## 5 Experiment Analysis
### Comparative Analysis: Qualitative and Quantitative  
In this section, the reason is provided for selecting the TLBO nature-inspired clustering algorithm to extract the foreground cells of the _in vitro_ 3D cell spheroid. However, comparing the ground truth images of colon-cancer cells was not possible due to the unavailability of segmentation masks to compare them with the TLBO clustering segmentation results. Therefore, the TLBO clustering algorithm results were compared with other nature-inspired clustering and traditional clustering approaches: Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Invasive Weed Optimization (IWO), k-means (KM), k-medoids (KMed), and Fuzzy C-means (FCM). Results were compared on the basis of qualitative and quantitative results. On 200 iterations, the value of the fitness metrics (clustering cost as shown in Equation (3)) converged, as shown in Figure 4. Thus, all clustering experiments were performed by running the algorithms on 200 iterations. The parameter values used for each algorithm are shown in Table S1 (provided in the supplementary material).  
\[Cost_{j}=\frac{\sum_{k=1}^{n_{max}}(d_{k})}{n_{max}} \tag{3}\]  
\[d_{k}=\sqrt{(x_{s}-y_{t})^{2}+(x_{s}-y_{t})^{2}}\]  
\(\forall s,t\in{1,2,...,C_{n}}\), where \(n_{max}\) is the number of distances \(d_{k}\) calculated within the clusters.  
A qualitative comparison among clustering algorithms is shown in Tables 1-3 for the cellular ratio of 2:0.5 using three different images. Different cellular ratios of 2:1, 2:2, and 2:4 are shown in Tables S2-S4, respectively. The tables' information contains labeled images, the three clusters, and the graphical representation of clusters and their centroids. In the clustering of HCT-8 cells, the TLBO algorithm had greater potential than that of other algorithms. A similar phenomenon was observed for other cellular ratios, as shown in Tables S2-S4. In the quantitative comparison, all clustering algorithms were compared on the basis of quantization error (QE) [21] and best cost (BC) (Equation (3)). The quantization error of 2:0.5 ratio images is shown in Figure 5a,b, and the best cost is shown in Figure 5c,d. The different cellular ratios of quantization error and best cost are shown in Figures S5-S10.  
Qualitative and quantitative analysis suggested that TLBO clustering performance was better than that of other nature-inspired clustering approaches (PSO, GA, IWO) and traditional clustering approaches (k-means, k-medoids, FCM). Therefore, the TLBO clustering algorithm was selected for foreground cell clustering in the proposed methodology.  
Figure 4: Cost of clustering graph of each algorithm to show convergence up to 200 iterations.  
\begin{table}
\begin{tabular}{c c c c c c} \hline TIBO & PSO & GA & INO & k-kmeans & k-MHD & ICM \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparative Analysis of visual results of TLBO with other clustering algorithms for 2:0.5 ratio image of Figure 1a.  
Figure 5: Comparative analysis between teacher learning based optimization (TLBO) and other existing nature-inspired clustering techniques using 2:0.5 ratio slices based on (**a,b**) quantization error (QE) and (**c,d**) best cost (BC).