A comparative study of mutual information-based input variable selection strategies for the displacement prediction of seepage-driven landslides using optimized support vector regression

Abstract

Artificial intelligence (AI) is becoming increasingly popular and useful for modeling landslide movement processes due to its advantages of providing excellent generalization ability and accurately describing complex and nonlinear behavior. However, the identification of key variables is a crucial step in ensuring robustness and accuracy in AI modeling, but thus far, little attention has been given to this topic. In the present study, mutual information (MI)-based measures are proposed for input variable selection (IVS) and incorporated into optimized support vector regression (SVR) for the displacement prediction of seepage-driven landslides. The performance of optimized SVR models with ten MI-based IVS strategies is compared. A typical seepage-driven landslide was chosen for comparison. The experimental results indicate that IVS-based optimized SVR can significantly improve predictions. When the variable-reduced inputs were input into the optimized artificial bee colony (ABC)-SVR model, the mean values of normalized root mean square error (NRMSE) and Kling-Gupta efficiency (KGE) decreased and increased by as much as 71.6 and 95.2%, respectively, relative to those for the base model with all candidates. Furthermore, the joint mutual information (JMI) and double input symmetrical relevance (DISR) criteria are recommended for IVS for seepage-driven landslides because they achieve the best tradeoff between accuracy and stability.

Appendices

Appendix 1

Selected publications that use IVS with AI methods for landslide displacement prediction.

Reference	Algorithm	Basis of IVS	Selected input variables	Evaluation criteria
Du et al. (2013)	Back-propagation neural network (BP)	Empirical expert knowledge	Accumulated precipitation in the previous month, accumulated precipitation in the past two months, variations in the reservoir level during the previous month, accumulated displacement increment for 1 year, and average reservoir level in the current month	Average RE: 1.3/3.04%
Li and Kong (2014)	Genetic algorithm-optimized support vector machine (GA–SVM)	Empirical expert knowledge	Average displacement rate, average reservoir level, accumulated precipitation, and average monthly groundwater flow in the current month	RMSE: 0.0009 mm R: 0.9992
Ren et al. (2014)	Particle swarm-optimized support vector machine (PSO-SVM)	Empirical expert knowledge	Accumulated precipitation in the previous month, accumulated precipitation in the past two months, maximum continuous decrement in reservoir level during the current month, and variation in the reservoir water level during the current month	MSE: 2.45/10.64 mm R2: 0.945/0.981
Cao et al. (2016)	Extreme learning machine (ELM)	Empirical expert knowledge and grey correlation coefficient	Accumulated precipitation in the past 1 and 2 months, average reservoir level in the current month, variation in the reservoir level during the previous 1 month, groundwater level in the current month, and displacement in the past 1, 2 and 3 months	RE: 0.69—5.94% R: 0.984
Zhou et al. (2016)	Particle swarm-optimized support vector machine (PSO-SVM)	Empirical expert knowledge	Accumulated precipitation in the current month and over the past 2 months, average reservoir level in the current month, variation in the reservoir level in the current month, and displacement in the past 1, 2 and 3 months	MAPE: 13.28% RMSE: 25.95 mm
Huang et al. (2017)	Multivariate chaotic model and extreme learning machine (Multivariate chaotic ELM)	Empirical expert knowledge	Periodic displacement in the past 1, 2, 3, and 4 months, accumulated precipitation in the past 1 and 2 months, and variation in the reservoir level in the past 1 and 2 months	RMSE: 23.71 mm R2: 0.908
Wen et al. (2017)	Particle swarm-optimized support vector machine (PSO-SVM)	Empirical expert and grey correlation coefficient	Cumulative precipitation in the current and past 2 months, reservoir water level, variation in the reservoir level in the current and past 2 months, and groundwater depth	RMSE: 49.0485 mm MAE: 48.5392 mm MAPE: 3.131%
Ma et al. (2018)	Bootstrap, extreme learning machine, and artificial neural network (Bootstrap-ELM-ANN)	Empirical expert knowledge	Accumulated precipitation in the past one and 2 months, average reservoir level in the current month, variation in the reservoir level in the current month, and displacement in the past 1, 2, and months	PICP: 97.5%
Li et al. (2019)	Continuous wavelet analysis and deep belief network (CWT-DBN)	p values less than 0.05	First two monthly precipitation lags, eighth to tenth monthly lags in reservoir water level fluctuations, second and fourth monthly lags for precipitation, and first, seventh, and eighth lags in reservoir water level fluctuations, and historic lags in past-month displacement	MAE: 6.89 mm MAPE: 14.59% RMSE: 24.63 mm
Wang et al. (2019)	Lower and upper bound estimation, double exponential smoothing, and particle swarm-optimized extreme learning machine (LUBE- DES-PSO-ELM)	Partial autocorrelation function and maximum information coefficient	Displacement in the past 1 and 2 months, average reservoir level during the current month versus that in the previous one, two and three months, and variation in the reservoir level in the current and past 2 months	AIC: − 76.77
Xing et al. (2020)	Double moving average, support vector machine, and long short-term memory (DES-SVR-LSTM)	Grey correlation coefficient	Maximum daily rainfall in the current month, accumulated rainfall in the current month and over the past 1 and 2 months, reservoir level in current month, variation in the reservoir level in the current and past 2 months, displacement in the past 1, 2, and 3 months	RMSE: 6.18 mm MAE: 4.97 mm
Li et al. (2021)	Greedy algorithm, complementary ensemble empirical mode decomposition, and random forest (GA-CEEMD-RF)	Empirical expert knowledge and grey correlation coefficient	Accumulated precipitation in the past one and 2 months, average precipitation in the first three months, average reservoir level in the current month, maximum variation in reservoir level in the current month and the first two months, and the high-frequency components of accumulated precipitation in the past one month and reservoir level in the current month	R2: 0.98

