**1. Introduction**

A submarine landslide is a destructive phenomenon of marine geological disasters. Large-scale submarine landslides can even cause long-distance migration of thousands of cubic kilometers of sediment [1], damage various engineering facilities such as offshore oil production platforms [2] and submarine optical cables [3], and even cause tsunamis [4]. This can result in a number of incidents, such as communication failure and platform collapse, which pose a significant risk to human life and property. Therefore, there is a pressing need for submarine landslide stability before engaging in offshore engineering activities.

At present, the main research directions of submarine landslides include: using highprecision geophysical detection to identify and classify landslide morphology [5,6], carrying out stability calculations of submarine landslides by the numerical analysis method [7–9], and simulating the landslide process through physical model tests such as a conventional water tank or centrifuge [10,11]. Despite attempts through the above traditional studies, the research on risk assessment and categorization is still insufficient due to the complicated control circumstances of submarine landslides, the large number of trigger factors, and the difficulty of monitoring.

Machine learning and deep learning techniques have been proven to be powerful and promising tools in many geotechnical applications [12–16]. Chen et al. [12] designed

**Citation:** Du, X.; Sun, Y.; Song, Y.; Xiu, Z.; Su, Z. Submarine Landslide Susceptibility and Spatial Distribution Using Different Unsupervised Machine Learning Models. *Appl. Sci.* **2022**, *12*, 10544. https://doi.org/10.3390/app122010544

Academic Editors: Yuzhu Wang, Jinrong Jiang and Yangang Wang

Received: 1 September 2022 Accepted: 14 October 2022 Published: 19 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

landslide spatial models using maximum entropy, support vector machine, and artificial neural network methods. Tse et al. [15] performed an unsupervised learning approach to study the synchroneity of past events in the South China Sea. Qi and Tang [16] used integrated metaheuristic and machine learning approaches for slope stability prediction. Deep learning convolutional neural networks [17] and support vector machines [18] are also used in landslide detection. Even though the mentioned methods performed well for landslide modeling in a given area, there is no conclusive information about which model is the best for other regions. In addition, the application of the recently developed techniques and methods for a more accurate evaluation of the predictive capability of landslide susceptibility models should be evaluated further.. At present, the main research objects of landslides using machine learning are landslides on land, but few types of research are on submarine landslides. The problem of zoning submarine landslide hazards is still a difficult area for landslide research. On the other hand, machine learning excels at resolving nonlinear problems without the need of explicit mathematical relationships. Therefore, it is essential to investigate if machine learning algorithms can be utilized for zoning undersea landslide hazards and to research how well various machine learning methods perform.

The primary purpose of this study is to offer an integrated strategy for assessing submarine landslide susceptibility that uses unsupervised machine learning models to evaluate landslide risk and partition the affected region. Submarine landslides in the Yellow River Estuary are selected for study and validation of the suggested method. Three machine learning models based on k-means, spectral clustering, and hierarchical clustering are developed and compared for performance evaluation.
