# MFCDR: A Meta-Learning-Based Model for Federated Personalized Cross-Domain Recommendation
## 3 Model
### Overall Procedure
Since these three domains are highly interrelated, three cross-domain recommendation scenarios can be constructed in pairs: \"Books\" to \"Movies and TV\", \"Movies and TV\" to \"CDs and Vinyl\", and \"Books\" to \"CDs and Vinyl\". In each scenario, the one with more users is selected as the source domain, and the one with fewer users is selected as the target domain. We randomly chose 30% of the users as cold-start users whose interactions in the target domain were unknown to the model and were used to verify and test the model, while 70% of the users were used to train the model. To simulate varying amounts of overlapping users, we evaluated our model by randomly picking overlapping users from the training set and adjusting the proportion \(\eta\) to \(\eta\in\{5\%,10\%,20\%,50\%,60\%\}\). The situations for cross-domain recommendations are detailed in Table 1.

### Baseline Methods

We have compared this to the following classic and contemporary benchmarks. * CMF: A migration learning method that uses other relational data related to the predicted relationship to improve prediction performance when doing relational learning tasks. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Scenario** & **Domain** & **Dataset** & **Overlap Users** & \(\mathbf{\eta}\) = 5\% & \(\mathbf{\eta}\) = 10\% & \(\mathbf{\eta}\) = 20\% & \(\mathbf{\eta}\) = 50\% & \(\mathbf{\eta}\) = 60\% \\ \hline \multirow{2}{*}{Scenario 1} & S & Books & & & & & & \\  & T & Movies and TV & 6053 & 149 & 302 & 604 & 1517 & 1815 \\ \hline \multirow{2}{*}{Scenario 2} & S & Movies and TV & & & & & & \\  & T & CDs and Vinyl & 2839 & 67 & 135 & 276 & 673 & 803 \\ \hline \multirow{2}{*}{Scenario 3} & S & Books & & & & & & \\  & T & CDs and Vinyl & 1692 & 38 & 81 & 160 & 412 & 487 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Statistics of the Amazon datasets. * EMCDR: A framework for cross-domain mapping and recommendation that uses a multi-layer perceptron to capture non-linear mapping functions across domains, followed by the learning of mapping functions using entities with adequate data to enhance robustness. * CDLFM [40]: The cross-domain latent feature mapping model takes into account the similarity link between users in terms of rating behavior and provides a matrix decomposition that includes user similarity and three similarity measures. A domain-based gradient boosting tree approach was used for cross-domain knowledge transfer. Mapping functions are learned for cold-start users utilizing latent attributes of users in the auxiliary domain with similar ratings to cold-start users. * DFM [39]: A deep fusion model based on comments and content is utilized to preserve more semantic information by expanding the stacking noise reduction autoencoder and then transferring user latent factors across the two domains using a multi-layer perceptron. * ANR [41]: A comprehensive aspect-based model that performs aspect-based representation learning on users and things using an attention-based component to describe the aspect process underlying the user's evaluation strategy. After training the model on the target domain, related source domain comments are utilized to provide recommendations. ### Experimental Setup

We used PyTorch to implement our proposed MFCDR model, preprocessing all user and project documents in the datasets to remove deactivated words and words with high document frequency. We used grid search to adjust the hyperparameters of all methods and Adam to optimize the model, and we set the learning rate to {0.001,0.005,0.01,0.05,0.1,0.5}, the embedding dimension range for users and items to {8,16,32,64}, and the batch size test range to {64,128,256,512}. The activation function was set to sigmoid, and the performance of all methods was reported after five runs. We found that the MFCDR model works well when the Adam learning rate is set to 0.01, the user and item embeddings are set to 32, and the batch size is set to 128.