{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T17:44:08Z","timestamp":1776707048325,"version":"3.51.2"},"reference-count":53,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["42201006"],"award-info":[{"award-number":["42201006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["20221105"],"award-info":[{"award-number":["20221105"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["CXCY2024055"],"award-info":[{"award-number":["CXCY2024055"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Key Laboratory of Deep-time Geography and Environment Reconstruction and Applications of the Ministry of Natural Resources, Chengdu University of Technology","award":["42201006"],"award-info":[{"award-number":["42201006"]}]},{"name":"Key Laboratory of Deep-time Geography and Environment Reconstruction and Applications of the Ministry of Natural Resources, Chengdu University of Technology","award":["20221105"],"award-info":[{"award-number":["20221105"]}]},{"name":"Key Laboratory of Deep-time Geography and Environment Reconstruction and Applications of the Ministry of Natural Resources, Chengdu University of Technology","award":["CXCY2024055"],"award-info":[{"award-number":["CXCY2024055"]}]},{"name":"Liaocheng University College Students innovation and Entrepreneurship Project","award":["42201006"],"award-info":[{"award-number":["42201006"]}]},{"name":"Liaocheng University College Students innovation and Entrepreneurship Project","award":["20221105"],"award-info":[{"award-number":["20221105"]}]},{"name":"Liaocheng University College Students innovation and Entrepreneurship Project","award":["CXCY2024055"],"award-info":[{"award-number":["CXCY2024055"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Accurate prediction of geological hazard susceptibility forms the foundation of effective risk management, yet small-sample constraints often limit model generalization. In order to address this issue, this study applied an ensemble method based on predictive symmetry quantification, using Mount Tai, China, as a test case. Thirteen influencing factors were integrated using six machine learning algorithms\u2014Logistic Regression (LR), Multilayer Perceptron (MLP), Random Forest (RF), Gradient Boosting Decision Tree (GBDT), eXtreme Gradient Boosting (XGB), and Support Vector Machine (SVM)\u2014trained on 34 hazard sites. Symmetry breaking in model outputs was quantified, and XGB and MLP, which showed the lowest correlation (0.59), were selected for dynamic weighted integration. Symmetry-adjusted weighting counteracts bias from individual models. For hyperparameter tuning, grid search was employed, while SHapley Additive exPlanations (SHAP) was used to quantify factor contributions. The performance of each model was evaluated using AUC and AP metrics. The key results show that all base models performed robustly (AUC &gt; 0.8), with XGB showing high consistency (AUC = 0.927), and the performance of the symmetry-optimized ensemble (MLP + XGB) exceeded that of all the individual models (AUC = 0.964). The dominant drivers of Geohazards included elevation, slope, the topographic wetness index, and road adjacency, with high-susceptibility zones clustered in southeastern high-altitude terrain, central mountains, and road-intensive north-central sectors. The approach presented here provides an ensemble method based on predictive symmetry quantification that is effective under the constraints of small sample sizes.<\/jats:p>","DOI":"10.3390\/sym17081353","type":"journal-article","created":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T07:56:06Z","timestamp":1755590166000},"page":"1353","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Ensemble-Based Susceptibility Modeling with Predictive Symmetry Optimization: A Case Study from Mount Tai, China"],"prefix":"10.3390","volume":"17","author":[{"given":"Zhuang","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-5671-1871","authenticated-orcid":false,"given":"Bin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"},{"name":"Key Laboratory of Deep-Time Geography and Environment Reconstruction and Applications of Ministry of Natural Resources, Chengdu University of Technology, Chengdu 610059, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pan","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiong","family":"Duan","sequence":"additional","affiliation":[{"name":"Sichuan Provincial Engineering Laboratory of Monitoring and Control for Soil Erosion in Dry Valley, School of Geographical Sciences, China West Normal University, Nanchong 637009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhonglin","family":"Ji","sequence":"additional","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changjuan","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xin","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yixin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Geography and