FedGR: Federated Graph Neural Network for Recommendation Systems
Abstract
:1. Introduction
2. Related Work
2.1. Social Recommendation
2.2. Graph Neural Network for Recommendation Systems
2.2.1. For General Recommendation
2.2.2. For Sequential Recommendation
2.3. PrivacyProtection Recommendation
3. Proposed Framework
3.1. Model Overview
3.2. Item Model
Algorithm 1 Item Embedding 
Input: feature set of item i
$${F}_{i}={f}_{1},{f}_{2}\cdots {f}_{n}$$

3.3. User Model
3.3.1. Item Graph Representation
Algorithm 2 Item Graph Representation 
Input: Input of the user–item graph and the embedding representation of the corresponding item (obtained from the server side)
$${G}_{i}^{I},{E}_{i}^{h}$$

3.3.2. Social Aggregation
Algorithm 3 Social Representation 
Input: input social graph/user–friend–item graph/friends itemembedding set
$${G}_{i}^{s},{G}_{i}^{f},{E}_{i}^{f}$$

3.4. Security Model
4. Experiment
4.1. Experimental Settings
4.1.1. Datasets
4.1.2. Evaluation Metrics
4.1.3. Parameter Settings
4.1.4. Baselines
 SoReg [28]: A factor analysis recommendation algorithm based on the probability matrix decomposition.
 SocialMF [29]: Introducing trust propagation in matrix decomposition, the user indicates that friends close to that user indicate.
 GraphRec [2]: Graph neural networks are used to learn user embeddings and item embeddings from user history product graphs and social graphs.
 GCMC+SN [25]: A graphneuralnetworkbased recommendation model is used to generate embeddings for each user in the social network using the node2vec technique.
 FeSoG [30]: A social recommendation system with privacy protection, using local differential privacy (LDP) and pseudoitem labeling as a means of user data privacy protection.
 FedMF [26]: The representation of each user is computed by matrix factorization, and homomorphic encryption is used to protect the user data from disclosure.
4.2. Quantitative Results
4.3. Analysis of Parameters
5. Conclusions and Future Work
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbol  Definitions and Descriptions 

${p}_{i}$  embedding of user i 
${q}_{j}$  embedding of item j 
$f{e}_{i}$  friends embedding of user 
${r}_{ij}$  user i’s rating score for item j, ${r}_{ij}$ in [0,1,2,3,4,5] 
${\alpha}_{ij}$  weighting factor of item j to user i 
${\beta}_{ij}$  weighting factor of friend j and user i 
${\upsilon}_{i}$  product of the item embeddings of user i and the corresponding score embeddings 
${h}_{i}$  collection of historical interaction item IDs for user i 
${h}_{i}^{noise}$  collection of noise item IDs added by user i 
${F}_{i}$  a set of features of item i,${F}_{i}$ = ${f}_{1},{f}_{2}\cdots {f}_{n}$ 
$F{E}_{i}$  a set of features embedding representation of item j,$F{E}_{i}$ = $f{e}_{1},f{e}_{2}\cdots f{e}_{n}$ 
${\psi}_{i}$  embedding representation learned by user i in the user–item graph 
${\psi}_{i}^{f}$  the embedding representation learned by user i friends in the user–item graph 
${\mu}_{i}$  embedding representation learned by user i in the social graph 
${G}_{i}^{I}$  history item graph of user i 
${G}_{i}^{s}$  social relation graph of user i 
${G}_{i}^{f}$  friends item graph of user i 
${E}_{i}^{h}$  history item embedding set of user i 
${E}_{i}^{f}$  friends history item embedding set of uer i 
${e}_{ij}$  user i’s rating of item j embedding 
${\Delta}_{i}$  user i obtains the set of item IDs from the server 
Datasets  Ciao  Epinions 

Users  2248  22,168 
Items  16,862  296,277 
Ratings  36,065  920,075 
Social Connections  57,545  355,812 
Rating Scale  [1,5]  [1,5] 
Method  Ciao MAE  Ciao RMSE  Epinions MAE  Epinions RMSE 

SoReg  0.8627  1.1021  0.9119  1.1703 
SocialMF  0.8270  1.0501  0.8837  1.1328 
GraphRec  0.8141  1.0133  0.8326  1.0814 
SoRGCMC+SN  0.7824  1.0031  0.8480  1.1070 
FeSoG  1.4937  1.9136  1.3847  1.7969 
FedMF  2.0792  2.4216  1.5254  2.0685 
FedGR  1.3650  1.7941  1.2773  1.5806 
Improvement (%)  8.6  6.2  7.7  12.1 
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Ma, C.; Ren, X.; Xu, G.; He, B. FedGR: Federated Graph Neural Network for Recommendation Systems. Axioms 2023, 12, 170. https://doi.org/10.3390/axioms12020170
Ma C, Ren X, Xu G, He B. FedGR: Federated Graph Neural Network for Recommendation Systems. Axioms. 2023; 12(2):170. https://doi.org/10.3390/axioms12020170
Chicago/Turabian StyleMa, Chuang, Xin Ren, Guangxia Xu, and Bo He. 2023. "FedGR: Federated Graph Neural Network for Recommendation Systems" Axioms 12, no. 2: 170. https://doi.org/10.3390/axioms12020170