Federated Prototype-based Contrastive Learning for Privacy-Preserving Cross-domain Recommendation
Li Wang Quangui Zhang Lei Sang Qiang Wu Min Xu


 

 





Journal of  Class Files, Vol. 14, No. 8, August 2021
Shell et al.: A Sample Article Using IEEEtran.cls for IEEE Journals





Federated Prototype-based Contrastive Learning for Privacy-Preserving Cross-domain Recommendation
    Li Wang, Quangui Zhang, Lei Sang, Qiang Wu, Senior Member, IEEE, and Min Xu^*, IEEE, Member


Li Wang, Qiang Wu, and Min Xu are with the School of Electrical and Data Engineering, University of Technology Sydney, Sydney 2000, Australia. Shoujin Wang is with the institute of data science, University of Technology Sydney, Sydney 2000, Australia.  Quangui Zhang is with the School of Artificial Intelligence, Chongqing University of Arts and Sciences, Chongqing 402160, China. *Corresponding author: Min Xu (e-mail: Min.Xu@uts.edu.au)
    September 9, 2024
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§ ABSTRACT 
 

Cross-domain recommendation (CDR) aims to improve recommendation accuracy in sparse domains by transferring knowledge from data-rich domains. However, existing CDR methods often assume the availability of user-item interaction data across domains, overlooking user privacy concerns. Furthermore, these methods suffer from performance degradation in scenarios with sparse overlapping users, as they typically depend on a large number of fully shared users for effective knowledge transfer. To address these challenges, we propose a Federated Prototype-based Contrastive Learning (CL) method for Privacy-Preserving CDR, named FedPCL-CDR. This approach utilizes non-overlapping user information and prototypes to improve multi-domain performance while protecting user privacy. FedPCL-CDR comprises two modules: local domain (client) learning and global server aggregation. In the local domain, FedPCL-CDR clusters all user data to learn representative prototypes, effectively utilizing non-overlapping user information and addressing the sparse overlapping user issue. It then facilitates knowledge transfer by employing both local and global prototypes returned from the server in a CL manner. Simultaneously, the global server aggregates representative prototypes from local domains to learn both local and global prototypes. The combination of prototypes and federated learning (FL) ensures that sensitive user data remains decentralized, with only prototypes being shared across domains, thereby protecting user privacy. Extensive experiments on four CDR tasks using two real-world datasets demonstrate that FedPCL-CDR outperforms the state-of-the-art baselines.




Contrastive Learning, Federated Learning, Prototype, and Cross-Domain Recommendation




§ INTRODUCTION

Cross-domain recommendation (CDR) has emerged as a critical strategy to address the challenge of data sparsity in recommendation systems by transferring knowledge, such as user-item interaction histories and review texts, across domains <cit.>. 

Based on different recommendation scenarios, existing CDR can be divided into two categories: single-target CDR and multi-target CDR. The first genre <cit.> aims to improve recommendation performance in the target domain by utilizing rich information from the source domain. However, it cannot enhance model performance across multiple domains simultaneously. To address this issue, multi-target CDR <cit.> has emerged. Literature focusing on feature aggregation <cit.> and feature disentanglement <cit.> has been proposed to further improve recommendation performance. Feature aggregation methods typically learn representations in each domain separately and then design an aggregation function to combine these representations. On the other hand, feature disentanglement approaches concentrate on separating domain-common and domain-specific embeddings and transferring domain-common embeddings across domains. Although these works have achieved good performance, they still face two major challenges.

CH1. How to effectively protect user privacy when transferring knowledge across domains?
Most existing literature <cit.> cannot solve this problem well. They usually assume that the user-item ratings or representations are directly transferred across domains. However, in the setting of privacy-preserving, these methods are unsuitable <cit.>. 
To resolve this problem, some privacy-preserving CDR methods <cit.> have gained lots of attention. For example, PriCDR <cit.> first introduces Differential Privacy (DP) technology to publish the source rating matrix and subsequently conduct CDR modeling. P2FCDR <cit.> independently learns embeddings in each domain using orthogonal functions and applies the local differential privacy (LDP) technique to protect these embeddings. 