Environment, Liaocheng University, Liaocheng 252000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fuhai","family":"Cui","sequence":"additional","affiliation":[{"name":"Heze Municipal Water Conservancy Survey and Design Institute, Heze 274000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Mokhtari, M., Faridi, P., Masoodi, M., and Ahmadi, S.M. (2023). Perspective chapter: A global view of natural hazards related disasters. Natural Hazards-New Insights, IntechOpen.","DOI":"10.5772\/intechopen.111582"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Xiao, W., Zhou, Z., Ren, B., and Deng, X. (2025). Integrating spatial clustering and multi-source geospatial data for comprehensive geological hazard modeling in Hunan Province. Sci. Rep., 15.","DOI":"10.1038\/s41598-024-84825-y"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Comegna, L., Rianna, G., Sequino, G., Reder, A., Picarelli, L., and Urciuoli, G. (2025). Climate change and landslide hazard in stiff clays and clay shales. Landslides.","DOI":"10.1007\/s10346-025-02487-x"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1033","DOI":"10.1007\/s12303-017-0034-4","article-title":"Landslide prediction, monitoring and early warning: A concise review of state-of-the-art","volume":"21","author":"Chae","year":"2017","journal-title":"Geosci. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1061\/(ASCE)0733-9410(1985)111:3(302)","article-title":"The arch in soil arching","volume":"111","author":"Handy","year":"1985","journal-title":"J. Geotech. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"155337","DOI":"10.1016\/j.scitotenv.2022.155337","article-title":"Spatiotemporal distribution characteristics, causes, and prevention advice of fatal geohazards in Jiangxi Province, China","volume":"834","author":"Shao","year":"2022","journal-title":"Sci. Total Environ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"808","DOI":"10.1111\/j.1755-6724.2004.tb00199.x","article-title":"Analysis of the geomorphology and environmental geological problems of Huzhou on the Yangtze River delta","volume":"78","author":"Jiang","year":"2004","journal-title":"Acta Geol. Sin.-Engl. Ed."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/s11069-010-9525-6","article-title":"Waterlogging and flood hazards vulnerability and risk assessment in Indo Gangetic plain","volume":"55","author":"Pandey","year":"2010","journal-title":"Nat. Hazards"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"28033","DOI":"10.1109\/ACCESS.2020.2972005","article-title":"Linking the random forests model and GIS to assess geo-hazards risk: A case study in Shifang County, China","volume":"8","author":"Huang","year":"2020","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Chen, B., Wei, N., Qu, T., Zhang, L., Li, Y., Long, X., and Lin, Y. (2023). Research on weighting method of geological hazard susceptibility evaluation index based on apriori Algorithm. Front. Earth Sci., 11.","DOI":"10.3389\/feart.2023.1127889"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s40515-025-00553-4","article-title":"Geotechnical Characterization and Stability Prediction of Nano-Silica-Stabilized Slopes: A Machine Learning Approach to Mitigating Geological Hazards","volume":"12","author":"Thapa","year":"2025","journal-title":"Transp. Infrastruct. Geotechnol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ahmad, H., Ningsheng, C., Rahman, M., Islam, M.M., Pourghasemi, H.R., Hussain, S.F., Habumugisha, J.M., Liu, E., Zheng, H., and Ni, H. (2021). Geohazards susceptibility assessment along the upper indus basin using four machine learning and statistical models. ISPRS Int. J. Geo-Inf., 10.","DOI":"10.3390\/ijgi10050315"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"454","DOI":"10.1007\/s10064-024-03931-3","article-title":"Small-scale, large impact: Utilizing machine learning to assess susceptibility to urban geological disasters\u2014A case study of urban road collapses in Hangzhou","volume":"83","author":"Yu","year":"2024","journal-title":"Bull. Eng. Geol. Environ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"103225","DOI":"10.1016\/j.earscirev.2020.103225","article-title":"Machine learning methods for landslide susceptibility studies: A comparative overview of algorithm performance","volume":"207","author":"Merghadi","year":"2020","journal-title":"Earth-Sci. Rev."},{"key":"ref_15","first-page":"1815","article-title":"Assessment of landslide susceptibility in xinyuan county based on machine learning models","volume":"25","author":"Yuan","year":"2025","journal-title":"Sci. Technol. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s00477-024-02885-y","article-title":"Landslide susceptibility assessment for the Darjeeling Toy Train route: A GIS and machine learning approach","volume":"39","author":"Sarkar","year":"2024","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1186\/s40068-024-00382-3","article-title":"Spatial assessment employing fusion logistic regression and frequency ratio models to monitor landslide susceptibility in the upper Blue Nile basin of Ethiopia: Muger watershed","volume":"13","author":"Hailu","year":"2024","journal-title":"Environ. Syst. Res."