Enhancing Dual-Target Cross-Domain Recommendation with Federated Privacy-Preserving Learning

1 Introduction

Targeting the existing problem of data sparsity in the realworld scenarios, dual-target cross-domain recommendation (DTCDR) has been widely employed in a myriad of real-life applications [Zhang et al., 2023]. Different from the so-called single-target CDR exploiting abundant information from a relatively richer domain to improve recommendation performance on a sparser domain [Guo et al., 2021], DTCDR aims to improve the recommendation accuracies on both sparse domains simultaneously by making good use of the knowledge from both domains, shown in Fig. 1(a).

However, most existing DTCRD methods often assume that the personal data of shared users, serving as the bridge for knowledge transferring, can be directly accessed or available in every situation [Zhu et al., 2021a]. This is unrealistic and may raise trust concerns of users about privacy leakage problems. For example, any user is unwilling to share his or her sensitive data when two company attempt to collaborate on a promotion campaign based on these shared users. Besides, many law regulations [Du et al., 2021; Liu et al., 2023a] (e.g., GDPR and CCPA) are adopted to limit the transportation and exploitation of personal data, resulting in the prohibition of collecting user data. Since public awareness of privacy protection results in a controversial view of DTCDR, a nature question is raised: How can we design a novel DTCDR while protecting the user privacy?

∗Yanchao Tan is the corresponding author.

To solve this problem, we need to focus on two central challenges. Challenge I: what to transfer aims at mining valuable transferable knowledge from different domains under a privacy-preserving scenario; Challenge II: how to recommend is dedicated to designing appropriate DTCDR paradigm based on the protected transferable knowledge. For the first challenge, a straightforward idea is to exploit federated learning (FL) to collaboratively learn inter-client knowledge across a variety of clients without sharing private data. Nevertheless, most of these methods depend on gradientbased aggregation, resulting in heavy reliance on homogeneous local models but also expose clients' models, which further raise privacy concerns [Wang et al., 2023]. For the second challenge, existing DTCDR methods perform the recommendation based on direct usage of the knowledge from the auxiliary domain. When transferred data is protected, most of the DTCDR models may fail or obtain rather inaccurate representations [Yang et al., 2022]. Besides, most federated DTCDR often assumes a high ratio of shared users (even completely overlapping) between domains and the ID of shared users can be obtained as prior knowledge, shown in Fig 1(b), which is not so practical under the federated scenarios. Hence, how to recommend the items based on the protected knowledge under the privacy-preserving settings is still an open problem.

To alleviate the above challenges, in this paper, we introduce the P2DTR framework, a novel approach in Dual-Target cross-domain Recommendation with federated Privacy-Preserving Learning, which consists of two pivotal technical components. For Challenge I, we design a novel inter-client knowledge extraction mechanism under a privacy-preserving scenario. That is, we exploit the prototypes of user preferences to solely share class representatives as common knowledge, e.g. the users who have cartoon taste may also like the comedy theme, while maintaining the privacy of clients' models shown in Fig 1(c). Specifically, we first perform the private set intersection (PSI) to find out the same users between different domains as the bridge to exchange the inter-domain knowledge. Then, we enable the users in both domains and a server to collaboratively learn the privacy-preserved common knowledge through federated prototype-based learning. For Challenge II, we propose intra-client enhanced recommendation to improve the recommendation performance based on the extracted common knowledge across domains. Specifically, the novel constrained dominant set (CDS) propagation mechanism is designed to enhance the DTCDR based on the extracted common knowledge. And dual recommendation is proposed to inject the collaborative relations into recommendation.

Finally, we evaluate the proposed P2DTR with extensive experiments on four real-world benchmark datasets for federated DTCDR. Extensive experimental results show that the proposed P2DTR is able to significantly improve the recommendation performance under privacy-preserving scenarios over all baselines (e.g., with up to 18.32% improvements in NDCG@10 on the cloth dataset over the best baseline).