However, these approaches introduce a trade-off between privacy preservation and recommendation accuracy, as the added noise can distort the underlying data patterns.


CH2. How to improve recommendation performance with few overlapping users across domains? Many existing CDR methods depend on fully overlapping users as a bridge to transfer knowledge across domains <cit.>. For example, as shown in Figure <ref>, John is an overlapping user with interactions in both the Movie and Book domains. If knowledge transfer is solely based on fully overlapping users, John may be interested in the comedic book “Bossypants" because he watches movies in the same genre, like “Anchorman."  However, in real-world datasets, there are very few overlapping users. For instance, the Amazon dataset has only a 5% overlapping user ratio <cit.>. As a result, the model performance will be degraded with such sparse overlapping users.
To address this problem, we can utilize non-overlapping user information to improve recommendation performance. For instance, Lily shares similar interests with John based on their common interaction with the movie “Anchorman". By effectively utilizing Lily's interests, we can infer that John may like the thriller book “Gone Girl" based on Lily's preference for the thriller movie “Get Out", which couldn't be realized by relying solely on fully overlapping users. 


To address these challenges, we propose FedPCL-CDR, a federated prototype-based contrastive learning (CL) approach for privacy-preserving CDR (PPCDR). Our method consists of two key modules, i.e., local domain learning and global server aggregation, where user-item interaction histories and review texts are stored in local domains and knowledge is transferred via prototypes within the federated learning (FL) framework, ensuring user privacy. Specifically, in the local domain, we first learn comprehensive user and item embeddings from user-item interactions and review texts. Subsequently, we utilize k-means clustering <cit.> to generate prototypes (cluster centroids). On one hand, these prototypes convey overlapping and non-overlapping user preferences as they are derived from the interest alignments of all entities in the domain. On the other hand, these prototypes serve as generalized representations of group-level preferences, making it more difficult for attackers to infer sensitive information about individual users. We then select representative prototypes based on overlapping users and upload them to the global server. The global server, in turn, models both local and global prototypes by aggregating these representative prototypes and transmits them back to the respective local domains. To effectively transfer knowledge, the local domain refines user embeddings by using both local and global prototypes in a CL manner. This dual-prototype approach allows for transferring knowledge at varying granularities, enabling more nuanced learning of user embeddings from different perspectives.

In summary, our proposed model makes the following contributions:

    
  * We introduce a novel federated prototype-based CL approach for PPCDR that aims to solve the sparse overlapping user and privacy protection concerns.
    
  * Our method effectively leverages non-overlapping users for knowledge transfer by clustering all users, thereby enhancing model performance in scenarios with sparse overlapping users across domains.
    
  * We utilize local and global prototypes to transfer knowledge within the FL framework, protecting user privacy.
    
  * Extensive experiments on four CDR tasks from two large-scale real-world datasets, Amazon and Douban, demonstrate the effectiveness of FedPCL-CDR compared to state-of-the-art baselines.




§ RELATED WORK




 §.§ Cross Domain Recommendation

Cross-domain recommendation (CDR) aims to address the challenge of data sparsity by transferring cross-domain knowledge <cit.>. The core step in CDR involves designing an effective transfer method to improve recommendation accuracy in sparse domains.
With the advancements in deep learning, various transfer methods have emerged in CDR, including 

learning mapping functions across domains <cit.>, feature combination <cit.>, feature alignment <cit.>,

and transfer methods based on Graph Neural Networks (GNNs) <cit.>.

However, these approaches depend on fully overlapping users for knowledge transfer and overlook concerns about user privacy leakage. In this paper, we propose FedPCL-CDR to address these challenges.