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jin, R., Wang, S., and Liu, J. (2024). Multi-Index Fusion Debris Flow Early Warning Model Based on Spatial Interpolation and Support Vector Machine. Water, 16.","DOI":"10.3390\/w16050724"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1007\/s11629-023-8395-9","article-title":"Comparison of debris flow susceptibility assessment methods: Support vector machine, particle swarm optimization, and feature selection techniques","volume":"21","author":"Zhao","year":"2024","journal-title":"J. Mt. Sci."},{"key":"ref_20","unstructured":"Chen, H., Zhang, H., Boning, D., and Hsieh, C.-J. (2019, January 9\u201315). Robust decision trees against adversarial examples. Proceedings of the International Conference on Machine Learning, Long Beach, CA, USA."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"nwab080","DOI":"10.1093\/nsr\/nwab080","article-title":"Reducing model biases is essential to projecting future climate variability","volume":"8","author":"Yamagata","year":"2021","journal-title":"Natl. Sci. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Strocchi, F. (2005). Symmetry Breaking, Springer.","DOI":"10.1007\/b95211"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4974","DOI":"10.1109\/TPAMI.2025.3552368","article-title":"Systematic bias of machine learning regression models and correction","volume":"47","author":"Lee","year":"2025","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_24","first-page":"134","article-title":"Assessing Geological Disaster Susceptibility in Taishan Area by Coupling Certainty Factor Model with Optimized Random Forest Model","volume":"44","author":"Xian","year":"2024","journal-title":"Bull. Soil Water Conserv."},{"key":"ref_25","first-page":"18","article-title":"Precambrian geology and geoparks in Shandong province, China","volume":"45","author":"Wang","year":"2022","journal-title":"North China Geol."},{"key":"ref_26","first-page":"3907","article-title":"The 30 m annual land cover datasets and its dynamics in China from 1985 to 2022","volume":"13","author":"Huang","year":"2023","journal-title":"Earth Syst. Sci. Data"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Tak, G.-M., Park, J.-H., Lee, C.-K., and Kim, H. (2023). Influence of altitude, slope, and waterway characteristics on the occurrence of slow-moving landslides in South Korea. Front. Earth Sci., 11.","DOI":"10.3389\/feart.2023.1276768"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Xie, C., Huang, Y., Li, L., Li, T., and Xu, C. (2023). Detailed inventory and spatial distribution analysis of rainfall-induced landslides in Jiexi County, Guangdong Province, China in August 2018. Sustainability, 15.","DOI":"10.3390\/su151813930"},{"key":"ref_29","first-page":"626","article-title":"Effects of drought and slope aspect on canopy facilitation in a mountainous rangeland","volume":"10","author":"Farzam","year":"2017","journal-title":"J. Plant Ecol."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Yang, W., Niu, R., Si, R., and Li, J. (2024). Geological hazard susceptibility analysis and developmental characteristics based on slope unit, using the xinxian county, henan province as an example. Sensors, 24.","DOI":"10.3390\/s24082457"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1324","DOI":"10.2166\/nh.2019.261","article-title":"The effect of roughness and rainfall on hydrodynamic properties of overland flow","volume":"50","author":"Wang","year":"2019","journal-title":"Hydrol. Res."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"6313","DOI":"10.1002\/2016GL069824","article-title":"On how spatial variations of channel width influence river profile curvature","volume":"43","author":"Chartrand","year":"2016","journal-title":"Geophys. Res. Lett."},{"key":"ref_33","first-page":"175","article-title":"Categorization of karst landform on the basis of landform factor eigenvalue","volume":"28","author":"Xue","year":"2009","journal-title":"Carsologica Sin."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"9582","DOI":"10.1007\/s11356-023-31739-3","article-title":"Influence of buffer distance on environmental geological hazard susceptibility assessment","volume":"31","author":"Wang","year":"2024","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Fang, L., Wang, Q., Yue, J., and Xing, Y. (2023). Analysis of optimal Buffer distance for linear hazard factors in landslide susceptibility prediction. Sustainability, 15.","DOI":"10.3390\/su151310180"},{"key":"ref_36","first-page":"1260","article-title":"Geological hazard risk assessment based on Information Model: A case study of Lufeng City in Yunnan Province","volume":"41","author":"Feng","year":"2024","journal-title":"World Nucl. Geosci."