## 4 Popularity Prediction
### Data Statistics  
The Web of Science data (WoS) [10] is investigated during the last two decades between 1991 and 2011, since publication data consistent for all target fields is only available during this period. The data contains publication records from a wide range of academic areas, each of which consists of paper profile (e.g., title, keywords, publication year, venue, and associated subjects) and citation relationships \begin{table}
\begin{tabular}{c l} \hline \hline
**Sym.** & \multicolumn{2}{c}{**Descriptions**} \\ \hline \(F\) & set of all research fields in science \\ \(f_{\text{cited}}\) & research field of the cited paper, \(f_{\text{cited}}\in F\) (usually ommited for brevity) \\ \(f\) & research field of the citing paper, \(f\in F\) \\ \(I\) & total number of papers in the cited field \\ \(i\) & \(i\)-th paper in the cited field, \(i=1,...,I\) \\ \hline \(N_{j}^{f}\) & citation count of paper \(i\), received from the citing field \(f\) \\ \(t_{n}^{f}\) & \(n\)-th citation timestamp of paper \(i\), received from the citing field \(f\), \(n=1,...,N_{i}^{f}\) \\ \(\mathbf{D}_{i}^{f}\) & citation timestamps of paper \(i\), received from \(f\) such that \(\mathbf{D}_{i}^{f}=\{t_{n}^{f}\mid n=1,...,N_{i}^{f}\}\) \\ \(\mathbf{D}^{f}\) & citation timestamps of the cited field, received from \(f\) such that \(\mathbf{D}^{f}=\{\mathbf{D}_{i}^{f}\mid i=1,...,I\}\) \\ \(\mathbf{D}\) & all citation timestamps of the cited field such that \(\mathbf{D}=\{\mathbf{D}^{f}\mid f\in F\}\) \\ \hline \(\lambda_{i}^{f}(t)\) & citation intensity of paper \(i\) at time \(t\) for the citations received from the citing field \(f\) \\ \(\lambda_{i}(t)\) & citation intensity of paper \(i\) at time \(t\) such that \(\lambda_{i}(t)=\sum_{f\in F}\lambda_{i}^{f}(t)\) \\ \(\xi^{f}\) & affinity of the citing field \(f\) towards the cited field \\ \(c_{i}^{f}(t)\) & citation count of paper \(i\), received from the citing field \(f\) up to time \(t\) \\ \(c_{i}(t)\) & citation count of paper \(i\) in the cited field up to time \(t\) such that \(c_{i}(t)=\sum_{f\in F}c_{i}^{f}(t)\) \\ \(p_{i}^{f}(t)\) & aging effect of paper \(i\) in the citing field \(f\) after time \(t\) since its publication \\ \(\theta_{i}^{f}\) & lognormal distribution parameters \(\theta_{i}^{f}=(\mu_{i}^{f},\sigma_{i}^{f})\) such that \(p_{i}^{f}(t)=\text{Lognormal}(t;\mu_{i}^{f},\sigma_{i}^{f})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Notation. Figure 3: Graphical model of the Affinity Poisson Process. The citation timestamps \(t_{n}^{f}\) of paper \(i\) receiving from the citing field \(f\) depend on the affinity \(\xi^{f}\) of the citing field \(f\) toward the cited field, and the lognormal aging effect of paper \(i\) in the citing field \(f\) is parameterized with \(\mu_{i}^{f}\) and \(\sigma_{i}^{f}\). Latent affinity \(\xi^{f}\) has hyperparameters, \(\alpha\) and \(\beta\). Empty circles represent unknown random variables, a solid circle denotes observed data, and dark dots indicate parameters. Note that the only graphical model of the cited field is presented. (e.g., cited and citing articles). This study focuses on STEM field publications covering 108 subjects, where some disciplines such as Biology and Engineering are more fine-grained. For the less biased and macro-level observations of interdisciplinary citation flows in sciences, these 108 subjects are grouped into higher-level research areas, i.e., 37 subfields and 4 fields, by referring to the classifications of academic programs, conducted by the National Research Council (NRC) [11]. The four NRC fields are Agricultural Sciences, Biological & Health Sciences, Engineering, and Physical & Mathematical Sciences, and the detailed correspondence between the WoS and NRC classifications is presented in Tables A2-A4 in Appendix F.  
As data preprocessing steps, journals are first targeted, whose publication records are available during the entire data period (i.e., from 1991 to 2011).