## 5 Application Instances of Proposed SDP
### Application Instance-2: SDPTrustSVD
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Metrics** & **TrustSVD** & **SDPTrustSVD** & \begin{tabular}{c} **Improved** \\ **(vs. TrustSVD)** \\ \end{tabular} \\ \hline \multirow{3}{*}{\begin{tabular}{c} Flixster \\ (d = 5) \\ \end{tabular} } & RMSE & 0.92323 & 0.90564 * & 1.91\% \\ \cline{2-5}  & RE & 0.23451 & 0.23032 * & 1.79\% \\ \cline{2-5}  & MAE & 0.68654 & 0.66460 * & 3.20\% \\ \hline \multirow{3}{*}{\begin{tabular}{c} Flixster \\ (d = 10) \\ \end{tabular} } & RMSE & 0.92337 & 0.91548 * & 0.85\% \\ \cline{2-5}  & RE & 0.23455 & 0.23254 * & 0.86\% \\ \cline{2-5}  & MAE & 0.68669 & 0.67480 * & 1.73\% \\ \hline \multirow{3}{*}{\
\begin{tabular}{c} FilmTrust \\ (d = 5) \\ \end{tabular} } & RMSE & 0.81201 & 0.79262 * & 2.39\% \\ \cline{2-5}  & RE & 0.25856 & 0.25241 * & 2.38\% \\ \cline{2-5}  & MAE & 0.63938 & 0.61474 * & 3.85\% \\ \hline \multirow{3}{*}{
\begin{tabular}{c} FilmTrust \\ (d = 10) \\ \end{tabular} } & RMSE & 0.81924 & 0.79148 * & 3.39\% \\ \cline{2-5}  & RE & 0.26086 & 0.25205 * & 3.38\% \\ \cline{2-5}  & MAE & 0.64495 & 0.61352 * & 4.87\% \\ \hline \hline \end{tabular}

Note: * is the best value.

\end{table} 
Table 6: Performance of SDPTrustSVD. The results show that the predictive accuracies of the proposed SDPTrustSVD are superior to the original TrustSVD. On full ratings of Flixster with d = 5, the improvements of RMSE, RE, and MAE by SDPTrustSVD are 1.91%, 1.79%, and 3.20% higher than the original Trust SVD. On FilmTrust with d = 5, the proposed SDP could also improve TrustSVD effectively, where the performances of RMSE, RE, and MAE are 2.39%, 2.38%, and 3.85% higher than TrustSVD. On both datasets with d = 10, the improvements are also distinct. The results prove that the proposed SDP can efficiently improve the existing TrustSVD. ## 7 Conclusions

In this paper, we investigated how to improve the baseline estimation accuracy. Observed from real datasets, we found that different users usually have different rating criteria, and the real rating range of users is usually a subset of the system's rating range. Further observations from ratings' global and local distributions showed that ratings generally follow the normal distribution and different personalized rating ranges result in different standard deviations. Moreover, we analyzed the ratings' distribution and found that the proportion of users' personalized local deviation \(\sigma_{u}\) to the system's global deviation \(\sigma\) can improve the baseline estimation accuracy and proposed an improved novel model named SDP, which can be conveniently applied to all existing latent factor-based CF recommendations that utilize classical baseline estimation, by adding a proportion \(\left(\frac{\sigma_{u}}{\sigma}\right)\) to the global \(b_{i}\). Two application instances of SDP, SDPSVD++ and SDPTrustSVD, were proposed in this paper to

Figure 6: Performances (MAEs, RMSEs, and REs) of the predictive accuracies of different models: TrustSVD, and proposed SDPTrustSVD. The results show that the proposed SDP can effectively improve the performance of TrustSVD. illustrate how to apply SDP and how to improve the learning algorithms. The experiments showed that the proposed SDP is superior to classical baseline estimation on all datasets with full ratings evaluation by cross validation. The experiments also showed that the proposed instances SDPSVD++ and SDPTrustSVD have dramatical improvements on predictive accuracies compared to original algorithms. The results prove that SDP can not only improve baseline estimation accuracy effectively but also efficiently improve existing latent factor-based CF recommendations. Conceptualization, Z.T. and L.H. ; methodology, Z.T. ; formal analysis, L.H. and Q.C. ; data curation, D.W.; validation, D.W. and Q.C. ; writing--original draft preparation, Z.T. and L.H. ; writing--review and editing, B.Z. ; project administration, B.Z. ; funding acquisition, Z.T. ; supervision, Z.T. All authors have read and agreed to the published version of the manuscript.