# FONDUE: A Framework for Node Disambiguation and Deduplication Using Network Embeddings +
## 4 Experiments
### Node Deduplication
#### 4.3.1 Quantitative Evaluation of Node Deduplication
Thus, we introduce few parameters to better model node splitting:  
* Edge distribution: We employ 2 different ways to reassign the edges, from 1 node to 2 different nodes, either by randomly distributing the edges with at least 1 edge per node, or by ensuring equal distribution for each one;
* Minimum degree: We only choose to split nodes with a degree larger than a specified minimum;
* Overlap: We specify if there is an overlap in the edge reassignment for the different nodes, i.e., percentage of common edges for each node. **Datasets. ** As indicated earlier, we have used the three semi-synthetic datasets (Table 2), lesmis, polbooks, and netscience, mainly for their relatively small size, additionally we tested FONDUE-NDD on part of the PubMed dataset (described earlier in Section 4.2.3), a network of 2122 nodes, including one duplicate node. **Baselines. ** As all competing methods [22; 23] require additional labels and attributes for NDD, so we opted to use a simple baseline to assess the performance of FONDUE-NDD, namely the L2-norm of the embedding distance between the candidate duplicate node-pairs \(\{i^{\prime},i^{\prime\prime}\}\) using CNE (referred to as ED). \[ED_{\{i^{\prime},i^{\prime\prime}\}}=||\mathbf{x}_{i^{\prime}}-\mathbf{x}_{i ^{\prime\prime}}||_{2}\]  
**Metric. ** As described in the previous section, we compute the value of the objective function after the re-embedding for the different merged nodes. We then rank the different node pairs by their value. We use that rank as a metric to predict whether our approach can successfully predict which node-pair is a duplicate. The best value would be 1, which means that 100% of the time, FONDUE-NDD is able to identify the node pairs, as the cost of the re-embedding is the lowest. **Results. ** The results in Table 8, represent the average ranking of objective cost function over 100 different trial. We ran a 2-side Fisher test to test if the differences between the averages for the two methods are significantly different (\(p<0.05\)), and the averages are highlight \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Edge**} & \multirow{2}{*}{**Minimum**} & \multirow{2}{*}{**Edge**} & \multicolumn{2}{c}{**Lemis**} & \multicolumn{2}{c}{**Polbooks**} & \multicolumn{2}{c}{**Netscience**} \\ \cline{3-8}  & & & **FONDUE-NDD** & & **ED** & **FONDUE-NDD** & **ED** & **FONDUE-NDD** & **ED** \\ \hline \multirow{8}{*}{Balanced} & \multirow{3}{*}{None} & 0\% & 18.775 & **18.2** & 30.025 & **17.85** & 6.975 & **4.2** \\  & & 20\% & 15.55 & **8.75** & 22.475 & **10.65** & 3.9 & 2.825 \\  & & 30\% & 14.125 & **9.35** & 20.4 & **8.5** & 3.225 & **1.775** \\ \cline{2-8}  & \multirow{3}{*}{Graph} & 0\% & **10** & 15.806 & 17.676 & 20.941 & 5.325 & 5.7 \\  & & 20\% & 10.167 & 11.083 & 11.471 & 12.941 & 2.775 & 3.025 \\  & & 30\% & 8.611 & 9.333 & 10.794 & 11.176 & 2.725 & 2.625 \\ \cline{2-8}  & \multirow{3}{*}{2x Graph} & 0\% & **3.857** & 24.857 & **5.277** & 23.364 & **3.471** & 5.029 \\  & & 20\% & **5** & 17.429 & **3.818** & 15.909 & **1.735** & 3.412 \\  & & 30\% & **2.857** & 13.429 & **2.545** & 14.091 & **1.735** & 3.206 \\ \hline \multirow{8}{*}{Unbalanced} & \multirow{3}{*}{None} & 0\% & 25.9 & **22.75** & 36.425 & **26.325** & 6.9 & 2.85 \\  & & 20\% & 16.75 & **10.75** & 25.875 & **10** & 3.75 & **2.55** \\ \cline{1-1}  & & 30\% & 16.3 & **10.525** & 22.875 & **12.075** & 3.65 & 2.775 \\ \cline{1-1} \cline{2-8}  & \multirow{3}{*}{Graph} & 0\% & 13.5 & 17.306 & 27 & 23.176 & 5.125 & 5.075 \\ \cline{1-1}  & & 20\% & 12.417 & 13.278 & 13.029 & 11.706 & 3.1 & 3.15 \\ \cline{1-1}  & & 30\% & 12.944 & 12.167 & 14.265 & 12.029 & 3.025 & 2.675 \\ \cline{1-1} \cline{2-8}  & \multirow{3}{*}{2x Graph} & 0\% & 18.143 & 40.143 & **11.545** & 22.545 & 5.735 & 8.147 \\ \cline{1-1}  & & 20\% & 9.429 & 18.429 & **8.364** & 16.182 & **2.118** & 3.5 \\ \cline{1-1}  & & 30\% & **5.714** & 19.286 & **7** & 12.182 & **1.735** & 2.794 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of the controlled experiments for each dataset.