Our overall contributions are summarized as follows:

• Formulation of federated DTCDR: We propose a privacypreserving setting tailored for dual-target cross-domain recommendation that considers a more general federated scenario across local clients.
• Effective model designs: We propose an effective framework P2DTR to perform dual-target cross-domain recommendation while protecting the user privacy, through interclient knowledge extraction mechanism and intra-client enhanced recommendation module.
• Extensive experiments on real-world datasets: Extensive experiments show the superiority of our proposed method in terms of test performance under a privacy-preserving guarantee in several benchmark datasets.

2 RelatedWork

2.1 Cross-Domain Recommendation

Cross-domain recommendation (CDR) is widely employed to overcome the issue of data sparsity in recommendation systems. Traditional methods, like single-target CDR, leverage the richness of information from the source domain to improve recommendations in sparser target domains. For example, NCF [He et al., 2017] employs multi-layer perceptrons to learn the user-item interaction arbitrary function, replacing the inner product. DCDCSR [Zhu et al., 2018] combines matrix factorization models and addresses challenges in cross-domain and cross-system recommendations. In recent years, the introduction of dual-target CDR seeks to enhance recommendation performance in both domains concurrently. For example,VDEA [Liu et al., 2022] utilizes dual variational autoencoders with both local and global embedding alignment to exploit domain-invariant user embeddings. CPKSPA [Liu et al., 2023f] introduces a cross-domain recommendation framework with three modules, which demonstrates superior performance compared to the state-of-the-art models. IESRec [Liu et al., 2023e] incorporates an internal multi-interest exploration module and an external domain alignment module.

The aforementioned methods are having significant risks to user's privacy security, where every piece of content they use is closely associated with the user themselves. Different from these approaches, our proposed framework is designed with considerations for a federated scenario to ensure the protection of user privacy.

2.2 Federated Recommendation

Federated Learning (FL) is widely applied in various applications, enabling collaborative learning across diverse clients without the need to share private data. Traditional federated learning methods rely on gradient-based aggregation. In FedAVG [McMahan et al., 2017], local devices upload their model parameters to the server, which computes the global average parameters and broadcasts them back to all devices. This process iterates until convergence. PFedRec [Zhang et al., 2023] was proposed to effectively learn fine-grained personalization on both users and items. To address the high communication costs in gradient aggregation and the heavy reliance on homogeneous local models, a prototype-based federated learning approach has been proposed. For example, FedProto [Tan et al., 2022a] aggregates local prototypes and maintains proximity to the global prototype to regularize the training of local models, minimizing classification errors, which achieved desired performance with limited users. FPPDM [Liu et al., 2023b] integrates local domain modeling, global server aggregation, and the compact co-clustering strategy from FPPDM++ to enhance the extraction of semantic neighbor information among the whole overlapping users.

Unlike the aforementioned methods assuming a high ratio of shared users (even completely overlapping) between domains and the ID of shared users can be obtained as prior knowledge, our method considers DTCDR with a few unknown shared users.

3 Methodology

3.1 Problem Statement and Overall Architecture

Our goal of P2DTR aims to perform dual-target cross-domain recommendation while protecting user privacy. Formally, there exist two domains (clients), e.g., client A and client B. We use DA = (UA, VA, EA) and DB = (UB, VB, EB) to represent the data included in two clients, where U, V and E are the user set, item set and edge set in each client, respectively. Here, we define UA = {Ua, Us} and UB = {Ub, Us}, where Us = UA∩UB is the shared user across two clients and Ua, Ub are the users belonging to the specific client. Besides, we introduce RA ∈ R|UA|×|VA| and RB ∈ R|UB|×|VB| to represent their user-item interactions in the clients A and B. The value of Rij is set to 1 if the i-th user ui ∈ U has interacted with the j-th item vj ∈ V. Otherwise, Rij = 0. The inputs of our proposed P2DTR are user-item interactions RA and RB on two clients. The outputs are the predicted probability matrices ˆRA and ˆRB, where the value of ˆRij represents the probability that the j-th item is recommended to the i-th user in each client. Scenarios with multiple clients can be easily extended from this scenario.

