## 4 Experimental Analysis
### Parameter Settings
#### 4.3.2 Effect of \(\varepsilon\) on Experimental Results  
To ensure the effectiveness of privacy protection, we set the value of the privacy budget to be in the range of [0.1,1]. Figures 4 and 5, respectively show the changes of \(MAE\)  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Dataset** & **Indicator** & **Algorithm** & \(N\) **= 20** & \(N\) **= 40** & \(N\) **= 60** & \(N\) **= 80** & \(N\) **= 100** \\ \hline \multirow{8}{*}{\
\begin{tabular}{c} MovieLens \\ 1M \\ \end{tabular} } & IBCF-DS & 0.7219 & 0.7176 & 0.7169 & 0.7170 & 0.7171 \\  & DPLCF & 0.8912 & 0.8722 & 0.8718 & 0.8726 & 0.8694 \\  & & LDP & & & & & \\  & & item-base CF & 0.8666 & 0.8484 & 0.8407 & 0.8361 & 0.8330 \\  & & PNCF & 0.9600 & 0.9290 & 0.9110 & 0.8960 & 0.8870 \\  & & Truncated & 0.8582 & 0.8527 & 0.8537 & 0.8502 & 0.8498 \\  & & PPPCE & 0.7911 & 0.7830 & 0.7783 & 0.7781 & 0.7798 \\ \cline{2-8}  & & IBCF-DS & 0.9288 & 0.9220 & 0.9208 & 0.9207 & 0.9208 \\  & & DPLCF & 1.1284 & 1.1050 & 1.1049 & 1.1050 & 0.1021 \\  & & LDP & & & & & \\  & & item-base CF & 1.1217 & 1.0983 & 1.0888 & 1.0825 & 01.0784 \\  & & PNCF & 1.2470 & 1.2040 & 1.1790 & 1.160 & 1.1480 \\  & & Truncated & & & & & \\  & & PPPCE & 1.0944 & 1.0868 & 1.0883 & 1.0840 & 1.0837 \\  & & PPPCE & 1.0071 & 0.9974 & 0.9220 & 0.9913 & 0.9932 \\ \hline \multirow{8}{*}{
\begin{tabular}{c} Yahoo Music \\ \end{tabular} } & IBCF-DS & 0.9482 & 0.9484 & 0.9484 & 0.9485 & 0.9486 \\  & DPLCF & 1.0218 & 1.0243 & 1.0228 & 1.0235 & 1.0213 \\ \cline{1-1}  & & LDP & & & & & \\ \cline{1-1}  & & item-base CF & 1.0461 & 1.0438 & 1.0427 & 1.0433 & 1.0414 \\ \cline{1-1}  & & PNCF & 1.0700 & 1.0620 & 1.0530 & 1.0389 & 1.0339 \\ \cline{1-1}  & & Truncated & & & & & \\ \cline{1-1}  & & PPPCE & 1.0052 & 1.0038 & 1.0014 & 1.0037 & 1.0026 \\ \cline{1-1}  & & PPPCE & 0.9981 & 0.9980 & 0.9996 & 0.9989 & 0.9987 \\ \cline{1-1} \cline{2-8}  & & IBCF-DS & 1.2464 & 1.2449 & 1.2447 & 1.2446 & 1.2445 \\ \cline{1-1}  & & DPLCF & 1.2842 & 1.2827 & 1.2813 & 1.2813 & 1.2790 \\ \cline{1-1}  & & LDP & & & & & \\ \cline{1-1}  & & item-base CF & 1.3298 & 1.3257 & 1.3265 & 1.3260 & 1.3247 \\ \cline{1-1}  & & PNCF & 1.5120 & 1.4950 & 1.4790 & 1.4500 & 1.4290 \\ \cline{1-1}  & & Truncated & & & & & \\ \cline{1-1}  & & PPPCE & 1.2830 & 1.2777 & 1.2756 & 1.2765 & 1.2751 \\ \cline{1-1}  & & PPPCE & 1.2727 & 1.2689 & 1.2713 & 1.2699 & 1.2685 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the algorithm performance with different values of \(N\).  
and _RMSE_ on the dataset as the value of \(\varepsilon\) changes. Due to the lack of the differential privacy protection mechanism, the curve of IBCF-DS remains unchanged.  
With the increase in \(\varepsilon\) of the two datasets, both _MAE_ and _RMSE_ show a downward trend. This is because as \(\varepsilon\) increases, the noise of data decreases and the availability of data increases. Seen from the above figures that PPPCF outperforms other algorithms except IBCF-DS on both datasets. First, each algorithm performs in terms of _MAE_ on the dataset of MovieLens 1M, PPPCF is 9.2% (0.083) less than the Truncated PPPCE, 9.7% (0.089) less than DPLCF, 3.3% (0.028) less than LDP item-base CF, and 5.1% (0.044) less than PNCF. Then, each algorithm performs in terms of _RMSE_ on the dataset of MovieLens 1M, PPPCF is 9.3% (0.106) less than the Truncated PPPCE, 10.6% (0.123) less than DPLCF, 4.2% (0.046) less than LDP item-base CF, and 5.7% (0.063) less than PNCF. Second, due to the data on the dataset of Yahoo Music is sparser, causing the effect of the Bayesian estimation mechanism, the cardinality estimation mechanism, and the frequency estimation mechanism is not obvious, but compared with PNCF without the data reconstruction module, these three data reconstruction algorithms can still bring obvious improvement in utility. Among the three algorithms with data reconstruction, the prediction error of PPPCF still performs best, indicating that PPPCF can indeed improve the accuracy of the recommendation algorithm.