Landslide Susceptibility Prediction Considering Spatio-Temporal Division Principle of Training/Testing Datasets in Machine Learning Models
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摘要: 滑坡易发性预测时大多按空间随机来划分模型训练/测试数据集，但随机划分方式难免将不确定性因素引入建模中.因为理论上滑坡易发性是基于过去的滑坡来预测将来发生滑坡的空间概率，具有显著的时间顺序特征而非单纯的空间随机，可见有必要探索基于滑坡发生的时间顺序划分模型训练/测试集.以浙江文成县为例获取11类环境因子及128个时间准确的滑坡；之后将联接了环境因子的滑坡-非滑坡样本分别按照滑坡时间顺序和空间随机的原则，划分为两类不同训练/测试集；其划分比例分别设定为9∶1、8∶2、7∶3、6∶4和5∶5等以避免不同比例影响研究结果，由此得到10种组合工况下的训练/测试集；最后再训练测试支持向量机（SVM）、多层感知器（MLP）和随机森林（RF）等模型以预测滑坡易发性并分析其不确定性.结果表明：（1）训练/测试集按时间顺序划分的SVM、MLP和RF模型预测的滑坡易发性的不确定性略低于按空间随机性划分的模型，验证了按时间顺序划分的可行性；（2）训练/测试集按时间顺序划分实际上是其在空间随机划分下的一种更符合滑坡发生实际情况的“确定性”特征，当然对缺乏滑坡发生时间的数据集开展空间随机划分也是可行的.Abstract: In most of the landslide susceptibility prediction (LSP) models, the landslide-non landslide spatial datasets are divided into training/testing datasets according to the principle of spatial random, however, this spatial randomness division inevitably introduces uncertainties into LSP modelling. Theoretically, LSP modelling is based on past landslide inventories to predict the spatial probability of future landslides, which has significant time series characteristics rather than only spatial random characteristics. Therefore, we believe that it is necessary to divide spatial datasets into the model training/testing datasets based on the time series of landslide occurrence. Taking Wencheng County in China as an example, 11 types of environmental factors and 128 time-accurate landslides are obtained; Then, the landslide and non-landslide samples connected with environmental factors are divided into two different types of training/testing datasets according to the principles of landslide time series and spatial random, respectively. The division ratios of training/testing datasets are set as 9∶1, 8∶2, 7∶3, 6∶4 and 5∶5, respectively, to avoid the influences of different ratios on the LSP results. Thus, the training/testing datasets under 10 combined working conditions are obtained. Finally, several typical machine learning models, such as Support Vector Machine (SVM), Multi-Layer Perceptron (MLP) and Random Forest (RF), are then trained and tested to perform LSP and analyze their uncertainties. Results show that: (1) The LSP uncertainties performed by the time series-based SVM, MLP and RF models are slightly lower than those by spatial random-based models, which verifies the feasibility of dividing by time series; (2) The time series division of training/testing datasets is actually a "deterministic" case among the spatial random division, which is more consistent with the actual situation of landslides. Of course, it is also feasible to carry out spatial random division for training and testing datasets when lacking landslide occurrence time.
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图 3 水文环境、基础地质和地表覆盖因子
Fig. 3. Hydrological environment, basic geology and land cover factors
图 4 时间顺序(a~c)和空间随机(d~f)两种工况在9∶1和7∶3两种训练/测试集比例下的SVM预测易发性
Fig. 4. The susceptibility distribution of SVM model under the time series (a‒c) and spatial random (d‒f) conditions and the two training/testing set ratios of 9∶1 and 7∶3
图 5 时间顺序(a~c)和空间随机(d~f)两种划分在9∶1和7∶3两种训练/测试集比例下MLP预测易发性图
