## 2 Materials and Methods
### Test Setup and Input Data  
In order to provide an application-related proof of concept, the present work makes use of spectral data obtained from a real multi-channel LED luminaire, in this case a direct/indirect floor lamp with three distinct, individually addressable LED channels found in both the direct and the indirect component. Figure 1a shows the corresponding relative spectral power distributions (SPDs). This mixture comprises two phosphor-converted white LEDs (cool and neutral white) and an additional single-peaked cyan emitter, whose chromaticities are depicted Figure 1b. While the former allow for adjusting the luminaire's overall light emission over a wide range of different correlated color temperatures (CCTs), the latter--showing a peak wavelength of 475 nm--is used to specifically trigger the intrinsically photosensitive retinal ganglion cells (ipRGGs) for an additional stimulation of the human circadian system [38]. The corresponding LED drivers are controlled via a DALI-bus [39] and can receive values from 84 to 254 in order to dim the brightness of each channel between 1% and 100%, respectively. These 171 dimming steps for each of the luminaire's six individual LED channels (three within each directional component), yield a total number of \(1716=25.002\times 10^{12}\) possible light spectra that may differ in their spectral compositions and absolute light levels.  
This set of light spectra appears to be an adequate input to validate the proposed diversifying strategy on realistic data. As shown in Figure 2, which gives an overview of the computational structure, an unbiased clustering can be performed by using the complete physical information of the light spectra encoded as features in a 401 dimensional vector space. The clustered raw data are further processed by dividing each of the found main clusters into characteristic sub-clusters based on a selection of lighting parameters that are calculated for all clustered light spectra. The resulting parameterized sub-clusters can thus be used to efficiently filter the data to eventually come up with the most diverse selection of light spectra that comply with certain pre-defined user requirements. In order to avoid the bias introduced by the sub-clustering process, even though desired in most cases, the corresponding computational step can be skipped or bypassed entirely so that the final selection of diverse light spectra can be carried out on the unbiased main clusters only.  
Due to the tremendous computational resources that would be needed to process the complete set of possible light spectra, a more practical approach had to be chosen. For this work, the size of the input data was limited in an unbiased way by randomly sampling \(1\times 10^{5}\) data from a uniform distribution representing the total set of \(25.002\times 10^{12}\) possibilities. Following this strategy, the overall computation time could be limited to a feasible range of a few days. All calculations were performed on a linux server with 45 CPUs running at 2.6 GHz, 80 GB of RAM and a NVIDIA Quadro P4000 GPU.  
Figure 1: (**a**) Normalized LED spectra for the neutral white, cool white, and cyan primaries constituting the test luminaire’s direct and indirect components. (**b**) \(x,y\) coordinates of the LED primaries illustrated in CIE 1932 chromaticity space. The corresponding gamut is shown as a red triangle.  
Figure 2: Overview of the computational structure of the proposed diversifying strategy. The input light spectra are clustered in an unbiased way by using their complete physical information encoded as features in a 401 dimensional vector space. Sub-clustering can eventually be performed based on pre-defined lighting parameters and may serve for a respective filtering of the main clusters. Light spectra belonging to different main clusters are maximally diverse to each other.