# Asymmetric Distance in K-Means Clustering Enhances Quality of Cells Raman Imaging
## 6 Conclusions  
In this study, we demonstrated that the incorporation of an asymmetric metric matrix into K-means clustering significantly enhances the segmentation quality of Raman imaging data from cells. By systematically varying the eccentricity parameter (_ecc_), we evaluated the impact of this novel distance metric on the clustering performance compared to conventional Euclidean and polar metrics.  
Our results indicate that the asymmetric metric provides a more refined and biologically meaningful segmentation of cellular regions, particularly at intermediate values of eccentricity (_ecc_ = 0.25 and _ecc_ = 0.10). At these settings, the algorithm effectively distinguishes subcellular structures, such as lipidic compartments, mitochondria, and nuclear regions, while minimizing redundant segmentation. Furthermore, this improved segmentation is achieved with a lower number of clusters compared to the Euclidean metric, which requires additional clusters to resolve the same biochemical features. This highlights the efficiency of the asymmetric metric in capturing relevant spectral variations without excessive cluster fragmentation. In contrast, the polar metric, although effective in distinguishing lipid compartments, introduced excessive noise and instability in clustering results.  
Moreover, we observed that increasing the number of clusters beyond an optimal threshold does not necessarily improve segmentation accuracy. Instead, excessive clustering introduces redundancy, particularly in lipid-rich regions and the outer membrane. This finding suggests that the choice of both an appropriate distance metric and an optimal cluster number is crucial for obtaining biologically interpretable results in Raman-based cell imaging.  
Overall, the implementation of asymmetric metric distances in K-means clustering represents a promising approach for cellular analysis through Raman microimaging. By providing a flexible and tunable metric, this method enhances spectral biochemical differentiation while preserving a more regular shape of cellular subregions. Future work may explore the extension of this approach to other spectral imaging techniques and its potential integration with advanced machine learning techniques for automated biochemical characterization of cells. Additionally, further research could investigate the application of asymmetric metrics in other clustering techniques or mathematical frameworks where distance metrics play a critical role, such as hierarchical clustering, graph-based segmentation, or manifold learning.  
The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15084461/s1](https://www.mdpi.com/article/10.3390/app15084461/s1)]([https://www.mdpi.com/article/10.3390/app15084461/s1](https://www.mdpi.com/article/10.3390/app15084461/s1)).  
Conceptualization, P.C.; Data curation, B.S.; Formal analysis, B.S. and P.C.; Investigation, B.S. and P.C.; Methodology, B.S. and P.C.; Software, P.C.; Supervision, P.C.; Validation, B.S. and P.C.; Visualization, B.S. and P.C.; Writing--original draft, P.C.; Writing--review and editing, B.S. and P.C. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in this study are included in the article and Supplementary Material. Further inquiries can be directed to the corresponding author.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
KCAK-means clustering analysis  
Three dimensional  
CytC Cytochrome C  
Hepatic stellate cell