# Automated Exploratory Clustering to Democratize Clustering Analysis
## 4 Experimental Works
### Compared Methods  
While there does not (to our knowledge) exist another method directly comparable to our approach, we do benchmark three AutoML methods for clustering using the standard parameters and the implementation (available at [[https://github.com/biagiolicari/Benchmark_result_AutoML/tree/main](https://github.com/biagiolicari/Benchmark_result_AutoML/tree/main)]([https://github.com/biagiolicari/Benchmark_result_AutoML/tree/main](https://github.com/biagiolicari/Benchmark_result_AutoML/tree/main)) accessed at 19 May 2025) of [2] on our datasets. We opted for the standard parameters, as we wanted to simulate a practitioner without knowledge in clustering, unable to select apt parameters. We used autoCluster [18], Automl4 Clust [19], and ml2 dac [20] (with all available meta-features), which, however, only output a single \"best\" clustering. In order to enable a fair comparison, we set the number of evaluations to 100, the same number used in our experiments. For this reason, every comparison has this big caveat, as a single shot must not always find all relevant clusterings. However, as only a single clustering is returned, the choice for the user is much easier. We \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Name** & **Abbr.** & \(ec\) & \(uc\) \\ \hline Costly Usability & CU & 0 & 1 \\ \hline Thorough Search & TS & 0.25 & 0.75 \\ \hline Equal costs & EQC & 0.5 & 0.5 \\ \hline Quick Search & QS & 0.75 & 0.25 \\ \hline Costly Evaluation & CE & 1 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Different parameterisations for the Application Cost function. omitted cSmartMl [44], as the implementation did not work in a wide variety of our results and suffered from a slow execution time. We also include autoClues [21], adapting their public implementation (available at [[https://github.com/big-unibo/autoclues/](https://github.com/big-unibo/autoclues/)]([https://github.com/big-unibo/autoclues/](https://github.com/big-unibo/autoclues/)) accessed at 19 May 2025), which first computes a number of clusterings and then selects the most promising and diverse set of \(k\) clusterings for a given \(k\). We used the Adjusted Mutual Information as a target function according to the experiments conducted by the original authors. We computed the internal score for every \(k\in[1,100]\) and selected the clustering set with the highest score. Again, this comparison has to be taken with a grain of salt, as this method was developed to be used with a fixed \(k\). We could not set the number of executions for this method, so it has computed more than 100 clusterings for a number of datasets. On some other datasets, however, the method did not produce a single clustering as all clusterings have been pruned internally. An overview of all (including our) methods and their used clustering algorithms and CVIs can be seen in Table 6. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Algorithm/CVI** & **Our Pipeline** & **autoClues** & **autoCluster** & **Automl4 Clust** & **ml2 dac** \\ \hline \multicolumn{6}{c}{Clustering algorithms} \\ \hline kMeans & ✓ & ✓ 1  & ✓ 1  \\ \hline kMedoids & & & ✓ & & \\ \hline GMM & & ✓ & ✓ & ✓ & ✓ \\ \hline Meanshift & ✓ & ✓ & ✗ & & ✓ \\ \hline Affinity Propagation & & ✓ & ✗ & & ✓ \\ \hline Agg. Clustering & & ✓ & ✓ & ✓ & ✓ \\ \hline Birch & & ✓ & ✓ & & ✓ \\ \hline Spectral Clustering & & ✓ & ✓ & & ✓ \\ \hline DBSCAN & & & ✗ & & ✓ \\ \hline OPTICS & ✓ & ✓ & ✗ & & ✓ \\ \hline HDBSCAN & ✓ & & & & \\ \hline \hline \multicolumn{6}{c}{CVIs} \\ \hline DBI [72] & & ✗ 2  & ✓ & ✗ & ✓ \\ \hline VRC (CHI) & ✓ & & ✓ & ✗ & ✓ \\ \hline DI [73] & & & & & ✓ \\ \hline SWC & ✓ & ✓ 2  & ✓ & ✓ & ✓ \\ \hline DBCV & ✓ & & & & ✓ \\ \hline DSI & ✓ & & & & \\ \hline CDR & ✓ & & & & \\ \hline VIASCKDE & ✓ & & & & \\ \hline CJI [74] & & & & & ✓ \\ \hline COP [75] & & & & ✓ \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Clustering algorithms and CVIs used in our pipeline and the compared methods (✓), implemented in the framework but not used in the default configuration and our experiments (✗).