi-factor indicators for a topic of interest, such as the number of papers written about that topic, the number of citations they have attracted, and the total topic weight for the authors' papers; hence, a researcher's publication list presents all of their contributions to academia. In addition, exploring the data on the list of a single researcher will give an accurate and realistic evaluation of their expertise. It reflects the level of knowledge they have on the topics they have worked on and may also indicate their main research area and their field of expertise. Consequently, the papers' keywords convey an expert's research areas perfectly. In order to identify the expert author for a topic, first, the extracted topicsmust be converted into the vector format (1,0) for each publication in order to recognize the author with the highest number of publications relating to that topic. For each publication, the most common topic should be taken as its main topic. Instead of the weighted number, it converts to the vector format by assigning the main area of interest with 1 and 0 for other topics, while the citation number can be added to the corresponding topic. Additionally, for each topic, the author with the highest weight in that topic should be identified based on their papers and keywords, which reflect the depth of their publications on that subject area.