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"967","DOI":"10.1007\/s10346-022-02020-4","article-title":"Land use and land cover as a conditioning factor in landslide susceptibility: A literature review","volume":"20","author":"Korup","year":"2023","journal-title":"Landslides"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zhang, S., Tan, S., Zhou, J., Sun, Y., Ding, D., and Li, J. (2023). Geological disaster susceptibility evaluation of a random-forest-weighted deterministic coefficient model. Sustainability, 15.","DOI":"10.20944\/preprints202306.2075.v1"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Huangfu, W., Wu, W., Zhou, X., Lin, Z., Zhang, G., Chen, R., Song, Y., Lang, T., Qin, Y., and Ou, P. (2021). Landslide geo-hazard risk mapping using logistic regression modeling in Guixi, Jiangxi, China. Sustainability, 13.","DOI":"10.3390\/su13094830"},{"key":"ref_40","unstructured":"Cui, S., Sudjianto, A., Zhang, A., and Li, R. (2023). Enhancing robustness of gradient-boosted decision trees through one-hot encoding and regularization. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"119031","DOI":"10.1016\/j.ins.2023.119031","article-title":"Multiobjective bilevel programming model for multilayer perceptron neural networks","volume":"642","author":"Li","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Castro, W., Oblitas, J., Santa-Cruz, R., and Avila-George, H. (2017). Multilayer perceptron architecture optimization using parallel computing techniques. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0189369"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Chen, T., and Guestrin, C. (2016, January 13\u201317). Xgboost: A scalable tree boosting system. Proceedings of the 22nd ACM Sigkdd International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/2939672.2939785"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Zhou, Z.-H. (2025). Ensemble Methods: Foundations and Algorithms, CRC Press.","DOI":"10.1201\/9781003587774"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1023\/A:1022859003006","article-title":"Measures of diversity in classifier ensembles and their relationship with the ensemble accuracy","volume":"51","author":"Kuncheva","year":"2003","journal-title":"Mach. Learn."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Zhang, S., Ma, K., Wang, L., Zhang, Z., Ye, X., Zhang, J., and Li, H. (2024). Prediction of thermal protection performance and empirical study of flame-retardant cotton based on a combined model. Front. Mater., 11.","DOI":"10.3389\/fmats.2024.1454935"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"8737","DOI":"10.1007\/s00330-022-08887-0","article-title":"The radiomic-clinical model 788 using the SHAP method for assessing the treatment response of whole-brain radiotherapy: A multicentric study","volume":"32","author":"Wang","year":"2022","journal-title":"Eur. Radiol."},{"key":"ref_48","first-page":"37","article-title":"Landslide susceptibility modeling and interpretability based on CatBoost-SHAP model","volume":"35","author":"Zeng","year":"2024","journal-title":"Chin. J. Geol. Hazard Control"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1007\/s11069-020-03927-8","article-title":"Multi-geohazards susceptibility mapping based on machine learning\u2014A case study in Jiuzhaigou, China","volume":"102","author":"Cao","year":"2020","journal-title":"Nat. Hazards"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.earscirev.2018.03.001","article-title":"A review of statistically-based landslide susceptibility models","volume":"180","author":"Reichenbach","year":"2018","journal-title":"Earth-Sci. Rev."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"111574","DOI":"10.1016\/j.enbuild.2021.111574","article-title":"An online physical-based multiple linear regression model for building\u2019s hourly cooling load prediction","volume":"254","author":"Chen","year":"2022","journal-title":"Energy Build."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1937","DOI":"10.1007\/s10462-020-09896-5","article-title":"A comparative analysis of gradient boosting algorithms","volume":"54","year":"2021","journal-title":"Artif. Intell. Rev."},{"key":"ref_53","first-page":"507","article-title":"Why do tree-based models still outperform deep learning on typical tabular data?","volume":"35","author":"Grinsztajn","year":"2022","journal-title":"Adv. Neural Inf. Process. Syst."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1353\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:30:29Z","timestamp":1760034629000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1353"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"references-count":53,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081353"],"URL":"https:\/\/doi.org\/10.3390\/sym17081353","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,19]]}}}