# Automated Exploratory Clustering to Democratize Clustering Analysis
## 5 Results
### Coverage  
To evaluate whether good clusterings were selected, we look at the AMI [51] in comparison to the ground truth as proxy for the clustering desired by a user. In Figure 7, we show how many clusterings have a higher highest AMI than the x-axis refers to. In addition to the 10 approaches described earlier, we also plotted an angelic decider, always choosing the generated clustering with the highest AMI. We used the AMI as we expect to see clusterings of unbalanced sizes and small clusters, in which case AMI is to be preferred over ARI [76].  
We can see in Figure 7(a) that the skyline for five CVIs is almost on par with the angelic decider and hence almost always contains the best clustering for the real datasets. We can see that the tradeoff using five CVIs and \(\varepsilon=0.75\) has similar numbers up to an AMI number of 0.7, where it rapidly declines and has less results with an AMI higher than 0.8 than the skyline with two CVIs. The tradeoffs with five CVIs, and \(\varepsilon=0.5\) and \(\varepsilon=0.25\) also find clusterings with an AMI over 0.6 for most of the sets but drop quickly when looking at higher AMIs. The skyline with two CVIs has the third-to-most sets, where the highest AMI is bigger than 0.8 and above. We can see that the DBCV delivers the most results with the best AMI of less than 0.4. However, it produces more sets, which contain a higher AMI than the SWC, which is on a level with the tradeoff with five CVIs and \(\varepsilon=0.25\) around the last place of our proposed methods. We can see that all four compared state-of-the-art methods struggle to find sensible clusterings on these datasets.  
Figure 7: Empirical cumulative density plots of the best AMI in the selected sets. The plots depict on the \(y\)-axis how many sets have a bigger AMI than the value on the x-axis. Sets containing clusterings with a high AMI (large area under curve) are desirable.  
If we look at the results on real datasets (Figure 7b), we can see that the skyline using five CVIs is very close to the angelic decider. We can also see that, while a bit worse, the tradeoff using five CVIs and \(\varepsilon=0.75\) is almost on par with the original skyline. The tradeoffs with five CVIs and \(\varepsilon=0.5\) and \(\varepsilon=0.25\) have similar results up to a best AMI of 0.4. However, they have much fewer sets containing clusterings with high AMI. DBCV, SWC, and the skyline consisting of these two measures and the respective tradeoffs have bigger problems, found to have, e.g., around 20% more sets with a best AMI of under 0.2. However, the best results of these methods are on a level or even better than those of five CVIs with tradeoffs of \(\varepsilon=0.5\) and \(\varepsilon=0.25\) We can see, that autoCluster and ml2 dac have results better than the skyline with two CVIs, but worse than the skyline and tradeoffs with five CVIs. Automl4 Clust has results, which are in the lower half comparable to the skyline with two CVIs. However, it does not produce any clusterings with an AMI higher than 0.65 in contrast to any other method. AutoCluster delivers mediocre results if we consider that only 17 datasets actually generated clustering sets in contrast to the more than twice as many of all other algorithms.