## 5 Discussion  
### Model Performance Comparison  
To test the performance of cluster results, both internal validation measures and external validation measures were used. For internal validation measures, we validated the accuracy of three different submarine landslide susceptibility models by using the Calinski-Harabasz index, silhouette index, and Davies-Bouldin index. The three indexes use different algorithms to examine the merits of the classification results from a mathematical perspective. As shown in Figure 8, the k-means model performed best under the evaluation of the Calinski-Harabasz index, whereas the spectral clustering model performed best when evaluating the silhouette index and Davies-Bouldin index. Therefore, spectral clustering has the best performance compared to k-means and hierarchical clustering in the internal validation measures.  
In general, external causes of submarine landslides include earthquakes, gas hydration, wave action, volcanic activity, tsunamis, etc. There are no severe geological phenomena such as earthquakes, tsunamis, and volcanoes in the study area. The main external influence factor is the liquefaction of seabed soil caused by waves. Therefore, for the external validation measure, the three distributions of submarine landslide susceptibility were compared with the distribution of liquefaction depth (Figure 9). As shown in Figure 9, the area with the deepest liquefaction depth (ellipse A) is distributed at a water depth of 6-12 m. The area of ellipse A agrees well with the submarine landslide susceptibility results using k-means and spectral clustering, whereas the result obtained using hierarchical clustering is quite different from ellipse A. The area with a deep liquefaction depth (ellipse B) is distributed at a water depth of 12-15 m. It is in good agreement with the result obtained using hierarchical clustering, and the areas obtained by k-means and hierarchical clustering are different from the area of ellipse B. The area with a small, shallow liquefaction depth (ellipse C) is distributed at a water depth of less than 5 m, which agrees well with all the clustering results. The area with a very shallow liquefaction depth (ellipse D) is distributed at a water depth deeper than 15 m. It is in good agreement with the result obtained using  
Figure 7: Distribution of submarine landslide susceptibility using hierarchical clustering.  
hierarchical clustering, and the areas obtained by k-means and hierarchical clustering are larger than the area of ellipse D. As a result, the submarine landslide susceptibility results using spectral clustering performed better than those obtained using k-means and hierarchical clustering in the external validation.  
In conclusion, all three models used in this study are capable of producing correct clustering results, with the spectral clustering model being the most precise when grouping the undersea landslide susceptibility. Although the best algorithm can be obtained by internal verification methods, the scores of different algorithms are not different enough to represent the difference. To obtain the best results, it is still necessary to combine external verification methods at the same time.  
Figure 8: Comparison of clustering results validated with different internal validation measures. **(a)** Performance of different models under Calinski–Harabasz validation methods. **(b)** Performance of different models under silhouette validation methods. **(c)** Performance of different models under Davies–Bouldin validation methods. The higher the Calinski–Harabasz index and silhouette index are, the more accurate the clustering result will be. The lower the Davies–Bouldin index is, the more accurate the clustering result will be.  
Figure 9: Distribution of liquefaction depth in the Yellow River Estuary. The area of ellipses A, B, C, and D represents the very deep, deep, shallow, and very shallow parts of liquefaction depth, respectively.