# DPMF: Decentralized Probabilistic Matrix Factorization for Privacy-Preserving Recommendation
## 5 Conclusions  
In this study, we propose a privacy-preserving recommendation framework based on decentralized probabilistic matrix factorization called DPMF. Specifically, we devise a novel model combining explicit and implicit feedback into a probabilistic matrix co-factorization model by decomposing observed data into explicit and implicit data matrixes and mapping users and items to a shared subspace of low dimensionality. Besides, we propose a novel decomposing strategy under decentralized settings to keep users' private information at their end while users' public information is shared and helps to learn the model collaboratively. The experiments on two real-world datasets demonstrate that compared with classic models, the proposed model improves its performance in lower loss in rating prediction task and higher precision in item recommendation task. Furthermore, the complexity analysis shows that our method is practical with linear computation and communication complexity.  
In the future, we will focus on model compression. The recommendation model has made significant progress in using users' data to predict user preferences and model item characteristics. However, the scale of recommendation model is becoming larger since there are increasing parameters, thus the storage overhead is becoming higher. How to reduce the storage of the recommendation model will be our next stage of work.  
Conceptualization, X.Y., Y.L.; methodology, X.Y., Y.L. and S.F.; software, X.Y.; validation, X.Y.; formal analysis, X.Y. and Y.L.; investigation, X.Y.; resources, X.Y. and M.X.; data curation, X.Y. and M.X.; writing--original draft preparation, X.Y.; writing--review and editing, X.Y., S.F. and Y.C. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Nature Science Foundation of China (No.62102429, 62102422, 62072466, 61872372), the Natural Science Foundation of Hunan Province (No.2022 JJ30667), and the NUDT Grants (No.ZK19-38).  
Not applicable.  
The principal datasets used in this research can be downloaded from [[https://guoquibing.github.io/librec/datasets.html](https://guoquibing.github.io/librec/datasets.html)]([https://guoquibing.github.io/librec/datasets.html](https://guoquibing.github.io/librec/datasets.html)) and [[http://www.trustlet.org/epinions.html](http://www.trustlet.org/epinions.html)]([http://www.trustlet.org/epinions.html](http://www.trustlet.org/epinions.html)). Accessed 25 August 2022.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{_FilmTrust_} & \multicolumn{2}{c}{_Epinions_} \\ \hline Metrics & \(P\)@5 & \(R\)@5 & \(P\)@5 & \(R\)@5 \\ \hline Dimension & & \multicolumn{2}{c}{\(K=3\)} & \\ \hline PMF & 0.0332 & 0.0711 & 0.0715 & 0.1529 \\ \hline WRMF & 0.0352 & 0.0751 & 0.0717 & 0.1497 \\ \hline DPMF & 0.0342 & 0.0722 & 0.0716 & 0.1524 \\ \hline Dimension & & \multicolumn{2}{c}{\(K=6\)} & \\ \hline PMF & 0.0380 & 0.0771 & 0.0761 & 0.1571 \\ \hline WRMF & 0.0379 & 0.0763 & 0.0760 & 0.1563 \\ \hline DPMF & 0.0396 & 0.0796 & 0.0781 & 0.1599 \\ \hline Dimension & & \multicolumn{2}{c}{\(K=12\)} & \\ \hline PMF & 0.0410 & 0.0831 & 0.0781 & 0.1611 \\ \hline WRMF & 0.0404 & 0.0823 & 0.0789 & 0.1603 \\ \hline DPMF & 0.0435 & 0.0889 & 0.0821 & 0.1653 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance comparison for item recommendation task.