 §.§ Privacy-Preserving CDR

With the increasing attention on user privacy, many scholars have begun studying PPCDR methods <cit.>. 
PriCDR <cit.> and PPGenCDR <cit.> both use DP to protect user-item ratings during knowledge transfer. P2FCDR <cit.> is a privacy-preserving federated framework that learns an orthogonal mapping matrix to transform embeddings across domains and applies LDP to the transformed embeddings for user privacy protection. Meanwhile, PPCDR <cit.> introduces a federated graph framework that utilizes FL and LDP technologies to protect user privacy. Despite their effectiveness, these PPCDR methods must strike a balance between utility and privacy. We propose a prototype-based FL framework to address these limitations.




 §.§ Contrastive Learning

Contrastive Learning (CL) has been widely used in computer vision <cit.> and natural language processing <cit.>.
It is a self-supervised learning technique that aims to maximize the mutual information between two representations. To achieve this, InfoNCE <cit.> is proposed to 
learn representations by contrasting positive pairs (similar samples) against negative pairs (dissimilar samples), which
discovers the semantic information shared by different views. Nowadays, CL has been applied to the CDR to improve representation learning <cit.>. For instance, DCCDR <cit.> leverages CL to learn domain-specific and domain-invariant representations. Meanwhile, CL-DTCDR <cit.> utilizes CL to learn more representative user and item embeddings with user-item interaction data and side information. 
However, these methods directly utilize user-item ratings or representations to construct positive and negative pairs across domains, which is not feasible under privacy-preserving constraints.
In this work, we construct prototype-based CL tasks to transfer cross-domain user interests, thereby protecting user privacy.


§ METHODOLOGY



 §.§ Definitions and Notations
  We assume there are M domains (clients) denoted as {D^1, D^2,...,D^M} and a global server, where D^i denotes the i-th domain. 
Within each domain, there exists a user set U^i and an item set V^i. 
There are partial overlapping users and non-overlapping items across domains. The overlapping user set is denoted as U^o.
Let R^i∈{0,1}^|U^i|× |V^i| represent the binary user-item interaction matrix, which is private and cannot be shared across domains. 


Figure <ref> depicts the overall framework of FedPCL-CDR. We illustrate the paradigm for domain D^i, and the corresponding paradigm for other domains can be easily inferred accordingly.






 §.§ Local domain Learning Module



  §.§.§ Graph Representation Learning

Inspired by the effectiveness of GNNs in capturing high-dimensional and complex relationships between users and items, we adopt LightGCN <cit.> to learn embeddings for user and item IDs as well as their review texts. We construct a graph G^i, where nodes represent users and items, and edges indicate interactions between them. By utilizing the graph convolution and propagation layers of LightGCN, we encode user and item embeddings based on G^i. Specifically, we denote ID embeddings and review text embeddings at the l-th layer as E_l^i(id) and E_l^i(rev), respectively. Initially, ID embeddings E_0^i(id) are randomly initialized, while review text embeddings E_l^i(rev) are learned using the document embedding model Doc2Vec <cit.>.
Given the graph G^i, E_l^i(id) and E_l^i(rev) are calculated as follows:

    E_l^i(id)   = (D^-1/2AD^-1/2)E_l-1^i(id);
    E_l^i(rev)   = (D^-1/2AD^-1/2)E_l-1^i(rev),

where D is a diagonal matrix and A is a adjacency matrix.
After l times of propagation, we can generate the final user and item ID embedding matrices  E_u^i(id) and  E_v^i(id) by concatenating multiple embedding matrices from E_0^i(id) to E_l^i(id). Similarly, we obtain the user and item review text embedding matrix  
E_u^i(rev) and E_v^i(rev). Finally, we concatenate the ID embeddings and review text embeddings to learn comprehensive user and item embeddings:







    E_u^i = f(E_u^i(id);E_u^i(rev));
    E_v^i = f(E_v^i(id);E_v^i(rev)),

where f represents the concatenation function. Here, we use the element-wise sum aggregation method.



