*3.4. Validation*

Cluster results of k-means, spectral clustering, and hierarchical clustering validated with different measures are shown in Figure 4. It can be seen from (1)~(6) and (10)~(12) that all the three cluster methods performed best when the cluster number is 2, and decreased when the cluster number increased. In the mathematics view, the data should be divided into two classes as they performed best. However, we should consider our geological needs as an important classification factor as well. This sea area can be divided into two classes, with the seabed sediments mutating at about a 14 m water depth.

Nevertheless, we need a more accurate range of submarine landslide susceptibility with acceptable mathematical accuracy. The cluster number of 3 is still insufficient to classify the study region because the classification result may be easily inferred from the hydrodynamic characteristics. As a result, the final cluster number is 4, which corresponds to the classifications very high, high, low, and very low.

As seen from (7) to (9), the clustering result performed best when gamma was equal to 0.01 with the Calinski–Harabasz index and gamma equal to about 1 using the silhouette index and Davies–Bouldin index. Therefore, the kernel function parameter gamma is 1. It is shown in (13)~(15) that the result performed best when the affinity method is Manhattan. The specific parameters used in the three cluster models can be seen in Table 1.

**Figure 4.** Cluster results of k-means, spectral clustering, and hierarchical clustering were validated with the Calinski–Harabasz index, silhouette index, and Davies–Bouldin index. (1)~(3) Validate cluster numbers of k-means. (4)~(6) Validate cluster numbers of spectral clustering. (7)~(9) Validate kernel function parameter of spectral clustering. (10)~(12) Validate cluster numbers of hierarchical clustering. (13)~(15) Validate affinity of hierarchical clustering. The red circle indicates the location where the model achieved the best prediction.

**Model Cluster Number Gamma Affinity Linkage** k-means 4 None None None Spectral 4 1 None None Hierarchical 4 None Manhattan Average

**Table 1.** Parameters used in different models.

The parameters are not necessary for the model when it shows "None".

All machine learning calculations in the article were carried out using the scikit-learn machine learning package [26], an open-source python library, via a laptop with windows 10, 16G RAM, CPU R 5800H, and GPU 3060.
