# A Survey of Full-Cycle Cross-Modal Retrieval: From a Representation Learning Perspective
## 5 Evaluation Metrics  
There are a variety of evaluation indicators to demonstrate the efficacy of cross-modal retrieval. The effectiveness of a methodology in a particular scenario is evaluated using appropriate metrics [88]. In this section, we make a comparison with predominant evaluation metrics such as the precision (_P_), recall rate (_Recall@K_), PR curve (_PR_), mean average precision (_mAP_), F-score (_FS_), and normalized discounted cumulative gain (_NDCG_). Precision is the ratio of accurately recovered samples to total retrieved samples in cross-modal systems. Recall rate. The recall rate is an important performance metric in cross-modal retrieval, measured by _recall@k. Recall@1_, @5, and _@10_ represent the recall rate of the first k retrieved results. To evaluate the effectiveness of a retrieval system in specific scenarios, the _Recall@50_ and _Recall@100_ metrics are often used. It should be noted that achieving a balance between recall and accuracy is crucial since they are inversely related. Equation (5)) represents the calculation of the recall metric. \[Recall=TP/(TP+FN) \tag{5}\]  
where _TP_ stands for the total number of documents returned from the retrieval that matches the query and _FP_ represents the number of unmatched samples in the retrieved samples. The variable _FN_ denotes the number of documents that fail to match the query sample and are not returned from the dataset. PR curve. The performance of cross-modal retrieval can be evaluated by combining recall and precision measures to produce a precision-recall curve (_PR curve_). This curve displays the precision value at various recall levels and provides a visual representation. For example, Reference [89] utilized the _PR curve_ to demonstrate the effectiveness of their proposed cross-modal retrieval method. mAP. The _mAP_ metric evaluates the relevance of the retrieved results to the query and is calculated as the average accuracy of all queries. The studies cited in [74; 87; 90] employed the _mAP_ metric to improve retrieval performance. The average accuracy of a query and the top-K retrieved results can be computed using Equation (6):  
\[AP=\frac{1}{R}\sum_{r=1}^{R}P(r)\delta(r) \tag{6}\]  
where _P(r)_ signifies the precision of the top \(R\) retrieved outputs and \(R\) is the number of relevant outcomes, and if the retrieved \(R\) is relevant, the value is set to 1; otherwise, it is set to 0. The mean average precision (_mAP_) can be specified as (Equation (7)):  
\[mAP=\frac{1}{Q}\sum_{q=1}^{Q}AP \tag{7}\]  
A high _mAP_ value indicates that a specific cross-modal method performs well on a given dataset, based on a certain number of queries (_Q_). Unlike the _precision_, _recall_, and _F-score_, which are single-point values, the _mAP_ provides a comprehensive measure of retrieval capabilities and represents overall performance. F-score. The _F-score_, which is the weighted harmonic mean of the _precision_ and _recall_, is a widely used performance metric in various fields. It is calculated using the following formula (Equation (8)):  
\[F=\left(1+\beta^{2}\right)*\frac{\textit{precision}\;*\;\textit{recall}}{\beta^{ 2}*(\;\textit{precision}\;+\;\textit{recall}\;)} \tag{8}\]  
One important factor in measuring performance is the weight given to precision and recall. This weight can be adjusted using the \(\beta\) parameter, where a value of 1 corresponds to equal weighting of precision and recall, known as the _F1-score_. The \(\beta\) parameter can tune the relative importance of precision versus recall in the retrieval process. As a result, the _FS-score_ is a popular metric for evaluating retrieval performance, as it provides a balanced optimization of the precision and recall values. For example, in the study of [91], the _FS-score_ was used to measure the performance of the retrieval system. NDCG. Normalized discounted cumulative gain (_NDCG_) is a widely used method for evaluating search engine ranking performance. It assesses the quality of sorted recommended items, typically with a list length of \(L\).