  §.§.§ Clustering and Prototype Selection

In this subsection, our objective is to generate representative prototypes by clustering the user embeddings E_u^i. 
The clustering process incorporates data from all users within a domain, not limited to overlapping users.
This not only leverages the shared knowledge among overlapping users but also explores the effective 
utilization of knowledge from non-overlapping users.

We begin by introducing the k-means algorithm <cit.>, which aims to cluster user embeddings into K groups. 
We obtain the cluster centroid set with K clusters:

    T^i = {t_j^i}_j=1^K= Kmeans(E_u^i),

Each cluster is defined by its centroid, acting as the central representation for that particular group. 
These centroids are regarded as prototypes, providing a comprehensive integration of information from similar users. 
As a result, we derive the prototype set T^i={t_1^i, t_2^i, ..., t_K^i}.

We then select representative prototypes by considering overlapping users across domains. 
This involves choosing prototypes whose clusters include overlapping users. 
The rationale behind this choice lies in the intention that overlapping users have similar interests in different domains. 
The representative prototype set is calculated as follows:

    C^i = {t_j^i}_j=1^K {c_j^i}_j=1^K', K'≤ K.


In addition, we select overlapping users in each cluster to form the overlapping user set O^i:

    O^i = {o_j^i}_j=1^K', o_j^i ⊂ U^o.


Finally, we upload each domain's representative prototype set C^i and overlapping user set O^i to the global server.



  §.§.§ Prototype-based Contrastive Learning

In the previous subsection, we uploaded representative prototypes to the global server. 
The server then aggregates these prototypes to derive both local and global prototypes (as further discussed in the next section) 
and subsequently returns them to local domains. Due to data privacy constraints, direct transfer of original data is not feasible. To address this problem, we employ prototypes and introduce prototype-based CL losses, which comprise a global part and a local part. These prototypes represent the collective preferences of multiple users rather than any single individual, making it more difficult
for an attacker to associate a prototype with a specific user.

To transfer knowledge from other domains to domain D^i, we enforce the alignment of user embeddings with corresponding global prototypes while distancing them from distinct global prototypes. The global prototype-based CL loss is defined as follows:

    L_global^i = -logexp(f(e_u^i,g_k^i))/exp(f(e_u^i,g_k^i))+∑_g_j^i∈ A(g_k^i),j≠ kexp(f(e_u^i,g_j^i)),

where g_k^i denotes the global prototype corresponding to cluster k, to which the user embedding e_u^i belongs. We regard (e_u^i,g_k^i) that belongs to the same cluster as a positive pair.
Conversely, g_j^i denotes the global prototype corresponding to cluster j, to which user embedding e_u^i doesn't belong, and (e_u^i,g_j^i) forms a negative pair.
A(g_k^i) is the set of global prototypes excluding g_k^i.
f indicates a similar function. We define it as:

    f(e_u^i,g_k^i) = e_u^i·g_k^i/||e_u^i||×||g_k^i||/τ,

where τ represents the temperature coefficient, which controls the concentration strength of representation <cit.>.

In addition to the global prototype-based CL loss, we introduce the local prototype-based CL loss to align e_u^i with local prototypes of each domain through domain-wise CL in the latent space, enhancing inter-domain knowledge sharing. The local prototype-based CL loss is defined as follows:



    L_local^i=-1/M∑_m=1^Mlogexp(f(e_u^i,l_k^m))/exp(f(e_u^i,l_k^m))+∑_l_j^i∈ A(l_k^i),j≠kexp(f(e_u^i,l_j^i)),

where l_k^m denotes the local prototype of cluster k from domains that have overlapping users with the cluster to which the user embedding e_u^i belongs.
l_k^i indicates the local prototype of cluster k that includes e_u^i, and A(l_k^i) is the set of local prototypes excluding l_k^i.

The global and local prototypes capture cluster-relevant information at different granularity, guiding the transfer of user interests from various perspectives.




