# Perceiving Conflict of Interest Experts Recommendation System Based on a Machine Learning Approach
## 3 Proposed Methodology
### Expertise Score Computation and Reviewer Ranking
#### 3.4.2 Candidate Score Computation (C-Score)  
In a given domain, the subject relevance of the reviewer candidate is calculated using the TF-IDF matrix of the candidate keyword vector highly related to the manuscript's subject keyword. Then, the evaluated reviewer's expertise (through the review of their thesis, patent, and publishing history) is counted as the total score that allows ranking, using time weights reflecting the difference between the published and current times. The expertise may vary depending on published research achievements related to the domain because of the difference in the frequency of publication of papers and patents for each candidate. Further, the candidate's expertise may vary depending on the elapsed time since conducting the study. In other words, the longer the elapsed publication time, the longer the period of inactivity in the research field, which reduces the expertise in the domain. Therefore, there is a need to lower the weight of expertise or to penalize candidates for changes in interest. We introduce a Riemann zeta function as a weight to reflect the difference between the study and current points in time for each related keyword that undergoes similarity evaluation within the candidate group  
\[\zeta(s)\ =\ \sum_{n=1}^{\infty}\frac{1}{n^{s}} \tag{7}\]  
In this study, several integer representations are considered to evaluate the Riemann zeta function for points (s) > 1 as the time interval between the publication and current time point of the study deliverables (criteria for these time intervals vary depending on the situation or intention). The time weight \(\zeta(s)\) is calculated based on information from the current time point (y) to the publication time point (y\({}_{i}\)). The weights vary each year because the candidate's recent research direction is assumed to be strong information that can reflect the candidate's interest in the domain. Let K\({}_{i}\) represent a research career for a specific keyword at a specific time. y and y\({}_{i}\) represent the time of recommendation and the time of research, respectively, and C represents the number of projects performed for related research in the specific year y\({}_{i}\). For zeta function \(\zeta(s)\), s > 1, a new penalty score interval using the converging geometric series property can be defined as follows: when the difference \((y-y_{i})\) between the current and publication time points is zero, s \(\ =\ 1.1\); s increases by 0.1 with an increase in the time interval \((y-y_{i})\). Thus, \(\zeta(s)\) divides the difference \((y-y_{i})\) between the current and publication time points by 10 and converts the value added by 1.1 into a penalty score. Further, the converted figure is multiplied by the quantitative frequency of publications, which is a lower weight than the latest aspect because the number of related publications is an important indicator of a career even if it is not a relatively recent study. If the time weights are not applied (multiplied by the time interval \((y-y_{i})\) based on the frequency of publications (C)), the candidates with several past publications may be assigned a high ranking even if they have no recent publications. Thus, the recency of the expertise would be ignored, and only the frequency of publications would be reflected. However, the timing and frequency will matter, as demonstrated by the following case, if we compare the professional level (K\({}_{i}\)) using  
\[K_{i}\ =\ \zeta\bigg{(}1.1+\frac{y-y_{i}}{10}\bigg{)}\times C \tag{8}\]Candidate A has three publications in 2021, three in 2018, and two in 2014, whereas candidate B has three in 2021, and four in 2019. In this case, candidate A has C = 8, Ki = 42.7 and candidate B represents C = 7, Ki = 43.9. Therefore, candidate B has fewer publications than candidate A but a relatively recent publication.