## 4 Popularity Prediction
### Prediction of Interdisciplinary Citation Volumes  
Popularity prediction tests are conducted with real data and the prediction results are compared between our proposed model (APP) and the baselines (APP without a prior and RPP), as done in [9]. Individual journals' citation volumes are predicted by training the proposed and baseline models with at least 10 year citation histories. The first two plots in Figure 4 illustrate the prediction errors in MAPE (a) as increasing the length of training years (from 10 to 20 years) and (b) as varying the test years (from 1 to 10 years) after training with 10 year citation histories. In both cases, our proposed model outperforms the baseline models, improved by 15% over APP without a prior and by 27% over RPP on average when comparing the prediction performances with the least citation histories (10 years). Figure 4c compares the distributions of citation sizes between real data and prediction results from our proposed model. As shown in this figure, the predicted citation sizes are distributed quite similarly to ones from real data. That is, the APP well explains popularity dynamics of individual journals across fields of sciences, not limited to specific ones.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**NRC Field** & **\#Subfield** & **\#Subject** & **\#Journal** & **\#Paper** & **\#Citation** \\ \hline Agricultural Sci & 6 & 11 & 104 & 128,685 & 518,434 \\ Bio \& Health Sci & 12 & 29 & 362 & 832,805 & 4,201,683 \\ Engineering & 11 & 29 & 145 & 228,397 & 943,834 \\ Phys \& Math Sci & 8 & 39 & 267 & 537,658 & 1,914,953 \\ \hline Total & 37 & 108 & 878 & 1,727,545 & 7,578,904 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Data description. STEM field publications are selected during the first decade of a data period from 1991 to 2011. Detailed classifications of 108 subjects into NRC (sub)fields are presented in Tables A2–A4 in Appendix F.  
Figure 5 shows example prediction results from our model. In the figure, three journals are from different NRC subfields, but they all are paid interdisciplinary attention from different subfields. As the figure shows, the APP does not only predict an individual journal's total number of citations but also separately predict its citations received from each citing subfield.  
Figure 4: Experimental results with real data. Comparisons of prediction errors in MAPE between the Affinity Poisson Process (APP) and two baseline models (APP without a prior and RPP (Reinforcement Poisson Process)) (**a**) by increasing the length of training years and (**b**) by varying the test years based on 10 year citation histories. (**c**) The distributions of real (black) and predicted (red) number of citations of individual journals with the APP.  
Figure 5: Example results from predicting interdisciplinary citation volumes of individual journals with the APP. In each plot, predicted citation volumes are separated by citing NRC subfields. Each cited journal’s NRC subfield is respectively (**a**) Biochem/Biophysics & Structural Biology, (**b**) Cell & Developmental Biology, and (**c**) Immunology & Infectious Disease. Prediction tests are conducted for next 10 years (2002-2011) after training the model using the first 10 year citation histories (1992–2001) since each journal’s publication year (1992).  
Based on the parameter estimation, in the next section citation dynamics are analyzed in terms of affinity network, affinity density, and novelty decay across subfields of sciences.