## 4 KGs Evaluation
### Intrinsic Evaluation  
#### 4.1.1 What Is an Intrinsic Evaluation?  
Intrinsic evaluation offers a suite of quantitative metrics that assess the quality and performance of the outputs generated by a knowledge graph model, and each metric is particularly well-suited to different tasks and application scenarios. For example, classification metrics such as Precision, Recall, and F1-Score are advantageous when evaluating discrete prediction tasks--like determining whether a predicted RDF triple correctly represents the relationship between entities. In contexts where false positives are especially detrimental, a high Precision is critical, while Recall becomes paramount when it is crucial to capture all relevant relations. The F1-Score then serves as a balanced indicator when both types of errors are equally consequential.  
In contrast, rank-based metrics, such as Mean Reciprocal Rank (MRR) and Hits@K, are more appropriate for tasks involving link prediction or information retrieval, where the model generates a ranked list of candidate relations. MRR is beneficial because it captures the average rank of the first correct answer, thereby favoring models that bring correct candidates to the top, while Hits@K focuses on the proportion of cases in which the correct answer appears within the top K predictions--making these metrics particularly useful in systems that can operate effectively on a shortlist of candidates.  
For continuous numerical prediction tasks, regression metrics like Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) are used. RMSE is especially sensitive to large errors, which is advantageous in applications where significant deviations can have a profound impact, whereas MAE provides a straightforward average error measure that is easier to interpret. MAPE, which expresses errors as percentages relative to true values, is particularly useful in scenarios in which the relative scale of error is more informative than the absolute difference.  
Additionally, when assessing the quality of the learned embeddings, methods such as the Pearson correlation coefficient can quantify the linear relationship between embedding similarities and ground-truth semantic relationships. In some cases, an F1-Score is also computed for clustering or classification tasks performed on embedding spaces, providing further insight into the expressive power of the representations.  
Finally, evaluating algorithm optimization and efficiency through measures like average effectiveness, standard deviation, execution time, and memory usage is essential when scaling models to large datasets or deploying them in real-time applications. These metrics not only reflect the model's internal optimization and stability across various runs but also determine its practical viability in resource-constrained environments.  
By carefully selecting and interpreting these intrinsic evaluation metrics in accordance with the specific requirements and constraints of the knowledge graph application, researchers can gain a comprehensive understanding of the model performance and makeinformed decisions regarding further optimization and deployment strategies. Through Table 2, we can see how the evaluation metrics are assessed.