  §.§.§ Local Training

After refining the user embedding e_u^i, we concatenate it with the item embedding e_v^i and feed them into MLP layers to predict the user's preferences.
We aim to minimize the following loss function:

    L_prd^i = l(r̂^i,r^i),

where l denotes the cross-entropy loss function, r̂^i is the predictive label, and r^i is the ground-truth label.

The total loss function is defined as follows:

    L^i = L_prd^i + α(L_global^i +L_local^i),

where α is the trade-off parameter that balances the prediction loss and prototype-based CL losses. The detailed training process is in Algorithm 1 of Appendix A.


 §.§ Global Server Aggregation

After receiving representative prototype set C and overlapping user set O from all domains, the global server calculates global prototypes for each domain.
First, for overlapping user set o_k^i∈ O^i, we construct the prototype set Ĉ_k^i that includes all representative prototypes containing overlapping users with o_k^i across domains:

    Ĉ_k^i = ⋃_i'∈ D,k'≤K'{c_k'^i'|o_k'^i'∩ o_k^i ≠∅}.


Then, we calculate the global prototype g_k^i for cluster k:

    g_k^i= 1/K̂∑_k=1^K̂ĉ_k^i,

where K̂ is the length of prototype set Ĉ^i_k.

Finally, we form the global prototype set G^i={g_1^i, g_2^i,...,g_K'^i}.
The global prototype incorporates user preferences across domains from a high-level perspective.

Different from the global prototypes, for the local prototypes, we select some representative prototypes in all domains rather than a single one via similarity calculation.
Specifically, for each representative prototype c_k^i, we first calculate the cosine similarity between c_k^i and representative prototypes from other domains that include overlapping users with o_k^i. Then, we select the representative prototype with maximum similarity to c_k^i in each domain to form the local prototype set L_k^i for cluster k: 


    L_k^i = {ĉ_k^i}_k=1^K̂{l_k^i}_k=1^M, M≤K̂.


The local prototype set can be represented as L^i={L_1^i,L_2^i,...,L_K'^i}.

After aggregation, the global server sends the global and local prototype sets G^i and L^i into the local domain D^i.



 §.§ Privacy Preserving Analysis

The proposed FedPCL-CDR effectively ensures user privacy. Firstly, within the FL framework, the data in each domain remains private and localized, significantly reducing the risk of user privacy leakage <cit.>. Secondly, knowledge transfer across domains is facilitated through prototypes, which naturally protect data privacy <cit.>. These prototypes are 1-D vectors derived from averaging low-dimensional representations of samples within the same cluster, which is an irreversible process.
We provide a detailed example in Appendix B.




§ EXPERIMENTS



 §.§ Experimental Settings



  §.§.§ Datasets.

Motivated by CDR methods <cit.>, we conduct experiments on four real-world benchmark subsets from the Amazon dataset[https://cseweb.ucsd.edu/ jmcauley/datasets/amazon/links.html]: Phone, Electronics (Elec), Clothing, Shoes nad Jewelry (Cloth), and Sport, and three subsets from the Douban dataset[https://www.dropbox.com/s/u2ejjezjk08lz1o/Douban.tar.gz?e=2&dl=0]: Book, Movie, and Music.
We combine them into four CDR tasks. Table 1 of Appendix C presents basic statistics for these datasets.
For each dataset, we transform the explicit ratings into implicit feedback. 

To improve data quality, we employ filtering criteria, removing records with fewer than 10 interactions for all users and items, in accordance with existing research <cit.>.


































  §.§.§ Parameter Settings and Evaluation.

 We obtain optimal hyperparameters by optimizing the loss function (<ref>) using the Adam optimizer with a learning rate of 0.001. 
 The weight α for the prototype-based CL losses is set to 0.01. Additionally, the embedding size is fixed at 64, and the batch size is set to 128. The temperature coefficient in CL is established at 0.2, and the cluster number is set to 10. Furthermore, we apply batch normalization, dropout, and early stopping techniques to prevent overfitting. We use Hit Ratio (HR) and Normalized Discounted Cumulative Gain (NDCG) as evaluation metrics, which are frequently used in CDR methods <cit.>.

