# Asymmetric Distance in K-Means Clustering Enhances Quality of Cells Raman Imaging
## 4 Results
### Further Validation by Analysing LX-2 Cells upon Treatment  
Here, we propose a further example of K-means clustering with an asymmetric metric, still in the field of cellular spectral analysis. The cell under study is an LX-2 cell after proper treatment with Retinol and Palmitic acid (ROL+PA) [26]. LX-2 cells are human hepatic stellate cells (HSCs). HSCs are usually in a quiescent state, characterized by high expression  
Figure 5: Projection of clusters on the first two principal components for the six-cluster choice. In the absence of ground truth to compare with, this projection helps to visualize and to inspect how clustering is performing with the different distance metrics. The Euclidean metric (**top panel**) produces too redundant segmentation for lipids (red, magenta, purple, and dark red symbols) and fails to identify a mitochondrial cluster (absence of yellow symbols). On the other hand, the polar metric (**bottom panel**) addresses the lipids with only two clusters (red and purple) but produces an excessive overlapping of other clusters (yellow, green, and light green). The asymmetric distance (**middle panel**) behaves as a compromise between Euclidean and polar metrics: yellow, blue, and green clusters are well separated, while the three clusters for lipids do not produce an excessive redundancy. The color legend on the right is intended to be beneficial to color-blind individuals. of lipid droplets (LDs) for storing vitamin A. Upon liver injury, HSCs transdifferentiate towards a so-called active state, characterized by both high fibrogenesis and loss of LDs. In this active state, HSCs are a crucial player in originating and sustaining liver fibrosis. Upon specific treatments, or as the liver injury subsides, active HSCs could be reverted to a quiescent-like state, restoring a high expression of LDs. LX-2 cells are partly active HSCs, and when treated with a combination of Retinol and Palmitic acid are reverted to a quiescent-like state. Figure 6 shows the results achieved by KCA with six clusters performed on the Raman hyperspectral recorded over an LX-2 cell after ROL+PA treatment. Euclidean, _ecc_ = 0.10 asymmetric, and polar metrics have been used for KCA. As in the former case, by comparing the image obtained for Euclidean and asymmetric metrics, we can notice that subcellular regions are better defined in the case of asymmetric distance. The Euclidean metric leads to two subregions in the nuclear area, but with neatly overlapping average spectra (dark cyan and blue curves). Instead, the asymmetric metric correctly assigns a single cluster to the nuclear region, surrounded by a yellow area ascribable to the presence of CytC (mitochondria). The yellow average spectrum obtained with asymmetric metric has a spectral behavior that better resembles the pure CytC spectrum, while the yellow curve for Euclidean metric is partly a mixture of CytC and lipid spectra, as denoted by large intensities at 2850 and 2880 cm\({}^{-1}\). This is likely due to an overlap of the yellow cluster with lipid regions. This issue is better solved by asymmetric distance, which introduces a transition region (the magenta cluster in the second row of Figure 5) between LDs and mitochondria. Figure 6: K-means clustering analysis of an LX-2 cell after treatment with Retinol and Palmitic acid. Euclidean (**top row**), _ecc_ = 0.10 asymmetric (**middle row**), and polar (**bottom row**) metrics are used with KCA. For each metric, image segmentation is presented along with cluster average spectra. The scale bar (black line in the top image) is 10 \(\upmu\)m. The color legend on the left and the color labels on the curves are beneficial to color-blind individuals. The last row of the figure shows the results attained using the polar metric. We find again a noisy image, as observed above, with some mixing regions in the outer part of the cell where two redundant clusters (green and light green) are assigned. Correctly, a single cluster is assigned to the nuclear region, but its border is rough and irregular.