# Adaptive Hierarchical Density-Based Spatial Clustering Algorithm for Streaming Applications
## 4 Experiment Results and Discussions
### Experiment Setup to Assess the Accuracy of Clusters Generated by Adaptive HDBSCAN  
The experiment to assess the accuracy of the clustering is performed by simulating a variable number of clusters and assessing the accuracy of both the Adaptive HDBSCAN and the HDBSCAN when predicting the number of clusters in the dataset. The experiment is repeated 500 times to ensure results are consistent.  
Table 2 shows the table of the accuracies for both algorithms for different number of data points. The accuracy is calculated using the following formula:  
\[\begin{array}{l}\text{Number of accurate predictions of number of clusters per cluster set}\\ \hline\text{500}\end{array}\times\text{100\%} \tag{8}\]  
A sample of the accuracy results table is shown in Table 2. Each sample of the data point group consists of 500 experiments. The accuracy is the average across the 500 experiments. There is a slight difference between the accuracy numbers and this is caused by the excess of mass calculation, which is detailed in Section 3.10. However, in order to determine whether the difference is significant, a \(T\)-test was used to see if there is a significant difference between the means of two accuracy measurement groups.  
A total of 100 different cluster sets are used to assess the accuracy of the prediction of the algorithm and, for each of the clusters, the experiment is run 500 times to ensure consistency. As depicted in Figure 7, the Adaptive HDBSCAN has a median accuracy of 98.2% with an upper quartile of 98.9 and a lower quartile of 97.2. The maximum and minimum accuracy are 100% and 95.4%, respectively. The HDBSCAN on the other hand has a median accuracy of 98.6% with an upper quartile of 99.2 and a lower quartile of 97.4. The maximum and minimum accuracy are 100% and 95.8%, respectively. By this measure, the HDBSCAN appears to be slightly more accurate compared with the Adaptive HDBSCAN. To further confirm if the difference was significant, a \(T\)-test is used to determine if there is a significant difference between the means of two groups of accuracy measurement. The null hypothesis is that there is no significant difference between the mean of the accuracies for both the HDBSCAN and Adaptive HDBSCAN. With a test statistic value of 1.8301 and a p-value of 0.0688, we do not have significant evidence to reject the null hypothesis since the p-value is higher than the alpha value of 0.05. Therefore, we conclude that there is no significant difference between the accuracy of the HDBSCAN and the Adaptive HDBSCAN.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Number of Data Points**} & \multicolumn{2}{c}{**Accuracy (\%)**} \\  & **Adaptive HDBSCAN** & **HDBSCAN** \\ \hline
100 & 99.6 & 99.8 \\
200 & 100.0 & 100.0 \\
300 & 99.2 & 99.6 \\
400 & 98.6 & 99.2 \\
500 & 98.6 & 99.0 \\
600 & 98.4 & 99.0 \\
700 & 98.8 & 98.8 \\
800 & 98.4 & 98.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Table of accuracies of cluster prediction using the Adaptive HDBSCAN and the HDBSCAN.  
[PERSON]'s algorithm performs better for less dense data points in terms of speed of execution while maintaining accuracy. This is because [PERSON]'s algorithm grows a solution from a random vertex by adding the next cheapest vertex--the vertex that is not currently in the solution but connected to it by the cheapest edge--whereas [PERSON]'s algorithm begins by finding the minimum-weight edge incident to each vertex of the graph, and adding all of those edges to the forest. Then, it repeats a similar process of finding the minimum-weight edge from each tree constructed so far to a different tree, and adding all of those edges to the forest.