 


  §.§.§ Baseline Methods.


We compare the performance of FedPCL-CDR with SOTA baselines including NeuMF <cit.>, LightGCN <cit.>, FedNCF <cit.>, GA-DTCDR <cit.>, NMCDR <cit.>, CL-DTCDR <cit.>, GA-MTCDR-P <cit.>, PriCDR <cit.>, and P2FCDR <cit.>, which are widely used in CDR approaches <cit.>. In Appendix D, we provide detailed descriptions of these baselines. 






 
  


 §.§ Experimental Results and Analysis

 

  §.§.§ Performance Evaluation.

 We evaluate the performance of FedPCL-CDR and the baselines using commonly used evaluation metrics w.r.t. HR@10 and NDCG@10. From the experimental results in Table <ref>, We can observe that: 
 
 
  * Our model, FedPCL-CDR, surpasses other baselines, showcasing its capability to achieve satisfactory performance while also safeguarding user privacy. Specifically, FedPCL-CDR outperforms the top-performing CDR baseline by an average of 7.38% in HR@10 and 4.86% in NDCG@10 across all tasks. This improvement can be attributed to the following reasons: (1) 
 FedPCL-CDR efficiently utilizes non-overlapping user data to transfer cross-domain knowledge, which is particularly beneficial in scenarios with sparse overlapping users, such as Phone&Sport. (2) By constructing prototype-based CL tasks, FedPCL-CDR achieves more effective knowledge transfer.
  
  * FedPCL-CDR outperforms single-domain federated methods such as FedNCF. This demonstrates the significant role of cross-domain knowledge in enhancing recommendation performance within the FL framework. In addition, FedPCL-CDR performs better than PriCDR and P2FCDR, indicating that methods leveraging prototypes and FL for user privacy protection surpass those utilizing differential privacy technology. Moreover, FedPCL-CDR exceeds the performance of GA-DTCDR, which depends on fully overlapping users for knowledge transfer. This indicates that effectively utilizing non-overlapping user information can improve model performance. Finally, although our method and CL-DTCDR both use CL to transfer knowledge, FedPCL-CDR still performs better than CL-DTCDR, showing that our method not only protects user privacy but also improves model performance.
 
  * GNN-based methods outperform non-graph methods, such as LightGCN vs NeuMF. This demonstrates that incorporating high-order neighbor information can improve model accuracy.
 
  * CDR methods consistently outperform single-domain approaches, as evidenced by the comparison between GA-DTCDR and NeuMF. This shows that cross-domain knowledge can alleviate the data-sparsity issue.
 
 
 

  §.§.§ Ablation Studies.

To validate the effectiveness of each component in FedPCL-CDR, we conducted ablation experiments. 
We created two variants: 

(1) w/o loc-proto: we eliminate the local prototype-based CL loss.
(2) w/o glob-proto: we remove the global prototype-based CL loss.
The results of the ablation studies are shown in Table <ref>. We can observe that: 

(1) The inferior performance of models w/o loc-proto and w/o glob-proto demonstrates the significant contributions of local and global prototype-based CL to the outcome. 
(2) In general, w/o loc-proto contributes more, which shows that local prototype-based CL plays an important role in improving model performance.
In conclusion, each component in FedPCL-CDR plays a crucial role, demonstrating the rationality and effectiveness of our design.




  §.§.§ Performance for different proportions of overlapping users.

