## 6 Discussion  
Many combination methods try to find the nonlinear relation of every dimensions, and want to obtain a more reasonable fusion function to promote the prediction accuracy. For example, link prediction method based on the choquet fuzzy integral [7] uses fuzzy measures to measure the importance of each similarity index in the fusion process and the interaction between them. Logistic regression based index adopts logistic function to learn the relation of multiple structural features and obtain an adaptive link prediction method [38]. In fact, according to the limit theorem, the nonlinear relation is the ratio of two joint probability destiny functions or its monotone increasing transformation. The best fusion function is a measurement of difference between existing and nonexistent links, and it reflects the relativity of existing and nonexistent links. The essence of combination methods is trying to approximate the pdfs from many aspects. Limit theorem provides a unified interpretation for all combination methods. On the basis of theoretical limit theorem, \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Data** & **CN** & **AA** & **RA** & **PA** & **ACT** & **Cos+** & **Katz** & **NB** & **LR** & **TLF** \\ \hline FWEW & 0.687 & 0.694 & 0.714 & 0.819 & 0.793 & 0.511 & 0.727 & 0.825 & 0.832 & **0.876** (\(h=0.1\)) \\ FWFB & 0.624 & 0.624 & 0.624 & 0.742 & 0.727 & 0.649 & 0.680 & 0.749 & 0.762 & **0.781** (\(h=0.1\)) \\ PPI\_Cell & 0.736 & 0.745 & 0.740 & 0.699 & 0.779 & 0.783 & 0.822 & 0.753 & 0.679 & **0.831** (\(h=0.3\)) \\ CKM-3 & 0.661 & 0.665 & 0.661 & 0.585 & 0.560 & 0.535 & **0.928** & 0.683 & 0.675 & 0.713 (\(h=0.15\)) \\ Yeast & 0.918 & 0.918 & 0.915 & 0.869 & 0.903 & 0.958 & 0.962 & 0.925 & 0.934 & **0.968** (\(h=0.2\)) \\ PB & 0.922 & 0.928 & 0.928 & 0.906 & 0.890 & 0.932 & 0.934 & 0.931 & 0.936 & **0.949** (\(h=0.3\)) \\ NS & 0.994 & 0.994 & 0.995 & 0.709 & 0.558 & 0.507 & 0.996 & 0.998 & **0.999** (\(h=0.2\)) \\ Email & 0.849 & 0.852 & 0.851 & 0.817 & 0.801 & 0.889 & 0.908 & 0.865 & 0.870 & **0.912** (\(h=0.15\)) \\ CG & 0.966 & 0.965 & 0.967 & 0.992 & 0.549 & 0.679 & **0.996** & 0.984 & 0.991 & 0.994 (\(h=0.1\)) \\ CD & 0.962 & 0.968 & 0.971 & 0.943 & 0.912 & 0.971 & 0.915 & 0.975 & 0.973 & **0.982** (\(h=0.15\)) \\ EE & 0.981 & 0.984 & 0.984 & 0.927 & 0.903 & 0.980 & 0.514 & 0.985 & 0.987 & **0.992** (\(h=0.15\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of the AUC value between TLF and other combination methods or global indices. In each network, the selected window width \(h\) is along with the AUC value. The bold figure indicates the best AUC. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Data** & **CN** & **AA** & **RA** & **PA** & **ACT** & **Cos+** & **Katz** & **NB** & **LR** & **TLF** \\ \hline FWEW & 0.143 & 0.145 & 0.162 & 0.334 & 0.271 & 0.004 & 0.196 & 0.301 & 0.325 & **0.543** \\ FWFB & 0.071 & 0.072 & 0.083 & 0.240 & 0.184 & 0.029 & 0.148 & 0.249 & 0.283 & **0.382** \\ PPI\_Cell & 0.052 & 0.048 & 0.073 & 0.012 & 0.045 & 0.061 & 0.058 & 0.072 & 0.068 & **0.085** \\ CKM-3 & 0.051 & 0.059 & 0.062 & 0.011 & 0.001 & 0.003 & 0.061 & 0.060 & 0.062 & **0.064** \\ Yeast & 0.652 & 0.703 & 0.461 & 0.439 & 0.487 & 0.291 & 0.721 & 0.712 & 0.723 & **0.785** \\ PB & 0.381 & 0.320 & 0.212 & 0.100 & 0.129 & 0.298 & 0.381 & 0.411 & 0.395 & **0.452** \\ NS & 0.820 & 0.971 & 0.982 & 0.008 & 0.004 & 0.006 & 0.823 & 0.988 & 0.986 & **0.991** \\ Email & 0.202 & 0.253 & 0.214 & 0.039 & 0.031 & 0.086 & 0.231 & 0.263 & 0.289 & **0.347** \\ CG & 0.972 & 0.969 & 0.967 & 0.991 & 0.557 & 0.663 & **0.998** & 0.983 & 0.989 & 0.996 \\ CD & 0.901 & 0.924 & 0.931 & 0.892 & 0.867 & 0.937 & 0.912 & 0.939 & 0.942 & **0.951** \\ EE & 0.981 & 0.984 & 0.987 & 0.924 & 0.898 & 0.912 & 0.516 & 0.988 & 0.985 & **0.992** \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparisons of the Precision value between TLF and other combination methods or global indices.