# MFCDR: A Meta-Learning-Based Model for Federated Personalized Cross-Domain Recommendation
## 3 Model
### Overall Procedure
Because our meta-recommendation module needs to learn from interacting users, our model is not suitable for extreme cold-start situations. Additionally, because a federated learning approach is used to protect user privacy, this inevitably introduces noise that reduces the effectiveness of the model training. ### Impact of the Size of Overlapping Users (RQ3)

To investigate the influence of the number of overlapping users, further tests were performed at five percentage levels of 5%, 10%, 20%, 50%, and 60% in three cross-domain recommendation situations. Figure 4 depicts the outcomes. Observations indicate that MSE lowers as the fraction of overlapping users increases, which means that the larger the proportion of overlapping users, the more user preferences the model can learn and the better the model accuracy. The setting of the proportion of overlapping users directly affects the number of users from which the system learns similar preferences for cross-domain recommendations. Clearly, a greater amount of overlapping users allows the model to better understand the preferences of the cross-domain recommendation domain, thus improving the accuracy of the recommendations. Intuitively, the curve of our proposed MFPCR model is relatively flat. ### Effect of Source Domain Sparsity (RQ4)

To examine the impact of source domain sparsity on MFPCR performance, we altered the sparsity of the source domain by sampling from the original dataset so that the sparsity \(sp\) could be modified to \(\{1,1/2,1/4,1/8\}\), where \(sp=1\) signifies an unsampled original dataset. Figure 5 depicts the results of applying the MFPCR model to the setups of Scenario 1, Scenario 2, and Scenario 3 with the fraction of overlapping users in the training dataset set to 60% in the interest of fairness and consistency. We can observe from the findings that data sparsity decreases model performance. The graph demonstrates that the MSE performance curve with MFPCR is flatter in all three circumstances, which indicates that it has better sparsity perception and can be better adapted to real-world scenarios. We found that this is attributable to the attention mechanism used by MFPCR in obtaining the personalized transferable feature embeddings of the user, where different items contribute differently to obtaining the personalized preferences of the user, and it is the use of this approach that allows the MFPCR model to handle sparse data better. ### Classification Performance Evaluation of MFPCDR (RQ5)

To evaluate the classification performance of the MFPCDR model, we chose Precision, Recall and F-measure as important metrics to assess the model performance. Their mathematical formulas are defined as follows:

\[ \begin{array}{l}Precision=\frac{TP}{TP+TP}\\ Recall=\frac{TP}{TP+FN}\\ F-Measure=\frac{2*Precision+Recall}{Precision+Recall}\end{array}  \tag{12}\]

where \(TP\) indicates the number of samples that the model correctly predicts as positive, \(FP\) indicates the number of samples that the model incorrectly predicts as negative, and \(FN\) indicates the number of samples that the model incorrectly predicts as negative. _Precision_ measures the ratio of correct recommendations made by the recommendation system to the actual correct recommendations among all recommendations, while Recall measures the coverage of all possible correct recommendations by the recommendation system. _F-Measure_ is a combination of _Precision_ and _Recall_, which provides an overall assessment. _F-Measure_ measures the balance between Precision and Recall, and it is influenced by both Precision and Recall, so it can reflect the comprehensive performance of the recommendation system well.