# Effective Privacy-Preserving Collection of Health Data from a User's Wearable Device
## 5 Experimental Evaluation
### Experimental Results  
Table 1 lists the average error rates for varying privacy budget \(\epsilon\) and datasets of different sizes. In the experiments, the privacy budget \(\epsilon\) varied from 0.5 to 2.0 and the sizes of the datasets varied from \(290\times 10^{1}\) to \(290\times 10^{2}\). Key observations based on the table can be summarized as follows: As the number of collected data sizes increases, the error rate decreases, which implies that as additional data are collected from users of wearable devices, the estimation accuracy becomes high. As \(\epsilon\) decreases, the error rate increases. This is because a decrease in the privacy budget causes random noise, which is added to the original data by the perturbation phase of LDP, to increase, whereupon the level of privacy protection of the user's health data increases. As indicated by the results in the table, the method proposed in this paper significantly outperforms the naive solution for all privacy budgets and data sizes. These experimental results verify that the proposed method, which reports carefully selected salient data, is more effective than the naive solution, which reports the entire collection of health data. Figure 4 plots the actual and estimated aggregate static for datasets of various sizes. In this figure, the y-axis corresponds to the daily step-count and the x-axis represents the time between 10:00 and 21:00. In the experiment, the privacy budget is set to 1.0, whereas the amount of data varies from 290 to \(290\times 10^{2}\). As expected, as the amount of data increases, the aggregated health data sequence estimated by the proposed approach more closely approximates the actual data (which is represented by a blue curve). As can be seen in the figure, with the 290 dataset, an accurate estimation cannot be obtained due to the insufficient collected data. However, with the \(290\times 10^{2}\) dataset, a fairly good estimation can be achieved by the proposed approach in this paper. These experimental results indicate that the method proposed in this study effectively exploits the collected dataset. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Data Size**} & \multicolumn{3}{c}{**NS**} & \multicolumn{3}{c}{**OS (Proposed Method)**} \\ \cline{2-7}  & \(\epsilon=0.5\) & \(\epsilon=1\) & \(\epsilon=2\) & \(\epsilon=0.5\) & \(\epsilon=1\) & \(\epsilon=2\) \\ \hline \(290\times 10^{1}\) & 240,843.99 & 119,103.22 & 59,302.83 & 471.28 & 210.77 & 143.62 \\ \hline \(290\times 10^{2}\) & 7604.89 & 3783.73 & 1890.87 & 17.20 & 9.18 & 5.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of average error rates for varying privacy budget \(\epsilon\) and data sizes. We also evaluated the effectiveness of the proposed method for identifying a salient data set, as presented in Section 4.1. Figure 5 shows the average error rates for the three alternative methods, \(RS\), \(NS\), and \(OS\). In this figure, the y-axis corresponds to the error rate and the x-axis represents the number of salient data that are extracted from the given health data. In the experiments, the privacy budget \(\epsilon\) varied from 0.5 to 2, while the size of the dataset was fixed to \(290\times 10^{2}\). Furthermore, for the random and non-optimal selection methods, which require the number of salient data that are extracted from the given health data to be predefined, the number of extracted salient data varies from 3 to 6. We note that, unlike these two methods, for the proposed method explained in Section 4, the optimal number of salient data, which minimize the expected error incurred by using LDP, is determined by Algorithm 1. Key observations based on Figure 5 can be summarized as follows: as the privacy budget, \(\epsilon\), decreases, the error rate increases. This is because, as the privacy budget decreases, noises added by the wearable device-side increase, which, in turn, leads to decreased estimation accuracy at the data collection server-side.