## 3 Results  
### Autoencoding and Main Clustering of the Embedded Space Representation  
The training of the autoencoder was performed on the available GPU system. 60 million data were sampled uniformly from all possible light spectra of the test luminaire (see Section 2.1). All of these data were used for training. Afterwards, \(1\times 10^{5}\) spectra were randomly picked for evaluating the autoencoder performance. Taking approximately 1.5 days, the training of the autoencoder was completed after 400 epochs with a batch size of 1000, a learning rate of \(1\times 10^{-6}\), and a weight decay of \(1\times 10^{-5}\) and resulted in an average mean squared error loss of \(5.503\times 10^{-5}\) calculated on the evaluation data. For illustrative purposes, Figure 6 correspondingly shows the autoencoder results for two light spectra arbitrarily chosen from the evaluation set, one of low and the other of high intensity. In both cases, the black solid line depicts the ground truth, while the blue solid line represents the reconstructed spectrum obtained from the decoding stage. The red graphs on the right hand side show the respective loss between the original spectrum and the reconstructed spectrum per unit wavelength. As can be seen, the absolute loss \begin{table}
\begin{tabular}{l l} \hline \hline
**Lighting Parameter** & **Description** \\ \hline CCT & correlated color temperature \\ \(E_{\text{total}}\) & total illuminance \\ \(D_{\text{uv}}\) & distance from the planckian locus for a given CCT in CIE 1960 \\  & uniform chromaticity space \\ \(E_{\text{ind}}\) & illuminance of the indirect part of the luminaire \\ \(Q_{\text{a}}\)[56] & general color quality scale (NIST CQS 9.0) \\ \(\Delta C\) & average CIELAB chroma difference to reference illuminant \\  & calculated for the 15 NIST CQS 9.0 color samples \\ CS [57] & circadian stimulus \\ \(\text{CL}_{\text{A}}\)[57] & circadian light \\ \(\alpha\)[58] & \(E_{\text{ind}}/E_{\text{total}}\) \\ \(\alpha_{\text{opic}}\)[31] & integrated L-, M-, S-cone, rod, and ipRGC values \\ \(E_{\text{e}}\) & irradiance \\ \(R_{\text{f}}\)[31] & color fidelity index \\ \(R_{\text{g}}\)[31] & color gamut Index \\ \(R_{\text{t}}\)[31] & general metameric uncertainty index \\ FCI [59] & feeling of contrast index \\ MCRI [60] & memory color rendition index \\ CPI [61] & color preference index \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selection of lighting parameters used for dividing each main cluster into respective sub-clusters. Figure 5: Algorithmic pipeline of the sub-clustering process based on a pre-defined selection of different lighting parameters. is approximately the same for both low- and high-intensity spectra, which results in a considerably larger relative loss for the former compared to latter. This is reflected in pronounced ripples that can be observed on the blue curve in the upper left graph. Nevertheless, even for low intensities, it can be stated that the autoencoder is able to properly reconstruct the general trend in the data and, thus, provides sufficient accuracy for defining the main clusters. With regard to the density-based approach, it is sufficient that the reconstructed spectrum is close but not necessarily identical to the original input. After the autoencoder step, the evaluation set, which basically comprised a representative, unbiased selection of \(1\times 10^{5}\) input test spectra, was further processed to provide a proof of concept of the algorithmic pipeline proposed in this work. Figure 7 thus shows the corresponding results of the UMAP embedding after autoencoding and Laplacian score based feature reduction. The light spectra are represented as data points in the two-dimensional embedded space, where, for illustrative purposes, the color and transparency coding correspond to their respective CCT and illuminance values.