## 3 Results
### Clustering Analysis  
Clustering techniques are useful in identifying subgroups in all spatial dimensions. Its ability to group points into compact and separate clusters can help reveal underlying structures in the data and identify groups of similar points in a multidimensional space. Thus, the K-means algorithm is a valuable tool in the exploration and analysis of unlabeled data, facilitating pattern understanding and decision making based on the intrinsic structure of the data. For the choice of the number of clusters, the Jambu elbow technique is used (see Figure S2), where it is observed that there are four clusters before the inertia of the cluster decreases considerably [38]. Figure 1 shows the distribution of each of the clusters using principal component analysis (PCA), which projects each of the dimensions on the principal planes of the data. In general, orthogonal behavior formed between the four groups of points is observed, indicating that the data are distributed heterogeneously among each dependent variable, i.e., some formulations favor only tensile stress or elongation at break (purple and blue) and others favor in between (green and red). In addition, the figure allows the agglomerability of the groups to be evaluated, and good agglomeration of the data is observed, with the exception of some points that escape the average of the rest of the group. Now, a relevant point of study for materials developers is to identify components that allow desirable properties in terms of their specific application. As shown in Figure 2a-d, the formulations are represented in each of the clusters in these heat maps, where each combination (row) of the described components is presented on the \(x\)-axis (columns), and the intensity of the color represents the relative value between 0 and 1 of the concentration of the corresponding component (normalization is only for visualization). It can be observed that the last two columns are reserved for the dependent variables' tensile stress and  
Figure 1: Principal component visualization of clusters; it shows how each formulation is represented in the two principal components. elongation at break. That is, the heat map is like a large table where each row represents a different formula for making the bioplastic film and each column represents the specific ingredients one is using. The cells in the table indicate the concentration of the ingredient, except for the last two columns as mentioned. If we analyze the intensity levels with respect to the other clusters, they can be classified as follows:  
* Cluster a: High elongation at break, low tensile strength (Figure 2a). * Cluster b: Low elongation at break, medium tensile strength (Figure 2b). * Cluster c: Low elongation at break, high tensile strength (Figure 2c). * Cluster d: Medium elongation at break, low tensile strength (Figure 2d)  
From this analysis, it is interesting to observe how the components and level of concentrations are distributed according to each of the clusters, making it possible to identify the components and combinations that are most conducive to improving material performance on both tensile strength and elongation at break. For example, if one wanted to improve the properties of elongation at break, cluster a or d shows the highest performance. If one  
Figure 2: Components and composition of normalized data distribution of (**a**) cluster containing formulations with high elongation at break capacity and low tensile strength, (**b**) cluster b containing formulations with low elongation at break capacity and medium tensile strength, (**c**) cluster c containing formulations with low elongation at break capacity and high tensile strength, and (**d**) cluster d containing formulations with medium elongation at break capacity and low tensile strength.