## 3 Results
### Sub-Clustering and Data Filtering  
Figure 10 eventually illustrates the partitioning of an arbitrary main cluster into its respective sub-clusters based on the pre-selection of different lighting parameters discussed in Section 2.3. After Laplacian feature reduction, only the 11 most relevant lighting parameters were used for UMAP and subsequent HDBSCAN processing (see Figure 5). On this basis, the algorithmic pipeline is capable of finding within each main cluster distinct groups of light spectra that are more similar to each other in terms of their lighting parameters. In the example shown here, again, only for a subset of lighting parameters, the main cluster was divided into eight sub-clusters labelled from 0 to 7 and one noise cluster labelled by \(-1\). Note that the number of sub-clusters may vary between different main clusters.  
Figure 9: Result of the physical clustering of the \(1\times 10^{5}\) input test spectra for a selection of different lighting parameters. The labels on the \(x\)-axis denote the different main clusters.  
As can be seen, the sub-clusters of the present example mainly differ in the direct/indirect \(\alpha\) parameter of the assigned light spectra. The other lighting parameters depicted here show a similar range and a large overlap across the different sub-clusters. This basically emphasizes the large degree of similarity of the light spectra assigned to the same main cluster. A further differentiation between the spectra can usually be achieved only with regard to very few lighting parameters, where the importance of these parameters may differ between different main clusters.  
Nevertheless, the application of UMAP and HDBSCAN to each main cluster again yields selections of light spectra assigned to different sub-clusters that by definition are most diverse to each other. This assignment, as it is based on lighting parameters, can now be used to filter out light spectra that, on top of their diversity, are also in a certain parameter range or match a specific target definition. Examples for such target definitions could be a certain illuminance range or a specific correlated color temperature defined as a prerequisite for running subsequent subject studies. For illustrative purposes, the target value of the present work was to extract one spectrum out of each sub-cluster that best fits the corresponding medians for each considered lighting parameter in terms of an overall accumulating distance metric. Note that this specific example serves only as a proof of concept. Any other selection criterion could also be used here.  
Figure 11, finally, shows the accordingly filtered light spectra, one for each sub-cluster, as obtained for two different main clusters. As can be seen, the shape and intensities of the SPDs are quite similar for the same main cluster but vary significantly between different main clusters, confirming the suitability and performance of the data-based diversifying strategy proposed in this work. In addition, Figure 12 depicts the parameter representations of all likewise selected light spectra categorized according to their main cluster assignment. Again only a subset of lighting parameters is shown. In most cases, parameter deviations between the selected light spectra within a given main cluster are small compared to the  
Figure 10: Partitioning of an arbitrary main cluster obtained from the first processing stage into its respective sub-clusters. The plots show the results for a subset of lighting parameters. The labels from 0 to 7 represent the different sub-clusters, whereas a label of \(-1\) denotes the noise cluster.  
between-cluster differences. Overall, the main clusters cover a wide range of lighting parameter values, representing the diversity between them.