## 3 Results and Discussion
### Design of Ink Properties
#### 3.2.2 K-Means Clustering  
K-means clustering was subsequently performed to validate the grouping of the data points into clusters based on their similarities. In K-means clustering, the data points were partitioned into three clusters, as predefined via PCA. The algorithm that was trained seems to work iteratively by assigning each data point to the nearest centroid (mean) of a cluster and then recalculating the centroid of each cluster based on the newly assigned data points leading to Clusters 1, 2, and 3 with four, six, and one observation, respectively (Figure 8a). Through this process, the algorithm defined the means of all investigated variables for each cluster, as presented in Figure 8b. K-means clustering was performed two times. In the first run, the original dataset was used to provide better insight into the material properties of each cluster (Figure 8a,b). In the second run, the transformed dataset was used as input to the K-means clustering algorithm to improve the quality of the clusters by reducing the dimensionality of the data (Figure 8c,d).  
The K clustering results are in agreement with the PCA results. Based on the PCA analysis, it is concluded that the observations can be categorized into three clusters. Considering this parameter, the materials based on their similarities were divided in terms of their rheological properties and printing behavior. According to the centroids table (Figure 8b), materials that can be classified as liquids, as the liquid phase predominates even under low shear rate conditions (G\({}^{\prime\prime}\) > G\({}^{\prime}\)), belong to the first cluster. These materials have low viscosity and cannot be used as extrusion-based 3D printing inks. The second cluster includes materials that are characterized by the elastic solid phase. These materials exhibit low tan\(\delta\) values indicating their gel-like behavior. Cluster 2 displays a higher viscosity centroid than Cluster 1 and lower than Cluster 3. The fact that the elastic solid phase predominates affects the blends' printability, which is not adequate, and therefore, those materials are evaluated as not suitable for DIW. The third cluster combines a high viscosity value with higher tan\(\delta\) values (compared to Cluster 2's centroids), limiting to a certain extent the predominance of the viscous elastic phase. This ratio between the viscous liquid  
Figure 8: (**a**) Table of final partition of the initial dataset; (**b**) cluster centroids table of the initial dataset; (**c**) table of final partition of the PCA’s transformed dataset; (**d**) cluster centroids table of the PCA’s transformed dataset.  
phase and elastic solid phase, along with high values of viscosity and yield stress, is the required combination of rheological properties for the highest printability to be achieved. Cluster 3 is evaluated as the appropriate ink for DIW. The second run of the K-clustering based on the transformed dataset (scores of PC1, PC2, and PC3) is in total alignment with the PCA classification (Group 1, Group 2, Group 3), marking as printable both 6.0_4.0 and 8.0_4.0 alginate-gelatin blends, although the later exhibit the best printing behavior. Cluster 1 is characterized as liquid-like materials, and Cluster 2 as elastic solid-like materials (gels), both inappropriate for DIW inks.