## 5 Empirical Studies
### Results and Discussion
The more densely packed a cluster of dots is, the more elements that are close together and were changed together in the past. This can be an indication of some sort of relationship or pattern within the data. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Year** & **Metrics** & **A** & **B** & **C** & **D** \\ \hline
2003 & HR@10 & 52.77 \(\pm\) 0.0 & 55.55 \(\pm\) 0.0 & 59.72 \(\pm\) 1.07 & 51.85 \(\pm\) 5.35 \\
2003 & NDCG@10 & 0.244 \(\pm\) 2.09 & 0.29 \(\pm\) 0.0 & 0.32 \(\pm\) 0.0 & 0.25 \(\pm\) 4.18 \\  & HR@10 & 39.27 \(\pm\) 0.41 & 36.12 \(\pm\) 0.22 & 38.09 \(\pm\) 0.13 & 36.96 \(\pm\) 0.32 \\
2004 & NDCG@10 & 0.23 \(\pm\) 0.002 & 0.18 \(\pm\) 6.7 \(\times\) 10\({}^{-4}\) & 0.20 \(\pm\) 3.5 \(\times\) 10\({}^{-4}\) & 0.18 \(\pm\) 0.001 \\  & HR@10 & 41.59 \(\pm\) 0.67 & 41.34 \(\pm\) 0.19 & 35.61 \(\pm\) 0.069 & 35.48 \(\pm\) 0.74 \\
2005 & NDCG@10 & 0.26 \(\pm\) 0.005 & 0.24 \(\pm\) 0.001 & 0.20 \(\pm\) 2.1 \(\times\) 10\({}^{-4}\) & 0.21 \(\pm\) 0.003 \\  & HR@10 & 34.85 \(\pm\)1.32 & 34.26 \(\pm\) 0.74 & 35.56\(\pm\) 1.0 & 36.68 \(\pm\) 0.46 \\
2006 & NDCG@10 & 0.20 \(\pm\) 0.006 & 0.19 \(\pm\) 0.005 & 0.211 \(\pm\) 0.003 & 0.21 \(\pm\) 0.004 \\  & HR@10 & 35.89 \(\pm\) 0.76 & 35.17 \(\pm\) 0.79 & 38.86 \(\pm\) 0.71 & 39.09 \(\pm\) 0.42 \\
2007 & NDCG@10 & 0.19 \(\pm\) 0.002 & 0.20 \(\pm\) 0.004 & 0.22 \(\pm\) 0.004 & 0.22 \(\pm\) 0.004 \\  & HR@10 & 40.03 \(\pm\) 0.99 & 39.85 \(\pm\) 0.45 & 39.35 \(\pm\) 0.65 & 38.10 \(\pm\) 0.22 \\
2008 & NDCG@10 & 0.24 \(\pm\) 0.004 & 0.23 \(\pm\) 0.004 & 0.23 \(\pm\) 0.0058 & 0.31 \(\pm\) 0.003 \\  & HR@10 & 37.85 \(\pm\) 0.94 & 36.81 \(\pm\) 0.53 & 37.56 \(\pm\) 0.70 & 37.01 \(\pm\) 0.62 \\
2009 & NDCG@10 & 0.22 \(\pm\) 0.003 & 0.22 \(\pm\)0.004 & 0.22 \(\pm\) 0.004 & 0.21 \(\pm\) 0.003 \\  & HR@10 & 36.40 \(\pm\) 1.27 & 35.81 \(\pm\) 0.82 & 37.18 \(\pm\) 0.21 & 37.13 \(\pm\) 0.57 \\
2010 & NDCG@10 & 0.20 \(\pm\) 0.006 & 0.20 \(\pm\) 0.004 & 0.77 \(\pm\) 0.005 & 0.21 \(\pm\) 0.002 \\  & HR@10 & 36.20 \(\pm\) 1.27 & 37.11 \(\pm\) 0.60 & 39.66 \(\pm\) 0.80 & 36.09 \(\pm\) 0.56 \\
2011 & NDCG@10 & 0.20 \(\pm\) 0.006 & 0.20 \(\pm\) 0.003 & 0.22 \(\pm\) 0.003 & 0.20 \(\pm\) 0.002 \\  & HR@10 & 36.14 \(\pm\) 0.63 & 35.94 \(\pm\) 0.89 & 34.01 \(\pm\) 0.58 & 35.14 \(\pm\) 0.36 \\
2012 & NDCG@10 & 0.20 \(\pm\) 0.004 & 0.20 \(\pm\)0.004 & 0.19 \(\pm\) 0.003 & 0.20 \(\pm\) 0.002 \\  & HR@10 & 34.21 \(\pm\) 1.03 & 36.62 \(\pm\) 0.51 & 36.76 \(\pm\) 0.93 & 35.50 \(\pm\) 0.43 \\  & NDCG@10 & 0.20 \(\pm\) 0.007 & 0.21 \(\pm\) 0.005 & 0.21 \(\pm\) 0.002 & 0.20 \(\pm\) 0.002 \\  & HR@10 & 37.80 \(\pm\) 1.06 & 38.61 \(\pm\) 0.72 & 37.00 \(\pm\) 0.55 & 37.51 \(\pm\) 0.21 \\
2014 & NDCG@10 & 0.21 \(\pm\) 0.005 & 0.22 \(\pm\) 0.003 & 0.21 \(\pm\) 0.002 & 0.58 \(\pm\) 0.003 \\ \hline \end{tabular}
\end{table} 
Table 8: Evaluation performance of each study period using the normalized cumulative discount gain (NDCG) and the hit ratio (HR) of the FCP2 Vec model on Vuze dataset at file level. All trial II results from Bayesian optimization over hyperparameters. Based on the split ratios: A = 90:5:5, B = 85:7.5:7.5, C = 80:10:10, and D = 70:15:15. Figure 7: The two-dimensional vector representation of Vuze changelogs at file level in the vector space. The denser the dot cluster, the more files that are close together and the more frequently they were changed together in the past. For instance, as shown in the zoomed-in part of Figure 8, the following [\"DHTTransportUDP;java\", \"DHTUDPPacketReplyjava\", \"DHTUDPPacketReplyjava\", \"DHTUDPPacket.java\"] elements that experience simultaneous co-changes were chosen randomly from the input data. These data were used as input to our model except the last element of the list, which is [\"DHTUDPPacket.java\"]. Then, using (query element, next element) we found the following interesting results shown in Table 9.