Fig. 5. Susceptibility distribution of MLP model under the time series (a‒c) and spatial random (d‒f) conditions and the two training/testing set ratios of 9∶1 and 7∶3
图 6 时间顺序(a~c)和空间随机(d~f)两种工况在9∶1和7∶3两种训练/测试集比例下的RF模型易发性图
Fig. 6. Susceptibility distribution of RF model under the time series (a‒c) and spatial random (d‒f) conditions and the two training/testing set ratios of 9∶1 and 7∶3
图 7 各工况在9∶1、7∶3和5∶5三种训练/测试集比例下的RF模型ROC曲线
Fig. 7. ROC curves of RF models at 9∶1, 7∶3 and 5∶5 training/testing datasets for each working condition
表 1 按时间顺序原则划分的机器学习模型的滑坡训练集和测试集
Table 1. Landslide training set and test set of machine learning model divided according to chronological principle
训练集/测试集 时间节点（年） 训练集中滑坡栅格数 测试集中滑坡栅格数 滑坡‒非滑坡样本中的训练/测试集划分数 9∶1 2011 760 105 1 520∶210 8∶2 2009 655 207 1 310∶414 7∶3 2006 617 239 1 234∶478 6∶4 2005.7 507 347 1 014∶694 5∶5 2004.8 427 432 854∶864 
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表 2 时间顺序和空间随机两种划分工况SVM模型预测滑坡易发性的频率比分析
Table 2. Frequency ratios of LSP by SVM under two division conditions of time series and spatial random
训练/ 测试集比例 易发性等级 时间工况全区栅格比例(%) 时间工况坡内栅格比例(%) 时间工况频率比(FR) 随机工况全区栅格比例(%) 随机工况坡内栅格比例(%) 随机工况频率比(FR) 9∶1 极低 36.69 1.27 0.035 38.29 1.16 0.030 低 21.93 5.78 0.264 21.22 6.71 0.316 中 15.42 9.13 0.592 14.97 8.32 0.556 高 13.55 24.39 1.801 13.37 24.62 1.842 极高 12.41 59.42 4.787 12.14 59.19 4.874 8∶2 极低 34.53 1.51 0.044 36.42 1.86 0.051 低 22.12 5.80 0.262 22.38 6.61 0.296 中 16.51 11.37 0.689 15.65 9.05 0.578 高 14.36 23.20 1.616 13.48 26.80 1.988 极高 12.48 58.12 4.655 12.08 55.68 4.611 7∶3 极低 34.63 1.29 0.037 34.46 1.75 0.051 低 21.68 5.61 0.259 22.31 6.78 0.304 中 16.57 11.33 0.684 16.39 7.71 0.471 高 14.29 21.85 1.529 14.12 24.65 1.746 极高 12.82 59.93 4.675 12.73 59.11 4.643 6∶4 极低 33.59 1.87 0.056 35.70 1.99 0.056 低 22.17 5.27 0.238 21.58 7.14 0.331 中 17.04 12.65 0.742 16.18 9.48 0.586 高 14.72 23.65 1.607 14.08 24.36 1.729 极高 12.48 56.56 4.533 12.46 57.03 4.576 5∶5 极低 33.82 2.91 0.086 34.36 2.44 0.071 低 21.96 8.27 0.376 21.52 7.68 0.357 中 17.31 15.83 0.915 17.28 15.13 0.876 高 14.71 24.10 1.639 15.07 27.60 1.831 极高 12.20 48.89 4.009 11.77 47.15 4.004
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表 3 各工况下SVM、MLP、RF模型ROC曲线的AUC值
Table 3. AUC values of ROC curves of SVM, MLP and RF models under various working conditions
机器学习模型 AUC (括号外为时间顺序划分而括号内为空间随机划分工况) 9∶1 8∶2 7∶3 6∶4 5∶5 SVM 0.847 (0.845) 0.809 (0.781) 0.824 (0.835) 0.816 (0.811) 0.807 (0.818) MLP 0.818 (0.802) 0.812 (0.794) 0.818 (0.821) 0.816 (0.809) 0.788 (0.791) RF 0.872 (0.911) 0.853 (0.855) 0.868 (0.901) 0.858 (0.849) 0.821 (0.880)
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表 4 各工况下SVM、MLP、RF模型的平均值和标准差
Table 4. Mean value and standard deviation of SVM, MLP and RF models under various working conditions
训练集/测试集 MEAN(括号外为时间顺序划分而括号内为空间随机划分) SD (括号外为时间顺序划分而括号内为空间随机划分) SVM MLP RF SVM MLP RF 9∶1 0.307 (0.301) 0.332 (0.306) 0.302 (0.319) 0.277 (0.276) 0.287 (0.259) 0.230 (0.210) 8∶2 0.316 (0.302) 0.315 (0.315) 0.318 (0.325) 0.272 (0.270) 0.299 (0.257) 0.213 (0.210) 7∶3 0.317 (0.314) 0.315 (0.352) 0.314 (0.331) 0.273 (0.271) 0.279 (0.244) 0.225 (0.208) 6∶4 0.315 (0.322) 0.318 (0.342) 0.328 (0.344) 0.269 (0.267) 0.264 (0.241) 0.216 (0.209) 5∶5 0.321 (0.321) 0.316 (0.331) 0.325 (0.329) 0.252 (0.265) 0.260 (0.247) 0.203 (0.195)
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