## 5 Simulation and Experiment
### Experiments in Real Networks  
The significance of simulation is that the theoretical limit can be derived by theoretical calculation or numerical calculation, and all combination methods can be used to compare with it, finding shortcomings and gaps to design a more rational method. However, the simulation data is different from real network data. We use TLF method to fuse several similarity indices and test in real networks. The basic similarity indices we use are Common Neighbor index (CN) [19], Adamic-Adar index (AA) [15], Resource Allocation index (RA) and Preferential Attachment index (PA) [21; 22]. These indices are local indices. Several global indices such as Katz index [23], Average Commute Time index (ACT) and Cosine Similarity Time index (Cos+) are served as comparisons [24; 25]. The definitions of the above indices and their meanings are listed as Table 4. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Parameters** & **Accuracy** & **Dim1** & **Dim2** & **Dim3** & **Dim4** & **NB** & **LR** & **TLF** & \
\begin{tabular}{c} **Theoretical** \\ **Limit** \\ \end{tabular} &
\begin{tabular}{c} **Transform by** \\ **Increasing Function** \\ \end{tabular} \\ \hline Group 1 & AUC & 0.554 & 0.566 & 0.547 & 0.585 & 0.610 & 0.668 & **0.691** & 0.738 & 0.738 \\  & Precision & 0.047 & 0.015 & 0.014 & 0.027 & 0.038 & 0.020 & **0.097** & 0.120 & 0.120 \\ \hline Group 2 & AUC & 0.569 & 0.660 & 0.604 & 0.622 & 0.765 & 0.676 & **0.786** & 0.792 & 0.792 \\  & Precision & 0.114 & 0.140 & 0.081 & 0.038 & 0.153 & 0.051 & **0.212** & 0.241 & 0.241 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation results of group 1 and group 2. The bold figure indicates the best accuracy in each dimension and combination method. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Accuracy** & **Dim1** & **Dim2** & **Dim3** & **Dim4** & **NB** & **LR** & **TLF** & \
\begin{tabular}{c} **Theoretical** \\ **Limit** \\ \end{tabular} &
\begin{tabular}{c} **Transform by** \\ **Increasing Function** \\ \end{tabular} \\ \hline AUC & 0.770 & 0.505 & 0.488 & 0.878 & 0.938 & 0.923 & **0.950** & 0.956 & 0.956 \\ Precision & 0.567 & 0.007 & 0.007 & 0.654 & 0.711 & 0.100 & **0.815** & 0.858 & 0.858 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation results of group 3. The bold figure indicates the best accuracy in each dimension and combination method. We use TLF method to fuse 4 local similarity indices, and compare with fusion method such as naive Bayes and logistic regression and other global indices. Our experiments are performed on 11 different real networks. (1) Food Web Everglades Web (FWEW) [26]; (2) Food Web Florida Bay(FWFB) [27]; (3) Protein-protein Interactions Cell (PPI Cell) [28]; (4) CKM-3 [29]; (5) Netscience (NS) [30]; (6) Yeast [31]; (7) Political Blogosphere(PB) [32]; (8) Email [33]; (9) CA-GrQc(CG) [34]; (10) Com-dblp(CD) [35]; (11) Email Enron (EE) [36; 37]. The basic topological features of 11 real networks are listed in Table 5. Each original data is randomly divided into training set of 90% links, and the probe set of 10% links. Tables 6 and 7 show the comparisons between TLF method and other combination methods or global indices using AUC and Precision metrics. Each result is the average of 10 realizations. When calculating the Precision metric in Equation (5), we take \(L=100\) in datasets 1 to 8, and take \(L=1000\) in datasets 9 to 11. In the large networks, TLF method needs to sample to save the computing sources, and in datasets 10 to 11, the under-sampling rate is set as 1000.