To assess FedPCL-CDR's capability in addressing sparse overlapping users within CDR, we manipulate the overlapping ratio specifically for Task 1 across different settings. These varying ratios signify different levels of commonality, where a higher ratio indicates a greater number of overlapping users across domains. For instance, in Task 1 with the “Phone-Sport" dataset and an overlapping ratio of 30%, the number of overlapping users is computed as 655 * 30% = 196. Due to space limitations, we report results about several representative CDR methods. The corresponding results with different overlapping ratios are shown in Table <ref>. As the overlapping ratio increases, the performance of all models demonstrates improvement. This is intuitively sensible, as a higher overlapping ratio implies a greater number of shared users, facilitating a more straightforward transfer of cross-domain knowledge. The performance of GA-DTCDR and PriCDR shows significant fluctuations, primarily because they heavily rely on fully overlapping users. In contrast, both NMCDR, CL-DTCDR and our method, FedPCL-CDR, demonstrate relatively minor changes, indicating that effectively transferring knowledge across non-overlapping users can enhance performance and ensure model stability.
 


  §.§.§ Empirical Study of Privacy.
 In this subsection, we demonstrate the privacy-preserving capabilities of our FedPCL-CDR model by simulating an attack in which an attacker attempts to reconstruct the original user embeddings from intercepted prototypes. We analyze the difficulty of this reconstruction and evaluate the effectiveness of our privacy-preserving mechanisms. We assume that an attacker intercepts the local prototypes during the client-server communication. The attacker employs a deep neural network model to infer the original user embeddings from these intercepted prototypes, training the model to minimize the difference between the reconstructed and actual embeddings.  

We use Mean Squared Error (MSE) as an evaluation metric to measure the accuracy of the reconstructed embeddings compared to the original ones. We conducted experiments on Tasks 1 and 2 and reported the results in Table <ref>. These high MSE values indicate that the attacker faces significant difficulty in accurately inferring the original user embeddings from the intercepted prototypes, demonstrating the strong privacy-preserving capabilities of our model.
 














  §.§.§ Impact of Hyper-parameters.

In this section, we assess the model's performance across different configurations of two pivotal parameters: the weight parameter α associated with prototype-based CL losses, and the cluster number c. Due to space limitations, we only report HR@10 and NDCG@10 on Tasks 1 (Phone&Sport) and 3 (Movie&Music).

    
  * Impact of α.
 We employ the parameter α to control the degree of knowledge transfer across domains. To evaluate its impact, we conduct experiments with different α values, namely [0.001, 0.01, 0.1, 0.2]. Figure <ref> illustrates the outcomes for HR@10 and NDCG@10.
We find that as the weight parameter α increases, the performance first rises and then decreases. FedPCL-CDR achieves optimal results when α is set to 0.01. 


  * Impact of cluster number c.
The number of clusters significantly influences the generalization of prototypes, thereby affecting the learning of user preferences. As shown in Figure <ref>, our model reaches its peak performance when the number of clusters is set to 10. With the increase in the number of clusters, the HR@10 and NDCG@10 metrics initially rise, reaching a maximum at c=10, and subsequently decline. This trend can be attributed to the fact that an excessive number of clusters results in overly specific prototypes, which lack generalization capabilities and lead to suboptimal knowledge transfer.








§ CONCLUSION AND FUTURE WORK

In this paper, we propose a Federated User Preference Modeling framework (FUPM) for PPCDR to address the data sparsity issue while protecting user privacy. Within FUPM, we first design a comprehensive preference exploration module to learn comprehensive user preferences from review texts and potentially positive items. 

We then devise a private preference transfer module to privately transfer user preferences within the FL framework. Importantly, in order to protect user privacy during cross-domain knowledge transfer, we learn local prototypes and apply LDP techniques to them before transfer. Extensive experimental results on four CDR tasks based on real-world Amazon and Douban datasets demonstrate the effectiveness of our proposed FUPM. 

Our study assumes overlapping users and non-overlapping items across domains. While our method can be extended to scenarios with partially overlapping users, it is not applicable to scenarios with no user overlap or only partial item overlap. Future work includes exploring effective methods to address these challenges.































 







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