## 3 Research Design
### Spatial Analysis Framework for Visual Attention
#### 3.3.1 K-Means Clustering Implementation  
This study employed the K-means clustering algorithm based on the scikit-learn library. The K-Means Fit function was defined to take two basic parameters: data \(\in\mathbb{R}^{2}\)  
\begin{table}
\begin{tabular}{l l} \hline
**Symbol** & **Definition** \\ \hline LT & Coordinate of the top-left corner of the stimulus image \\ RT & Coordinate of the top-right corner of the stimulus image \\ LB & Coordinate of the bottom-left corner of the stimulus image \\ \hline \end{tabular}
\end{table}
Table 1: Definition of reference points in the stimulus image.  
representing the fixation point coordinates, and count \(\in\mathbb{N}\), specifying the desired number of clusters. The clustering process transforms the continuous distribution of fixation points into discrete clusters using the following model:  
\[C\ =\ \{C_{1},C_{2},\ldots,C_{k}\},\ \text{where}\ k\ =\ \text{count}\ \text{and}\ c_{i}\in\mathbb{R}^{2} \tag{4}\]  
Each cluster \(C_{i}\) denotes a focal region of visual attention. This discretization method allows precise control over granularity via the count parameter while providing more interpretable visual results.  
To determine an appropriate number of clusters, we conducted multiple parameter tests and visually compared the clustering outcomes. The clustering results with different k values are illustrated in Figure 4, demonstrating the visual differences between under-segmentation (k = 3), optimal segmentation (k = 5), and over-segmentation (k = 8). As shown in Figure 4a (3 clusters), too few clusters tended to merge visually distinct regions, leading to under-segmentation and reduced interpretability. In Figure 4b (5 clusters) offered a more balanced representation, achieving a reasonable trade-off between structural coherence and visual clarity. In contrast, in Figure 4c (8 clusters) resulted in excessive fragmentation and structural noise due to over-segmentation. Based on this comparison, five clusters were selected for the current analysis.  
The resulting clusters represent data-driven centers calculated by the K-means algorithm. In addition, while quantitative validation results presented in Table 2 and in Figure 5 showed that k = 2 achieved the highest silhouette coefficient (0.497) and k = 7 minimized WCSS (1609.02), these purely statistical indicators do not fully meet the semantic and interpretive requirements of this study. Clustering with k = 2 created overly broad regions that failed to separate meaningful visual elements, while k = 6 and k = 7 produced fragmented and hard-to-interpret micro-clusters despite their lower WCSS. Similarly, k = 3 and k = 4 partially improved semantic segmentation but still merged critical Areas of Interest, such as the boat with the riverside or the village with the distant mountain, which would compromise subsequent gaze-verbal alignment. Therefore, we selected k = 5 as the optimal balance. It maintained a reasonable silhouette score (0.432), achieved a substantial WCSS reduction, and preserved five semantically coherent and interpretable regions  
Figure 4: Clustering results comparison with different k values: (a) k = 3 clusters (under-segmentation), (b) k = 5 clusters (optimal segmentation), (c) k = 8 clusters (over-segmentation).  
necessary for downstream structural modeling and multimodal analysis. This rationale demonstrates how domain-driven interpretability was carefully balanced with clustering performance metrics.