## 2 Method Development
### Task Definition  
In this study, all the features were calculated for the papers included in the largest connected component of the cited network and were treated as explanatory variables. The explained variable was whether the paper was an emerging paper. Emerging papers were defined as papers that were ranked in the top 5% of the dataset each year and whose citations increased for three years after publication. In fact, in the case of emerging papers included in the top 5% of the increase in the number of citations, a positive example was given a flag, and 50% or less was treated as a negative example, or as an explained variable. In other words, the emergence prediction problem in this study was considered to be a two-class classification problem, involving the identification of whether a paper satisfied the requirements for emergence within three years of publication. A logistic regression, which is a linear classifier, was adopted as the classifier, and LIBLINEAR was used for implementation. Among the data included in the negative example, the same amount of data as in the positive example were randomly extracted eight times, and eight kinds of datasets were constructed for each year. In addition, by performing a five-fold cross validation on each model, overlearning was avoided. The prediction model used learning data regarding whether a paper had become an emerging paper three years after publication and was actually applied to a group of papers published four years after the publication of the learning data as a prediction object. That is, when \(t_{1}\) (=\(t_{0}\) + 4) was set as the publication year of the prediction target paper, the learning data of \(t_{0}\) + 3, which was the learning window, were applied to the paper from \(t_{1}\) (=\(t_{0}\) + 4). The model could also be evaluated three years after the publication of the model (\(t_{1}\) + 3). This period was defined as the evaluation window. A schematic of the relationship between the learning and evaluation windows is provided in Figure 2. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Class of Feature** & **Name of Feature** & **Description** \\ \hline Network & & \multicolumn{2}{c}{Dataset in question and feature of network in the year in question.} \\ \cline{3-3}  & NW\_NODES & Number of papers in a network. \\ \cline{2-3}  & NW\_EDGES & Number of citation links in a network. \\ \cline{2-3}  & NW\_MAXQ & Maximum of \(Q\)-values of clusters in a network. \\ \hline Cluster & & Feature of the cluster to which a paper belongs. \\ \cline{2-3}  & CL\_QMAX & Maximum of \(Q\)-values of clusters to which a paper belongs. \\ \cline{2-3}  & CL\_NODES & Number of nodes in the cluster to which a paper belongs. \\ \cline{2-3}  & CL\_RANK & Rank of the cluster to which a paper belongs. \\ \hline Centrality & & Network centrality of a paper. \\ \cline{2-3}  & CNT\_DEGRE & Degree centrality. \\ \cline{2-3}  & CNT\_BETWE & Betweenness centrality. \\ \cline{2-3}  & CNT\_CLOSE & Closeness centrality. \\ \cline{2-3}  & CNT\_EIGEN & Eigenvector centrality. \\ \cline{2-3}  & CNT\_NETWO & Network constraint. \\ \cline{2-3}  & CNT\_CLUST & Clustering coefficient. \\ \cline{2-3}  & CNT\_PAGER & Page rank. \\ \cline{2-3}  & CNT\_HUBSC & Hub score. \\ \cline{2-3}  & CNT\_AUTHOR & Authority score. \\ \hline Property of reference & & The sum of the features of paper sets that a paper cites. \\ \cline{2-3}  & CITING\_MAX-[_feature_] & Maximum of features in questions in cited paper sets that a paper cites. \\ \cline{2-3}  & CITING\_MIN-[_feature_] & Minimum of features in questions in cited paper sets that a paper cites. \\ \cline{2-3}  & CITING\_AVC-[_feature_] & Average of features in questions in cited paper sets that a paper cites. \\ \cline{2-3}  & CITING\_SUM-[_feature_] & Sum of features in questions in cited paper sets that a paper cites. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Features used in the emergence prediction model.