# A Biased Proportional-Integral-Derivative-Incorporated Latent Factor Analysis Model
## 7 Conclusions  
This paper combines the prediction formula of the biased SVD model with the PSL model, designing a biased PSL model which achieves significantly higher computational efficiency, as well as highly competitive prediction accuracy. This method fuses the prediction method of biased SVD with the instantaneous error correction method of PSL. The biased SVD formula can take into account the scoring habits of different people and the different qualities of items, i.e., taking into account the individuation, to give the most appropriate score for users and items. The PSL model integrates the principle of the discrete PID controller into the SGD-based LFA model, to corrects the errors of the real and predicted scores according to the proportion (P), integral (I), and derivative (D). The biased PSL model blends the advantages of the two models to obtain a better recommendation effect. In the experiment, we use 3 datasets with different sizes and different densities to \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**K = 50**} & \multicolumn{2}{c}{**K = 100**} \\ \cline{2-5}  & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline SVD & 0.7973 & 0.6174 & 0.7943 & 0.6152 \\ BiasSVD & 0.7916 & 0.6089 & 0.7906 & 0.6084 \\ PSL & 0.7993 & 0.6134 & 0.7957 & 0.6108 \\ BiasPSL & 0.7885 & 0.6040 & 0.7862 & 0.6024 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The prediction result on MovieLen-10 M. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**K = 50**} & \multicolumn{2}{c}{**K = 100**} \\ \cline{2-5}  & **RMSE** & **MAE** & **RMSE** & **MAE** \\ \hline SVD & 0.8625 & 0.6817 & 0.8603 & 0.6805 \\ BiasSVD & 0.8566 & 0.6733 & 0.8540 & 0.6715 \\ PSL & 0.8635 & 0.6796 & 0.8589 & 0.6758 \\ BiasPSL & 0.8506 & 0.6666 & 0.8459 & 0.6627 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The prediction result on MovieLen-1 M.  
test the recommendation performance of the biased PSL model and other recommendation models (SVD model, biased SVD model, and PSL model). The prediction effect is evaluated in detail by measuring the results of RMSE and MAE. Eventually, the experimental result delivers that the biased PSL model performs better than the SVD and PSL models on the three HiDS matrices. Regarding future work, we hope to determine the best parameters appropriate for specific dataset. This model is mainly based on the PSL model, and the principle of the PSL model is discrete PID controller. Thus, its prediction results are greatly affected by the parameters of the PID controller. Owing to the wide range of \(K_{P}\), \(K_{I}\), and \(K_{D}\), it is difficult to ensure whether \(K_{P}\), \(K_{I}\), and \(K_{D}\) are most suitable parameters for this dataset. If a system can achieve the best parameters appropriate for the specific dataset, the best recommendation effect could be gained. Furthermore, despite having fewer iterations, the PSL algorithm takes longer to complete each iteration than the SVD algorithm due to the difficulty of vector changes in each iteration. Its capacity to run on a huge dataset is restricted, as it takes longer to complete a single training session. Since new users and items are be introduced regularly into a recommendation system, the lengthy preparation period is not conducive to the implementation of the model. It is difficult to label a recommendation system as outstanding if it cannot measure easily and make initial suggestions as new users and items are being introduced. Besides, we only attempted to combine the PSL model and the biased SVD model in this paper in the hope of a better recommendation effect. Now no attempt has been made to combine the PSL model with other recommendation models. In the future, we can try integrating PSL model with other recommendation models and test their recommendation performance. Conceptualization, J.S. ; methodology, J.S. ; software, J.S. ; validation, J.S. ; formal analysis, J.S. ; writing--original draft preparation, J.S.