## 4 KGs Evaluation
### Intrinsic Evaluation
#### 4.1.2 Intrinsic Evaluation: Metrics, Methods, and Case Studies  
In a study based on the public standard for public transportation data, researchers used the GTFS Madrid benchmark to precisely measure how well a CSV-based RML \begin{table}
\begin{tabular}{c c c} \hline
**Name** & **Equation** & **Definition** \\ \hline Precision & Precision \(=\frac{\text{TP}}{\text{TP}+\text{FP}}\) & TP: True Positives \\ \hline Recall & Recall \(=\frac{\text{TP}}{\text{TP}+\text{FN}}\) & TP: True Positives \\ \hline F1 score & F1 \(=2\times\frac{\text{Precision}\times\text{Recall}}{\text{Precision}+\text{Recall}}\) & Precision, Recall \\ \hline MRR (Mean Reciprocal Rank) & MRR \(=\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}\frac{1}{\text{rank}_{i}}\) & N: Total number of queries \(\text{rank}_{i}\); Rank position of the correct answer for the ith query \\ \hline Hits@K (Hits at K) & Hits@K \(=\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}1\{\text{rank}_{i}\leq\text{ K}\}\) & N: Total number of queries \(\text{K}\): Rank threshold \(\text{rank}_{i}\); Rank of the correct answer for the ith query \\ \hline RMSE (Root Mean Squared Error) & RMSE \(=\sqrt{\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}(\hat{y}_{i}-y_{i})^{2}}\) & N: Number of samples \(\hat{y}_{i}\): Predicted value for sample i \(\text{y}_{i}\): Actual value for sample i \\ \hline MAE (Mean Absolute Error) & MAE \(=\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}\left|\hat{y}_{i}-y_{i}\right|\) & Same variables as RMSE \\ \hline MAPE (Mean Absolute Percentage Error) & MAPE \(=\frac{100\%}{\text{N}}\sum\limits_{i=1}^{\text{N}}\left|\frac{\hat{y}_{i}-y_{i}} {y_{i}}\right|\) & N: Number of samples \(\hat{y}_{i}\): Predicted value \(y_{i}\): Actual value \\ \hline PCC (Pearson Correlation Coefficient) & r \(=\frac{\sum\
olimits_{i=1}^{\text{N}}(x_{i}-\overline{x})(y_{i}-\overline{y})} {\sqrt{\sum\
olimits_{i=1}^{\text{N}}(x_{i}-\overline{x})^{2}}\sqrt{\sum \
olimits_{i=1}^{\text{N}}(y_{i}-\overline{y})^{2}}}\) & x\({}_{i}\), y\({}_{i}\): Paired values from two datasets \(\overline{x}\), y\({}_{i}\): Mean of x and y values, respectively \\ \hline Average Effectiveness & \(Average\)\(Effectiveness=\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}E_{i}\) & N: Total number of runs \(\text{E}_{i}\): Effectiveness measure for the ith run \\ \hline SD (Standard Deviation) & \(\sigma=\sqrt{\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}(x_{i}-\overline{x })^{2}}\) & N: Total number of measurements \(\overline{x}\): Mean of the measurements \(\text{x}_{i}\): Individual measurement value \\ \hline Mean Execution Time & \(Mean\)\(Execution\)\(Time=\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}t_{i}\) & N: Total number of runs \(\text{t}_{i}\): Execution time for the ith run \\ \hline Execution Time Standard Deviation & \(\sigma_{t}=\sqrt{\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}(t_{i}-\overline {t})^{2}}\) & \(\text{t}_{i}\): Individual execution time \(\overline{t}\): Mean execution time \\ \hline Mean Memory Usage & \(Mean\)\(Memory\)\(Usage=\sqrt{\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}m_{i}}\) & N: Total number of runs \(\text{m}_{i}\): Memory usage for the ith run \\ \hline Memory Usage Standard Deviation & \(\sigma_{m}=\sqrt{\frac{1}{\text{N}}\sum\limits_{i=1}^{\text{N}}(m_{i}-\overline {m})^{2}}\) & \(\text{m}_{i}\): Individual memory usage \(\overline{m}\): Mean memory usage \\ \hline \end{tabular}
\end{table} 
Table 2: Comprehensive overview of intrinsic evaluation metrics and their mathematical definitions. mapping tool produced results that matched public transportation data and to evaluate the impact of data types (e.g., differences in handling ssd:long versus ssd:integer) on mapping errors and attribute matching success rates [166]. Additionally, a study was conducted that rigorously evaluated the performance differences among link prediction techniques using various knowledge graph datasets under the same preprocessing conditions and demonstrated the statistical significance between methods using the Wilcoxon test and the Kolmogorov-Smirnov test [167].