# MFCDR: A Meta-Learning-Based Model for Federated Personalized Cross-Domain Recommendation
## 3 Model
### Overall Procedure  
Figure 3 illustrates the general model architecture of MFPCDR. The training procedure consists of three modules: the local embedding module, the meta-recommendation module, and the prediction module, as shown in Algorithm 1. The local embedding module: this is primarily accountable for learning the possible spaces of the source and target domains. The client trains the model in the source domain using Equation (9), and, following training using a federated learning technique, we may receive the respective user and item embeddings in the source and target domains, as well as the user's personalized transferable user embedding. The meta-recommendation module: this is mainly responsible for training the meta-network to learn personalized transformed user embeddings; the meta-network is optimized by Equation (10). The prediction module: after obtaining the personalized transfer embeddings of cold-start users and the item embeddings of the target domain, we apply an internal product model to forecast the ratings of cold-start users. ``` Input:\(U^{s}\), \(U^{t}\), \(T^{s}\), \(T^{t}\), \(R^{s}\), \(R^{t}\), \(U^{l}\) Output:\(\hat{y}_{u,x}\) Local Embedding Module:
1. The client trains the model by optimizing Equation (9) and learns the representation vectors for users and items in the source and target domains \(p_{u}^{s}\), \(d_{v}^{s}\), \(p_{u}^{t}\), and \(q_{v}^{t}\), respectively. 2. Learn the personalized transferable feature embedding \(p_{u_{i}}\) of user \(u_{i}\). Meta-Recommendation Module:
3. Learn a meta-network \(f(\varphi)\) by minimizing Equation (10) to obtain personalized converted user embeddings \(\hat{p}_{u}\). Prediction Module:
4. The prediction score is calculated by the inner product model after obtaining the tailored conversion user embedding for the cold-start user \(\hat{p}_{u}\) and the item embedding in the target domain \(q_{v}^{t}\) for the cold-start user. Figure 3: The framework of MFPCDR model. ## 4 Experiments

In this section, we conduct experiments to evaluate the effectiveness of MFPCDR. We answer the following research questions: **RQ1:** How does MFPCDR perform in cold-start scenarios compared to other models? **RQ2:** How well does MFPCDR work in more realistic recommendation scenarios? **RQ3:** How does the proportion of overlapping users affect the model? **RQ4:** Does varying sparsity in the source domain influence MFPCDR performance? **RQ5:** What is the classification performance of MFPCDR? ### Datasets

To compare our model to a baseline, we conducted trials with the Amazon review datasets. The Amazon datasets were chosen because Amazon's data volume is large enough to provide more samples with diversity, and the Amazon datasets is real, stable, and repeatable enough to provide enough information to verify the effectiveness of the system. The Amazon datasets can be divided into sub-datasets such as \"Books\", \"Electronics\", and \"Movies and TV\" according to product categories, which can effectively help us conduct cold-start recommendation experiments across domains: e.g., the source domain is the \"Book\" domain and the target domain is the \"Movie and TV\" domain. For other e-commerce datasets, the MFPCDR model is also applicable as long as the samples are diverse and have overlapping users. Three major areas were selected as the three domains: \"Movies and Television\", \"Books\", and \"CDs and Vinyl\". In each domain, we deleted entries that had no review language and then filtered out people with fewer than 10 interactions and goods with fewer than 30 interactions. People with fewer than 10 interactions were deleted because they provided too few reviews or feedback to provide enough information for analysis, and items with fewer than 30 interactions were removed because the item's sales or market performance was insufficient to support analysis, or they were deemed unpopular or irrelevant. These filtering criteria ensure that only high-quality data are used for analysis, improving the credibility of the data and the accuracy of the results.