# Citation Oriented AuthorRank for Scientific Publication Ranking
## 3 Methodology
### AuthorRank by Author Ranking  
We introduced the concept of AuthorRank and its underlying assumptions in the previous section. Generally speaking, author ranking may influence publication ranking. Thus, a famous or important author on a specific topic will have his or her publications ranked higher, which will thereby have a greater chance to be recommended for the topic. To validate this hypothesis, in this section we propose to use AuthorRank with a topical author ranking score.  
Since AuthorRank is a query-independent criterion similar to PageRank, it should be calculated as offline processing, where content authority is measured by the authority accumulated from links, regardless of the query. The PRP algorithm based on the author-ranking method has been proposed before. It is effective for allowing an author to have a different rank for each topic. So, in this section, we propose a method for paper ranking (AuthorRank) via author ranking, which is also an offline and topic-based method.  
The following formula defines the relationship between paper and author.  
\[p_{i}=\{a_{1},a_{2},a_{3},\cdots,\ a_{s}\} \tag{8}\]  
where \(p_{i}\) is the paper, always created by at least one author \(a_{i}\). How the author affects the publication ranking score, \(I_{key_{m}}(p_{i}|\text{AR})\), can be calculated in at least four different ways: First Author, Last Author, Max Author, and Average Author.  
First Author: The ranking score of a publication (AuthorRank) depends only on the first author's ranking. In other words, the publication's topical importance, \(I_{key_{m}}(p_{i})\), is based on the score of only the first author (\(\pi_{key_{m}}(a_{1})\)).  
\[I_{key_{m}}(p_{i}|\text{AR})=\pi_{key_{m}}(a_{1}) \tag{9}\]  
Last Author: The AuthorRank score of a publication, \(p_{i}\), depends only on the last author's ranking, where \(a_{s}\) is the last author if \(p_{i}\) is co-authored by multiple (s) authors. Otherwise, as is decided by the unique author.  
\[I_{key_{m}}(p_{i}|\text{AR})=\pi_{key_{m}}(a_{s}) \tag{10}\]  
Max Author: The AuthorRank score of a publication is decided by the most popular author's score among all the authors.  
\[I_{key_{m}}(p_{i}|\text{AR})=\ \max\{\pi_{key_{m}}(a_{1}),\ \pi_{key_{m}}(a_{2}),\ \dots \dots,\pi_{key_{m}}(a_{s})\} \tag{11}\]  
Average Author: The AuthorRank score of a publication is determined by the average scores of all the publication's authors.  
\[I_{key_{m}}(p_{i}|\text{AR})=\frac{\sum_{j=1}^{n}\pi_{key_{m}}(a_{j})}{|s|} \tag{12}\]  
Example: To understand these methods better, we provide a simple example. Assume that there are two papers: \(paper_{1}\) and \(paper_{2}\), where \(paper_{1}\) is authored by \(author_{1}\) and \(author_{2}\), as \(p_{1}=\{a_{1},a_{2}\}\); and where \(paper_{2}\) is authored by \(author_{1}\), \(author_{3}\), and \(author_{4}\), as \(p_{2}=\{a_{1},a_{3},a_{4}\}\). The importance score of these four authors is shown in Table 1.  
From the four methods mentioned above, we obtain the two papers' ranking scores as shown in Table 2.  
In this example, we found that the papers' author ranking scores are different than their AuthorRank. We verify the effectiveness of publication ranking by AuthorRank in the following.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Author Name** & \(\mathbf{a_{1}}\) & \(\mathbf{a_{2}}\) & \(\mathbf{a_{3}}\) & \(\mathbf{a_{4}}\) \\ \hline score & 0.2 & 0.5 & 0.12 & 0.18 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Exemplar author ranking score.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **First Author** & **Last Author** & **Max Author** & **Average Author** \\ \hline \(paper_{1}\) & \(a_{1}=0.2\) & \(a_{2}=0.5\) & \(a_{2}=0.5\) & \((a_{1}+a_{2})/2=0.35\) \\ \(paper_{2}\) & \(a_{1}=0.2\) & \(a_{4}=0.18\) & \(a_{1}=0.2\) & \((a_{1}+a_{3}+a_{4})/3=0.167\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: AuthorRank for paper ranking.