We summarize the main steps of the P2DTR framework in Fig. 2 and provide an overview. Our proposed model has two main steps. Step 1: We peform inter-client knowledge extraction under privacy-preserving scenarios. Specifically, we first initialize the shared users between different domains by PSI algorithm. Then, to enable the users in both domains and a server to collaboratively capture the common knowledge, we propose a federated mechanism based on prototype learning. Step 2: To enhance the DTCDR based on the extracted common knowledge, we design a novel Intraclient Enhanced Recommendation, CDS propagation mechanism and dual-recommendation module.

3.2 Inter-client Knowledge Extraction

Private Set Intersection (Client-Client). To employ abundant information from both domains to improve dual-target recommendation performance, the first step is to find out the same users between different domains as the bridge to exchange the shared inter-domain knowledge. However, due to the privacy policies, the ID of the shared user can not be directly obtained. Therefore, we exploit the private set intersection (PSI) based on RSA encryption/decryption algorithm and hashing algorithm [Huang et al., 2023]. Specifically, client A first generates the public key: (n, b) and private key: (n, d) by the RSA algorithm, and passes the public key to client B. Then, client B encrypts the user ID x and returns encrypted YB to client A, which can be formulated as YB = {ri b%n ∗ Hash(x)}. Here, Hash(x) is the hash function equivalent to encryption and ri is a generated random number. After receiving YB, client A decrypts YB with the key d to get ˆ YB = {ri ∗ (Hash(x))d%n}, where the key b and d corresponding to ri are canceled, simultaneously. Then, client A makes one more hash with private key d as the index to get ˆ YA = {Hash(Hash(x))d%n | x ∈ clientA}. Here, client A returns ˆ YA and ˆ YB together to the client B. The random noise in ˆ YB can be eliminated and client B can perform one more hash to generate the user set ˜ YB. Finally, we get the intersection of ˆ YA and ˜ YB to obtain the shared user set Us. The process is formulated as

Prototype Learning (Client-Server). To enable the users in both domains and a server to collaboratively train models and help them supervise each other, we design a federated mechanism based on prototype learning. Specifically, we first extract the domain-specific by graph neural networks (GNNs) on each client. We first adopt a trainable lookup table to transfer the user and item one-hot coding and combine them as XA ∈ R(|UA|+|VA|)×d = [XUA;XVA], XB ∈ R(|UT |+|VB|)×d = [XUB ;XVB ], where XUA, XUB are the user embeddings and XVA, XVB are the item embeddings in client A and B. Then, we define the adjacency matrix Ak ∈ R(|Uk|+|Vk|)×(|Uk|+|Vk|) by combination of user-item ranking matrix Rk, formulated as Ak = [ Rk 0 0 RkT ], and k ∈ {A, B} means the k-th client. In consequence, the graph convolution can be formed:

where ˜D is the degree matrix of ˜ Ak and ˜ Ak = Ak +IN and IN is the degree matrix to add the self loop. We use W lσ,k andW lµ,k to represent the weights of graph convolution networks in l-th layers.

Since user behavior data contain abundant personal identifiable information, we use the prototypes (the group features of user preference) as the common knowledge to be aggregated on the server. Specifically, we assume two clients reach a protocol: the shared users have K common preferences. Then, we initialize the user prototype indicator matrix Hk ∈ R|Us|×K in k-th client, where |Us| is the number of shared users. Then, the prototypes Ck ∈ RK×d can be calculated by Ck = HTk XUk,s , where XUk,s ∈ R|Us|×d is the shared user embedding caculated by shared user set in Equation 1 and graph convolution in Equation 2. To further protect user privacy, we exploit the differential privacy (DP) [Li et al., 2016] to protect the prototype through data perturbation, which is defined as

