# FONDUE: A Framework for Node Disambiguation and Deduplication Using Network Embeddings +
## 4 Experiments
### Node Disambiguation
#### 4.2.2 Quantitative Evaluation of Node Identification
PrecisionThe number of correctly identified positive results divided by the number of all positive results  
Precision = \(\frac{TP}{TP+FP}\)  
RecallThe number of correctly identified positive results divided by the number of all positive samples  
Recall = \(\frac{TP}{TP+FN}\)  
\(F1\)-scoreIt is the weighted average of the precision where an F1 score reaches its best value at 1 and worst score at 0. \[\text{F1}=\frac{2*\text{Recall}\times\text{Precision}}{\text{Recall}+\text{ Precision}}\]  
Note that, due to the fact that in the binary classification case, the number of false positive is equal to the number of false negative, the value of the recall, precision and F1-score will be the same. Area Under the ROC curve (AUC)A ROC curve is a 2D depiction of a classifier performance, which could be reduced to a single scalar value, by calculating the value under the curve (AUC). Essentially, the AUC computes the probability that our measure would rank a randomly chosen ambiguous node (positive example), higher than a randomly chosen non-ambiguous node (negative example). Ideally, this probability value is 1, which means our method has successfully identified ambiguous nodes 100% of the time, and the baseline value is 0.5, where the ambiguous and non-ambiguous nodes are indistinguishable. This accuracy measure has been used in other works in this field, including [16], which makes it easier to compare to their work. Discounted Gain (DCG)The main limitation of the previous method, as we discussed earlier, is inability to account for graded scores, but rather only binary classification. To account for this, we utilize different cumulative gain based methods. Given a search result list, cumulative gain (CG) is the sum of the graded relevance values of all results. \[\text{CG}=\sum_{i=1}^{n}\text{relevance}_{i}\]  
On the other hand, DCG [34] takes position significance into account, and adds a penalty if a highly relevant document is appearing lower in a search result list, as the graded relevance value is logarithmically reduced proportionally to the position of the result. Practically, it is the sum of the true scores ranked in the order induced by the predicted scores, after applying a logarithmic discount. The higher the better is the ranking. \[\text{DCG}=\sum_{i=1}^{n}\frac{\text{relevance}_{i}}{\log_{2}(i+1)}\]  
Normalized Discounted Gain (NDCG)It is commonly used in the information retrieval field to measure effectiveness of search algorithms, where highly relevant documents being more useful if appearing earlier in search result, and more useful than marginally relevant documents which are better than non-relevant documents. It improves upon DCG by accounting for the variation of the relevance, and providing a proper upper and lower bounds to be averaged across all the relevance scores. Thus, it is computed by summing the true scores ranked in the order induced by the predicted scores, after applying a logarithmic discount, then dividing by the best possible score ideal DCG (IDCG, obtained for a perfect ranking) to obtain a score between 0 and 1. \[\text{NDCG}=\frac{\text{NDCG}}{\text{IDCG}}\]  
**Evaluation pipeline. ** We first perform network contraction on the original graph, by fixing the ratio of ambiguous nodes to \(r\). We then embed the network using CNE, and compute the disambiguation measure of FONDUE-NDA (Equation (7)), as well as the baseline measures for each node. Then, the scores yield by the measures are compare to the ground truth (i.e., binary labels indicating whether a node is a contracted node). This is completed for 3 different values of \(r\in\{0.001,0.01,0.1\}\). We repeat the processes 10 times using a different random seed to generate the contracted network and average the scores. For the embedding configurations, we set the parameters for CNE to \(\sigma_{1}=1\), \(\sigma_{2}=2\), with dimensionality limited to \(d=8\). **Results.