1. AIC Average interval score MAE Mean absolute error MAPE Mean absolute percentage error; MSE Mean squared error PICP Prediction interval coverage probability R Correlation coefficient R² Coefficient of determination RE Relative error RMSE Root mean square error.

Appendix 2

Typical seepage-driven landslides in the TGRA.

Landslide	Location	Features	Landslide mass materials and permeability coefficient	Description of landslide movement
Baishuihe landslide	Zigui County, right bank of the Yangtze River 110°36′35″, 31°01′24″	Length: 700 m; Width: 600 m; Average thickness: 30 m; Volume: 1260 × 104 m3; The elevations of the landslide toe and crown are 70 and 410 m, respectively	Silty clay with gravels with a permeability coefficient of 0.55 m/d Xue et al. (2020a)	Ancient landslide reactivated in June 2003 and continuously deformed; on June 30, 2007, an approximately 100,000 m3 collapse occurred in the warning zone; on July 13, 2007, the horizontal displacement reached 1760.7 mm (XD-03), with velocities of 26.2–50.85 mm/d
Woshaixi landslide	Zigui County, right bank of the Yangtze River 110°35′42.4″, 30°58′03.9″	Length: 400 m; Width: 700 m; Average thickness: 15 m; Volume: 420 × 104 m3; The elevations of the landslide toe and crown are 140 and 405 m, respectively	Silty clay with gravels with a permeability coefficient of 0.06–0.43 m/d Qian et al. (2014)	On February 24, 2007, a secondary landslide in the middle of the landslide front edge occurred; in May 2008, cracks with a length of 500 m and a vertical offset of 0.30 m appeared at the trailing edge; in May 2009, three new cracks with vertical offsets of 0.30–0.50 m appeared at the boundary of the landslide; on May 26, 2009, landslide displacement reached 3.4 m, with velocity of 1.96 m/d
Shuping landslide	Zigui County, right bank of the Yangtze River 110°36′46″, 30°59′38″	Length: 800 m; Width: 700 m; Thickness: 30–70 m; Volume: 2700 × 104 m3; The elevations of the landslide toe and crown are 65 and 400 m, respectively	Silty clay with gravels with a permeability coefficient of 0.78 m/d Wang (2014)	Ancient landslide reactivated in June 2003 and continuously deformed; seven collapses and eleven cracks appeared at the landslide surface; in June 2012, the landslide velocity reached 15 mm/d; cracks at the trailing edge have a maximum crack aperture of 0.2 m and a vertical offset of 0.18 m; En echelon cracks have appeared at the eastern boundary
Baijiabao landslide	Zigui County, right bank of Xiangxi River 110°45′29″, 30°59′00″	Length: 550 m; Width: 400 m; Average thickness: 45 m; Volume: 990 × 104 m3; The elevations of the landslide toe and crown are 125 and 272 m, respectively	Silty clay with gravels with a permeability coefficient of 0.0273–0.0455 m/d Deng et al. (2020)	The Baijiabao landslide only displayed low creep rates prior to the impoundment of the TGRA, but significant movements occurred shortly afterward. In June 2007, surface cracks first appeared at the road on the right side of the landslide, reaching approximately 160 m in length. In July 2008, cracks continued to appear in the middle of the road and at the boundary of the landslide. In June 2009, the cracks on each side began to connect at the trailing edge. In June 2010, new tension cracks occurred on each side. In July 2011, cracks appeared in the middle part and at the boundary on each side