Definition 1 (ϵ-Differential Privacy). Given two neighboring datasets D and D′ , a random algorithm P satisfies ϵ-DP if its all output O ∈ Range(P) satisfies

To start with, we first generate a random projection matrix P ∈ Rd×d from the normal distribution according to [Liu et al., 2023d]. Then, we further generate a noise matrix ∆ ∈ RK×d . Therefore, We can transform the source prototype Ck Client B

Figure 2: The overall architecture of P2DTR. Firstly, the shared users are initialized by PSI algorithm (client-client). Then, the shared user embeddings are fed to the prototype learning under federated scenarios to capture the common knowledge (client-server). Based on extracted common knowledge, CDS propagation is exploited to enhance the recommendation.

into PCk = CkP +∆. Therefore, we upload the encrypted prototype PCk from k-th client to the server for aggregation. The aggregation formula of the prototype is shown as

where Avg(·) is the average function of all prototypes uploaded to the server. Finally, to maintain inter-client consistency for common knowledge, the average prototype P ¯ C is downloaded to the local clients and we propose a regularization term to reduce the distance among the local and global prototypes. The loss function of above process can be formed in k-th client:

3.3 Intra-client Enhanced Recommendation

Constrained Dominant Set Propagation. To enhance the DTCDR based on the extracted common knowledge, we design the novel constrained dominant set (CDS) propagation mechanism and dual-recommendation module. We first calculate the enhanced shared user representations ZUk,s = Hk(P ¯ C) based on the average prototype P ¯ C . Then, following the theory of deep constrained dominant set [Alemu et al., 2019] to constrain that each cluster should contain the shared users, we exploit the CDS clustering to update the whole local user embeddings with shared features. Since the process of constrained clustering can be seen as finding constrained dominant sets under global similarity, we first need to construct the global similarity matrix ˆ Ak = ZUk (ZUk )T in kth client and select the constrained dominant sets Pk for graph Gk = (Uk, Vk, Ek). To alleviate computational costs, we adopt the mini-batch technique to sample M shared users and M unshared users randomly. We can combine them and define the sampled global similarity matrix as ˆ Amk ∈ R2M×2M . Considering the constrained sets P m k ⊆ Us ⊆ Uk, where Us is the shared user, we set the diagonal elements corresponding to the subset Uk\P m k to parameter α, where Uk\P m k means the the difference between set Uk and set P m k . Besides, the diagonal elements corresponding to the constraint sets P m k is set as zero. Then, we can obtain the final modification of the similarity matrix Bmk Next, the modified adjacency matrix Bmk is fed to the Replicator dynamics [Weibull, 1997] to ensure that all the users in the mini-batch are assigned equal membership probability to be part of the cluster. According to the optimization for constrained dominant sets [Zemene and Pelillo, 2016], finding a constrained cluster can be defined:

where we define ∆ = {h ∈ R2M : ∑2M i=1 hi = 1, and hi ≥ 0 for all i = 1, ..., 2M} and Bmk = Amk - αˆ IP m k . The elements of diagonal matrix ˆ IP m k ∈ R2M×2M are set to 0 in correspondence to the constrained dominant sets P m k and to 1 otherwise. From well-studied evolutionary game theory [Skoulakis et al., 2021], the straightforward continuous optimization technique of Equation 6 are as follows:

In consequence, we can obtain the optimal k-th domain solution hk,i ∗ ∈ R2M and we select the solution corresponding to M shared users as the final clustering results, written as ˆHmk ∈ RM×2M = [hk,1; . . . ; hk,M]. After obtaining the similarity between shared and global users, we exploit shared user representation to enhance the whole embedding as ZU,m k = ( ˆHmk )T ZU,m k,s where ZU,m k,s is the shared user representation in the minibatch of k-th client.

