## 4 Experimental Results and Discussions
### Comparison between Algorithms
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Dataset** & **Time (s)** & **Offline (s)** & **Sample (ms)** \\ \hline Macro SOStream & Horseshoe & 20.90 & - & 6.51 \\  & T & 22.31 & - & 5.84 \\  & Moon & 41.84 & - & 8.37 \\  & Three Spirals & 7.22 & - & 4.65 \\ \hline SOStream & Horseshoe & 12.17 & - & 3.74 \\  & T & 16.01 & - & 4.30 \\  & Moon & 28.79 & - & 5.80 \\  & Three Spirals & 0.84 & - & 1.35 \\ \hline DenStream & Horseshoe & 33.21 & 19.12 & 4.15 \({}^{1}\) \\  & T & 41.79 & 27.09 & 4.13 \({}^{1}\) \\  & Moon & 65.13 & 41.21 & 4.65 \({}^{1}\) \\  & Three Spirals & 0.36 & 0.27 & 0.15 \({}^{1}\) \\ \hline \hline \end{tabular} \({}^{1}\) Samples in the online phase.  
\end{table} 
Table 5: Average processing time of evolving algorithms. SOStream and DenStream obtained the maximum value from the ARI metric, and among them, Macro SOStream achieved a shorter processing time, having been 20.90 s.  
The SOStream also had the shortest time of execution with the T dataset, with 16.01 s. However, as shown in Tables 3 and 5, SOStream had the poorest cost. The second algorithm with less costly is the Macro SOStream algorithm, which analyzed the data in 22.31 s. The third algorithm is DenStream with 41.79 s.  
Regarding the Moon database, once again, SOStream stood out with 28.79 s of processing time, and the algorithm with the second-best time was Macro SOStream, obtaining 41.84 s. An important detail is that SOStream works only with microclusters, which may be why this algorithm has a faster execution time than the others, which also uses the concept of macroclusters. Unlike the others, the algorithm with the lowest processing time for clustering the Three Spirals dataset was DenStream with 0.36 s; SOStream and Macro SOStream performed 0.84 and 7.22 s of processing, respectively. One of the differences between the Three Spirals dataset and the other datasets is the number of samples, with the Three Spirals dataset having far fewer. Thus, it is interesting to note in Table 5 that SOStream and Macro SOStream had less processing time for all samples when it came to datasets with the highest number of samples. In addition to the algorithms' total execution times, we also obtained the average time that the algorithm took to analyze each sample of the datasets, as shown in the Sample column in Table 5. In the sample column, it is noticed that the values of DenStream are the lowest, 4.15, 4.13, 4.65, and 0.15 milliseconds for the sets Horseshoe, T, Moon, and Three Spirals, respectively. However, this execution time for the DenStream algorithm is only of the online learning phase, as it is impossible to measure each sample's time in the offline phase. It is also observed that, despite this low measurement per sample, DenStream has the highest processing values of the total time of the datasets. Thus, the predominant factor of DenStream being the most computationally expensive algorithm may be related to the processing time in the algorithm's offline phases. As shown in Table 5, the execution times for this offline phase were 19.12, 27.09, 41.21, and 0.27 s for Horseshoe, T, Moon, and Three Spirals bases, respectively. In the analysis time per sample of Macro SOStream and SOStream, it was expected that Macro SOStream's execution time would be higher than that of SOStream because it added the create function of the macroclusters in the algorithm. Another point to note is that, although the average time per sample of Macro SOStream is about 50% greater than the values of DenStream, the total average execution time for Macro SOStream is less than about 35% of DenStream's total, except for the Three Spirals dataset. These results show that, for three of four datasets used, the Macro SOStream stood out in terms of execution time.