## 5 Application
### Results and Analysis
(2) Correlations between the fixation count and layout aesthetics  
The correlations were calculated as \(\hat{R}_{H}(2,1)=-0.9300\), \(\hat{R}_{H}(2,2)=-0.5001\), \(\hat{R}_{H}(2,3)=-0.4819\), \(\hat{R}_{H}(2,4)=-0.4769\), and \(\hat{R}_{H}(2,5)=-0.9353\). Sorting based on the magnitude of the correlation between the two sequences revealed \(\hat{R}_{H}(2,5)>\hat{R}_{H}(2,1)>\hat{R}_{H}(2,2)>\hat{R}_{H}(2,3)>\hat{R}_{H} (2,4)\). Indeed, symmetry and dominance exhibit a stronger correlation with fixation count, whereas simplicity, order, and density demonstrate comparatively lower correlations. This suggests that in interface design, the layout information should be harmonized and consistent, adhering to specific user line-of-sight guidance principles. Such an approach serves to mitigate visual load and enhance reading speed and overall user experience. (3) Correlations between mean pupil diameter and layout aesthetics  
The correlations were calculated as \(\hat{R}_{H}(3,1)=-0.7124\), \(\hat{R}_{H}(3,2)=-0.4937\), \(\hat{R}_{H}(3,3)=-0.5077\), \(\hat{R}_{H}(3,4)=-0.4586\), and \(\hat{R}_{H}(3,5)=-0.4997\). Sorting based on the magnitude of the correlation between the two sequences revealed \(\hat{R}_{H}(3,1)>\hat{R}_{H}(3,3)>\hat{R}_{H}(3,5)>\hat{R}_{H}(3,2)>\hat{R}_{H }(3,4)\). Indeed, symmetry and simplicity exhibit the strongest correlation with mean pupil diameter, with dominance following closely behind, while density and order demonstrate relatively lower correlations. The notable correlation between simplicity and mean pupil diameter suggests that greater alignment and integration of layout information contribute to a more transparent and comprehensible interface. This in turn aids in reducing visual load and information search time, thereby enhancing overall user experience. (4) Correlations between gaze shift frequency and layout aesthetics  
The correlations were calculated as \(\hat{R}_{H}(4,1)=0.9720\), \(\hat{R}_{H}(4,2)=0.9382\), \(\hat{R}_{H}(4,3)=0.4504\), \(\hat{R}_{H}(4,4)=0.9808\), and \(\hat{R}_{H}(4,5)=0.4779\). Sorting based on the magnitude of the correlation between the two sequences revealed \(\hat{R}_{H}(4,4)>\hat{R}_{H}(4,1)>\hat{R}_{H}(4,2)>\hat{R}_{H}(4,5)>\hat{R}_{H }(4,3)\). Correlations among order, symmetry, density, and frequency of gaze shifts are notably strong, whereas dominance, simplicity, and gaze shift frequency exhibit relatively low correlations. The interface layout adheres to optimal visual principles and reading habits, effectively guiding the eye's scanning pattern. Moreover, interface density significantly influences gaze shift frequency, necessitating designers to adhere to standardized design principles and judiciously regulate the spacing between interface elements. (5) Correlations between gaze time percentage and layout aesthetics  
Correlations are obtained by calculating \(\hat{R}_{H}(5,1)=0.9155\), \(\hat{R}_{H}(5,2)=0.4764\), \(\hat{R}_{H}(5,3)=0.0178\), \(\hat{R}_{H}(5,4)=0.4213\), \(\hat{R}_{H}(5,5)=0.9710\), all positive correlations. This is based on the size of the correlation ordering: \(\hat{R}_{H}(5,5)>\hat{R}_{H}(5,1)>\hat{R}_{H}(5,2)>\hat{R}_{H}(5,4)>\hat{R}_{H }(5,3)\). Indeed, the percentage of gaze time exhibits the strongest correlation with dominance and symmetry, followed by density and order, while demonstrating the weakest correlation