Dual-target Cross Domain Recommendation. Obtaining the enchanted user embeddings, we exploit the paradigm of collaborative filtering (CF), which is often adopted in recommender systems. The final user embedding ΨUk and item embedding ΨVk can be obtained by the graph-based CF message aggregation mechanism:

Here, DV ∈ R|Vk|×|Vk | and DU ∈ R|Uk|×|Uk | are the diagonal degree matrices of user-item and item-user interaction matrices RTk ∈ R|Vk|×|Uk | and Rk ∈ R|Uk|×|Vk| . Then, the preference score ˆRk can be predicted by ˆRk = ΨUk (ΨVk )T and the value ˆ rij in ˆRk means the probability of item j recommended to user i in k-th client. We adopt the BPR loss, which is a common loss function in recommendation tasks:

where σ is the activation function. jp and jn denote the positive and negative samples for cold-start user i. Finally, We train our recommender systems with the combination loss to jointly optimize P2DTR:

where λ is the hyperparameter to control the strength of gradients. The loss functions LfA and LfB are the consistency loss calculated by Equation 5.

Note that, we only illustrate the federated DTCRD with two clients (K = 2). The multi-client scenario can be easily extended by adding the different clients to prototype-based federated learning, where each client can get the intersections of shared user ID in this domain with other domains, and then just merge these intersections to a union set to construct the multi-client PSI algorithm.

3.4 Convergence Analysis

In this part, we will demonstrate the theoretical analysis of our proposed P2DTR and illustrate the convergence guarantees under the specific hyperparameters. Firstly, to better represent the process of local model update, additional variables are introduced and we can rewrite the loss function of k-th client (domain) in Equation 10 as the formulation:

where LS(·) is the loss function about the local client (domain) and λ ∥∥fk (ϕk; x) -P ¯ Cj ∥∥22 means the loss function corresponding to the global server after j-th prototype aggregation. we define fk (ϕk) : Rdx → Rdc to be the embedding function of the k-th client, where dx and dc represent the dimension of the input x and the prototype c. The function gk (vk) : Rdc → Rdy means the prediction layer in the federated partial recommendation for all clients, in which dy represents the dimension of output y. In consequence, the whole federated DTCDR can be written as Fi (ϕk, vk) = gk (vk) ◦ fk (ϕk), where ϕk and vk are the learnable weights in networks. Furthermore, we make the following assumption, similar to existing general frameworks [Tan et al., 2022b]: (1) Lipschitz Smooth; (2) Unbiased Gradient and Bounded Variance; (3) Bounded Expectation of Euclidean Norm of Stochastic Gradients; (4) Lipschitz Continuity. More details about assumptions could be referred to Appendix due to space limitations.

Based on the above assumptions, we analyze the theoretical results under non-convex conditions. The expected decrease per round is given in Theorem 1. We denote e ∈ {1, 2, ...,E} as the local iteration, and t ∈ {1, 2, ..., T} as the global communication round. Moreover, we use 1/2 as the intermediate value to distinguish operations between clients and the central server. Specifically, tE represents the time step before prototype aggregation (clients complete iterations), and tE + 1/2 represents the time step between prototype aggregation and the first iteration of the current round. More proof details can be referred to the Appendix.

Theorem 1. (Non-convex convergence rate of P2DTR) When the learning rate satisfies η < 2(δ-λL2G) L1(δ+σ2 ) , and the hyperparameter satisfies λ < δ L2G , given any δ > 0 for an arbitrary client, we have

Corollary 1. Let η = O(1/√T) with the upper bound of 2 (δ - λL2G) /L1 (δ + σ2 ), and let λ = O(1/√T ) with the upper bound of δ/L2G, the proposed P2DTR achieves a convergence rate of O(1/√T ).

4 Experiment

In this section, we start with a brief description of conducted datasets on four real-world datasets and experimental settings. Then, we evaluate our proposed P2DTR framework focusing on the following research questions :

RQ1: How does P2DTR perform in comparison with other state-of-the-art models for federated DTCDR?

