## 4 PER-SAC based Optimal Parameter Autotuning for DBSCAN
### PER-SAC Algorithm
If not specified, the experimental results in this paper are the average of ten executions. According to Table 4, the parallel algorithms RP-DBSCAN and STRP-DBSCAN algorithms are far less efficient than the ordinary DBSCAN algorithm when on the 8.5K dataset. This is because the parallel DBSCAN algorithm adds the process of data partitioning, merging clustering and other processes that require the communication of different computing nodes compared to ordinary DBSCAN algorithm, which increases the time overhead in the case of small dataset. However, as the dataset size gradually increases, the performance advantages of the parallel DBSCAN algorithms appear. On the 50K and 217K datasets, the overall execution time of STRP-DBSCAN is reduced by 57.5% and 96.2% compared with DBSCAN in the current experimental environment. Compared with RP-DBSCAN, the clustering time of STRP-DBSCAN on the 8.5K, 50K, and 217K datasets is improved by 2.4%, 7.2%, and 31.2%, respectively. The experimental results show that the algorithm based on spatial-temporal random partitioning can achieve a more balanced partitioning and effectively reduce the communication overhead between nodes, which improves the overall execution efficiency of the parallel clustering algorithm. It is also consistent with the previous algorithmic complexity analysis of STRP-DBSCAN. Table 5 shows the evaluation result of the clustering accuracy of three algorithms on the same datasets. According to the results, STRP-DBSCAN has little or no impact on the clustering accuracy compared to DBSCAN and RP-DBSCAN. Combined with previous experimental results related to the clustering time, it shows that STRP-DBSCAN can improve the clustering efficiency for large data size, and the improvement becomes more obvious as the data size increases. \begin{table}
\begin{tabular}{c c c c} \hline
**Algorithms** & **8.5K** & **50K** & **217K** \\ \hline DBSCAN [5] & 0.643 & 13.290 & 349.520 \\ RP-DBSCAN [10] & 4.456 & 6.089 & 19.327 \\ STRP-DBSCAN & 4.350 & 5.651 & 13.290 \\ \hline \end{tabular}
\end{table} 
Table 4: Execution time (s) of different algorithms with different data sizes. \begin{table}
\begin{tabular}{c c} \hline
**Hardware/Software** & **Parameters** \\ \hline CPU & 12 th Gen Intel®® CoreTM [FOOTNOTE:]Footnote : footnotemark: [ENDFOOTNOTE] 17-12700H 2.30 GHz \\ PyTorch & Version 1.12.1 \\ CUDA & Version 11.3 \\ GPU & NVIDIA GeForce RTX 3070 Ti \\ Python & Version 3.7.16 \\ \hline \end{tabular}
\end{table} 
Table 3: Experimental configuration of the PER-SAC algorithm-based framework. ### Evaluation of PER-SAC

In this part of experiments, we verify the effect of the proposed PER-SAC algorithm on the clustering accuracy of DBSCAN. Since the PER-SAC-based parameter autotuning framework for DBSCAN uses NMI as the reward function, it requires labeled datasets for searching the optimal clustering parameters. Therefore, in this part of experiments, we use labeled datasets of two sizes, 3.3K and 8.5K. #### 5.3.1 Selection of Hyper-Parameters

Considering that DRL algorithms such as TD3 and SAC are somewhat randomized, the experimental results are the means as well as the standard deviations after 10 different random seed runs. The parameter autotuning framework for DBSCAN involves other hyperparameters not related to the DBSCAN algorithm, such as the size of the parameter space [41], the reward factor, and the number of recursive layers of the model, which will also have an impact on the final clustering effect, and thus it is necessary to carry out the hyperparameter selection first. We use the experimental method of empirical search to select the appropriate hyperparameters. Figure 8 demonstrates the effects of the parameter space size of _Eps_(\(\pi_{Eps}\)), the parameter space size of _MinPts_ (\(\pi_{MinPts}\)), the number of recursive layers of the DRL network, and the reward factor on the performance of the framework.