## 3 Results
### Autoencoding and Main Clustering of the Embedded Space Representation
Here, the min_distance parameter was set to 0.0 in order to preserve the locality of the data and, by bringing similar data points closer together, create dense regions for the subsequent application of the density-based clustering algorithm. At this processing step, a total of 90 neighbors was checked for each data point and compared for similarity to also take into account the global structure of the data. Note that as the number of neighbors that are checked increases, more weight is put on the latter. As a downside, this however also increases computational time. From Figure 7, it can be seen that the proposed algorithmic pipeline, starting from purely unbiased spectral data, is capable of arranging their embedded space representation in such a way that similar light spectra, here in terms of CCT and illuminance, are closer together. Spectra of lower CCT can for example be found close to the outer-contour of the embedded body structure constituted by the data points, while towards the more central parts the CCT increases. It should again be noted that the absolute distance between data points is no longer a meaningful measure of similarity or difference. This example confirms that the proposed algorithmic pipeline as discussed in Section 2.2 gives meaningful and interpretable results. It shows that 8 features (after autoencoding and Laplacian score filtering) are sufficient for encoding the most relevant information of the input light spectra. Using more input data, the shape of the embedded body structure will essentially remain the same and only the gaps will be filled. If another luminaire with different LED primaries is used, a different shape of the resulting embedded body structure  
Figure 6: (**a**) Convolutional autoencoder input (black solid line) and reconstructed (blue solid line) light spectra after encoding and decoding the corresponding \(1\times 15\) dimensional feature vectors. (**b**) Loss between input and reconstructed spectra. can be expected. With the proposed pipeline, an arbitrary number of LED primaries can be processed. Combinations of other light sources can be included as well. Figure 8 finally shows the output of the density-based clustering of the embedded UMAP space using HDBSCAN. Here, a minimum_cluster_size of 100 was chosen to also consider smaller groups of similar spectra. In order to prevent, at the same time, the formation of too many of such small clusters, an epsilon of 0.1, was used for counterbalancing purposes. The epsilon parameter ensures that neighboring clusters are not partitioned any further if the distance is less or equal to epsilon, resulting in bigger clusters in case that a sufficient degree of similarity is achieved. In addition, the clustering was performed with a minimum_samples parameter of 90, which results in a more conservative clustering with a considerably larger number of data points being identified as noise than when choosing a smaller value. In this example, 69 different main clusters have been found. As discussed before, these clusters are most diverse to each other in terms of their spectral features. As can be seen, they primarily cover the contour of the embedded body structure. Towards the more central parts, the density of neighboring data points in UMAP space decreases so that only smaller clusters could be identified in these regions. Figure 8: Results of the density-based clustering process of the \(1\times 10^{5}\) test spectra using the HDBSCAN algorithm. The different colors indicate the respective cluster assignment, while gray data points represent identified noise. Figure 7: Results of the UMAP algorithm applied to the test data set of \(1\times 10^{5}\) randomly selected input spectra of the test luminaire discussed in Section 2.1 after autoencoding and Laplacian score feature reduction. The color coding denotes different CCTs (**a**) and the grayscale in (**b**) indicates the corresponding illuminance \(E_{\text{total}}\).