RQ2: How does each component devised in the P2DTR contribute to performance improvement?

RQ3: How do the hyperparameters affect the prediction performance and how to choose optimal values?

4.1 Experimental Settings

Dataset. On the basis of the previous works, we build our scenarios using the chosen cross-domain recommendation datasets [Zhu et al., 2022], and the preprocessing settings with two domains (K = 2). In particular, we carry out experiments on the large-scale public Amazon datasets. To evaluate DTCDR models for the federated bi-directional CDR scenarios, we choose two pairs of domains from Amazon datasets: there are Game-Video and Cloth-Sport (four datasets). Note that, to validate the superiority of our proposed framework, we recommend items in both domains for the whole users and cold-start users. Specifically, in the data preprocessing, we filter out the items that have fewer than 10 interactions and the users that have fewer than 5 interactions in their domains as the previous works [Cao et al., 2022]. For each user, we use the first 40% of data as the training set, 30% data as the validation set, and 30% data as the testing set. Besides, we filter the users that have fewer than 3 interactions in the training data as the cold-start users. The concrete statistics of federated DTCDR scenarios are summarized in Table 1. Note that, we also conduct experiments under the multi-domain scenarios on Douban datasets with (K = 3), which follows [Liu et al., 2023c]. More details about the multi-domain results could be referred to Appendix due to space limitations.

Evaluation Protocol. On the basis of the previous works [Kang et al., 2019], the leave-one-out evaluation method is widely used [Zhu et al., 2021b]. To illustrate the effectiveness of methods, we adopted leave-one-out evaluation as well. Specifically, we calculate 1000 records (1 positive and 999 negative samples) and the three adopted metrics under federated DTCDR are MRR, NDCG@5,10 and HR@1,5,10, similar to [Cao et al., 2022; Liu et al., 2023c].

Compared Methods. To illustrate the effectiveness of our proposed framework, we compare P2DTR with the following SOTA baselines which can be divided into three branches. (1) Single-domain recommendation: PMLAM [Ma et al., 2020], LightGCN [He et al., 2020] and CGCL [He et al., 2023]; (2) Dual-target cross-domain recommendation: CoNet [Hu et al., 2018], ETL [Chen et al., 2023b] and CDRIB [Cao et al., 2022]; (3) Federated dual-target cross-domain recommendation: FedGNN [Meihan et al., 2022], PriCDR [Chen et al., 2022], FedCDR [Wu et al., 2022], P2FCDR [Chen et al., 2023a] and FPPDM [Liu et al., 2023c].

Parameter Settings. In our experiments, we use official implementations of other baselines. For the common hyperparameters in the baselines, we adopt the same value for all the methods, such as the embedding dimension d to 128, the batch size to 1024 and the minibatch size to 128 or 256. For the specific hyperparameters in the baselines, what we adopt are the values which have been reported in their original literature. For our proposed model P2DTR, we tune the hyperparameter λ in {102 , 10, 1, 1e-1 , 1e-2 }, the number of prototypes in {16, 32, 64, 128} and the number of graph encoder layer in {1, 2, 3, 4}. In our model, we use Adam optimizer and the decay learning rate. For all these methods, we run each experiment with a random seed for five times and select the best result according to the highest MRR performance on the validation set, tuned by grid search.

4.2 Overall Performance Comparison (RQ1)

To verify the effectiveness of our proposed model, we consider limited user transferring for the federated DTCDR. We compare the experimental results of our proposal P2DTR with other SOTA baselines, shown in Table 2, and we can have the following observations.

In general, our P2DTR outperforms all baselines across all evaluation metrics on all real-world datasets, which answers RQ1 with an effective framework. Note that, limited by the federated experimental settings, the privacy data from different domains are prohibited from transmitting data directly. Compared with the second-best performance, the performance gains of P2DTR range from reasonably large (2.83% achieved with HR@5 on sport) to significant large (16.82% achieved with MRR on video).

