# Asymmetric Distance in K-Means Clustering Enhances Quality of Cells Raman Imaging
## 4 Results
### Biochemical Assignment of Clustered Regions  
To elucidate the chemical meaning of the different clusters and to check redundant segmentation, Figure 4 shows the average spectra for the seven-cluster case. Since some clustering results are similar to each other, we examine the average curves resulting from Euclidean, asymmetric with \(ecc\) = 0.10, and polar metrics. Further, for clarity's sake, we divide the lipid-originated spectra (reddish tones) from other biological contributions. For all reddish spectra, we can see the presence of clear peaks at 2850 and 2880 cm\({}^{-1}\), which are well-known spectral markers for lipid molecules [17,18]. Moreover, the peaks at 1265 and 1300 cm\({}^{-1}\) are also related to lipids vibrations, and their intensity ratio \(l_{1265}/l_{1300}\) correlates directly with the unsaturation degree [19]. Another indicator for the presence of C=C double bonds in lipids is the intensity of the 1660 cm\({}^{-1}\) peak compared with the intensity at 1445 cm\({}^{-1}\)[19]. However, this marker is more useful in the context of pure molecule analysis than in cellular datasets, because in cellular and tissue samples, protein vibrations also contribute to the 1660 cm\({}^{-1}\) intensity. Among the other average spectra, the yellow curve is characterized by peaks at 750, 1130, and 1582 cm\({}^{-1}\), which are typical vibrations of Cytochrome C and can be ascribed to mitochondria [20, 21, 22], both in perinuclear regions (endoplasmic reticulum) and in cytoplasmic regions (branched to cytoskeleton). The blue spectrum exhibits characteristic peaks of DNA bases at 785, 1340, and 1575 cm\({}^{-1}\)[23,24], and, therefore, blue clusters can be assigned to nuclear regions. Finally, the green curve resembles the average Raman signal of the overall cell, but with a significantly smaller intensity. These features, along with the outer location of green clusters, suggest that this signal is originated by the thinner parts of the external cell membrane. The just described spectral features are shared among the average spectra obtained with the different metrics. At this point, we would like to mention that, although Raman microspectroscopy offers high chemical specificity and can, in principle, provide molecular fingerprints of proteins as well, in complex biological samples, such as whole cells and/or tissues, protein signals are generally less distinctive compared to those of lipids or nucleic acids. Raman bands associated with proteins are often more difficult to resolve due to overlap with other cellular components, and the most prominent protein-related Raman feature, the Amide I band (1600-1700 cm\({}^{-1}\)), would require spectral deconvolution (e.g., using Gaussian or Pseudo-Voigt fits) to extract information about protein secondary structures [25]. However, such further spectral analysis would be beyond the scope of the present work. In Figure 4, the lipid spectra for Euclidean and \(ecc=0.10\) asymmetric metrics can be considered redundant. As an example, if we consider the \(1_{1265}/1_{300}\) ratio and the 2850 and 2880 cm\({}^{-1}\) intensities, the red and magenta curves (the first two from the top) are quite overlapping each other, while the dark red curve (the bottom one) is significantly different from the others. The purple curve is a kind of hybridization between the red-magenta curves and the dark-red one, thus representing a kind of transition curve but it does not bring any new chemical information. Instead, the other curves (yellow, blue,  
Figure 4: Average spectra for the seven-cluster segmentation. The spectra on the left correspond to lipid-associated clusters, while those on the right are assigned to mitochondria (yellow), nuclei (blue), and the outer membrane (green). The average spectra are displayed for three different metrics: Euclidean (**first row**), asymmetric with \(ecc=0.10\) (**second row**), and polar (**third row**). The clustering images in each row correspond to those in Figure 3 and are included here for reference.