In particular, we compare the single-domain methods of collaborative filtering without auxiliary cross-domain contents with our P2DTR. The results by P2DTR outperform the three baselines across all evaluation metrics on all datasets, which illustrates the DTCDR is an effective way to alleviate data sparsity. Besides, by considering both DTCDR and privacy protection, P2DTR performs better than crossdomain baselines. Although existing cross-domain methods can jointly capture knowledge from both domains, it fails to transfer the knowledge when the user data user data cannot be directly accessed. In this way, P2DTR can outperform CDRIB by up to 34.3% in NDCG@10 on game dataset. Moreover, compared with the federated DTCDR models, although FPPDM can achieve the second-best performance via server aggregation to combine user characteristics across domains, our proposed P2DTR can still gain improvements by enhancing the local user embeddings via intra-client enhanced recommendation.

Furthermore, to provide a more comprehensive demonstration of our model in capturing the auxiliary information from both domains, we also present the experimental results for cold-start users with other SOTA federated DTCDR methods. From the Table 3, we can observe the performance gains of P2DTR in terms of FPPDM range from reasonably large (5.34% achieved with MRR on game) to significant large (17.31% achieved with MRR on video). The experimental results demonstrate the effectiveness of our proposed P2DTR in enhancing the federated DTCDR based on the transferred knowledge across domains.

4.3 Ablation Experiment (RQ2)

In order to comprehensively evaluate the performance of our method, we conducted ablation experiments on our framework by incrementally adding components to answer RQ2. We adopted the widely used model, LightGCN, as our base model. Subsequently, we introduced Inter-client Knowledge Extraction (+Inter) followed by Intra-client Enhanced Recommendation (+Intra). The conclusions can be drawn by taking insights into Table 4.

Compared with the base model, Base+Inter implementation achieved an increase in model capability from 12.2% (achieved in HR@5 on Game) to 63.3% (achieved in NDCG@5 on Game). The experimental results demonstrated superior performance, highly indicating the effectiveness of the inter-client knowledge extraction. In addition, the increase from Base+Inter+Intra (our proposed P2DTR) over Base+Inter within the range of 21.1% (achieved in MRR on Game) to 78.5% (achieved in MRR on Video). While the Base+Inter has already shown significant improvements, our P2DTR can further enhance the performance through a welldesigned intra-client enhanced recommendation.

4.4 Hyperparameter Study (RQ3)

Our proposed P2DTR framework mainly introduces two hyperparameters, i.e., the number of prototypes K and graph layers L, respectively. Here we show how these two hyperparameters impact the performance, which answers the RQ3. From Figure 3, we have the following observations: (1) L is the number of graph neural network layers, where we found that the optimal values are about 2, 3 and 4 layers, which is sensitive to the hyperparameter. We set L = 3, which seems to be the rule-of-thumb. (2) K is the number of prototypes, where we found the optimal values are 16, 32 and 128. In consequence, our P2DTR is reasonably sensitive to the prototype number K and the optimal parameters can be obtained by slight tuning.

5 Conclusion

In this paper, we propose a novel framework named P2DTR to perform DTCDR while protecting the user privacy. Specifically, we devise inter-client knowledge extraction to capture the inter-client knowledge under a privacy-preserving scenario. Furthermore, we design an intra-client enhanced recommendation to perform federated DTCDR based on the extracted common knowledge. Finally, we conduct extensive experiments to show the effectiveness of our proposed P2DTR framework under a privacy-preserving guarantee on both domains.

Acknowledgments

This work is in part supported by the National Natural Science Foundation of China under Grants 6230071268, U21A20472 and 62276065; the National Key Research and Development Plan of China under Grant 2021YFB3600503; the Fujian Provincial Youth Education and Scientific Research Project under Grant JAT220811.