A landslide susceptibility evaluation modeling sample selection method based on mixed sampling

Abstract

The application provides a landslide susceptibility evaluation modeling sample selection method based on mixed sampling. The method is aimed at the deficiencies of traditional under-sampling methods and over-sampling methods in sampling, optimizes the problem that important information is easily lost in the traditional under-sampling method, and combines the over-sampling technology to form a mixed sampling method. The application firstly applies a single classification support vector machine model (One-Class Support Vector Machine, OCSVM) to perform feature segmentation on original data, discriminates the similarity between non-landslide samples and landslide samples under the premise of analyzing the development characteristics of existing high-quality landslide samples, removes invalid and redundant non-landslide data, and purifies data characteristics, then performs over-sampling on the samples by using a synthetic minority over-sampling technique (Synthetic Minority Oversampling Technique, SMOTE), and finally randomly selects modeling samples for prediction, so as to improve the model prediction accuracy by purifying the samples and increasing the characteristics.

Description

Technical Field

[0001] This invention relates to the field of landslide susceptibility assessment, and more particularly to a method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling. Background Technology

[0002] With the improvement of computer performance, data processing and prediction have entered a stage of rapid development. Among them, methods based on Geographic Information Science (GIS) and combined with machine learning models are widely used in the field of landslide susceptibility assessment, such as Support Vector Machine (SVM), Gradient Boosting Tree (GPRS), and Random Forest (RBS). Compared with traditional mathematical statistical models, machine learning models have stronger quantitative capabilities. Although a large number of studies have demonstrated that machine learning and deep learning can adapt to samples under different sampling strategies as much as possible, it is undeniable that a large number of modeling samples are still a prerequisite for achieving high accuracy in modeling learning.

[0003] Based on actual survey results, the proportion of landslide and non-landslide samples often varies across different regions. In many areas, the number of landslide samples is significantly smaller than that of non-landslide samples. In binary classification modeling analysis, when the difference in data samples is too large, we can assume that there is a sample imbalance problem in the study area. The class with a larger number of samples is called the majority class, and the class with a smaller number is called the minority class. In landslide susceptibility assessment, landslides are more worthy of attention and statistical analysis than non-landslides. However, under data imbalance, when building a model, it often focuses too much on the characteristics of the majority class samples and ignores the information of the minority class samples, leading to biased prediction results and overfitting.

[0004] Currently, common sampling methods for addressing imbalanced datasets are mainly divided into random oversampling and random undersampling. Random oversampling involves randomly selecting some samples from the minority class, then copying these selected samples to generate a new dataset, which is then added to the original dataset to expand the minority class set. For random oversampling, the need to copy minority class samples to expand the dataset increases model training complexity. Furthermore, it can easily lead to overfitting because random oversampling simply copies the initial samples, causing the learner to learn overly specific rules, which is detrimental to the learner's generalization performance. Random undersampling, on the other hand, involves randomly selecting some samples from the majority class sample set S to form a sample set E. Then, sample set E is removed from S, resulting in a new dataset Snew = SE. Random undersampling modifies the sample distribution by changing the proportion of majority class samples, thus achieving a more balanced distribution. However, this method also has some drawbacks. Because the sampled set is smaller than the original sample set, some information loss occurs; specifically, deleting majority class samples may cause the classifier to lose important information about the majority class.

[0005] Currently, when assessing landslide susceptibility, landslide data is often obtained through actual field surveys and is very accurate. However, due to the vast area of ​​the study area and the large number of places that are difficult for people to reach, non-landslide data often has a certain degree of uncertainty. Researchers often use high-quality landslide data and low-quality non-landslide data to model at the same time, resulting in too much redundancy and erroneous data in the model, which leads to low model accuracy.

[0006] Landslides are a major type of geological hazard in my country, causing incalculable damage to the sustainable use of land resources and sustainable economic development. Especially since the 21st century, numerous human engineering activities have severely impacted the stability of the geological environment. Coupled with the influence of factors such as earthquakes, volcanic eruptions, and heavy rainfall, the frequency and scale of landslides have gradually increased, resulting in a sharp rise in casualties and economic losses. According to the 2020 National Geological Disaster Report released by the Ministry of Natural Resources, a total of 7,840 geological disasters occurred nationwide, causing direct economic losses of 5.02 billion yuan and 197 casualties. Among them, 4,810 were landslides, accounting for more than 60% of all geological disasters, a significant increase from the 4,220 landslides in 2019. Particularly in Sichuan and Chongqing, numerous potential landslide hazards exist, seriously threatening the lives and property of the people. Accurate landslide susceptibility assessments can provide strong technical support for the government's rational land use planning. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of traditional random oversampling and undersampling by combining One-Class Support Vector Machine (OCSVM) and Synthetic Minority Oversampling Technique (SMOTE) to form a hybrid sampling model, which is used to solve the sample imbalance problem in landslide susceptibility assessment and thus improve the prediction accuracy of landslide assessment.

[0008] A method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling, comprising:

[0009] S1: Load the original total index dataset and construct a hyperplane between all data points in the dataset and the origin;

[0010] S2: Input the raw data obtained in step S1 into the OCSVM model to perform undersampling processing to obtain landslide data and non-landslide data;

[0011] S3: Select a portion of similar landslide data and dissimilar non-landslide data as training data and input it into the SMOTE model to perform oversampling processing on the training data to obtain a new landslide dataset;

[0012] S4: For each sample x in the new landslide, calculate its distance to all samples in the new landslide dataset using Euclidean distance as the standard, and obtain its k nearest neighbors;

[0013] S5: Set a sampling ratio based on the sample imbalance ratio to determine the sampling multiplier N. For each sample x, randomly select several samples from its k nearest neighbors. Assume that the selected nearest neighbors are xn. For each randomly selected nearest neighbor xn, combine it with the original sample to construct a new sample, which is the selected sample.

[0014] Furthermore, in step S1, each data point in the dataset contains an independent variable x consisting of multiple indicator factors and a corresponding dependent variable y. The independent variable x includes elevation, aspect, and slope, while the dependent variable y indicates whether a landslide has occurred.

[0015] Furthermore, step S2 specifically includes the following steps:

[0016] S21: Based on correct classification, maximize the distance between the hyperplane and the origin;

[0017] S22: By handling the coupling problem and adding the slack variable ξ, the problem of maximizing the distance between the hyperplane and the origin is transformed into solving the objective function of optimization;

[0018] S23: By deriving the dual problem and using the kernel trick, the objective function of the above optimization is solved using support vectors to obtain the decision function;

[0019] S24: By using the decision function, the dual problem is derived, and samples similar to landslide data in non-landslide data are removed to obtain purer landslide and non-landslide data.

[0020] Furthermore, the formula for maximizing the distance between the hyperplane and the origin is:

[0021]

[0022] subject to (w·x) i )≥ρ

[0023] Where w is the slope, x i Let be the i-th independent variable, ρ be the constant term, F be the set of positive rational numbers, and R be the set of real numbers.

[0024] Furthermore, the objective function for optimization is:

[0025]

[0026] subject to (w·Φ(x) i ))≥ρ-ξ i ,ξ i ≥0

[0027] Where w is the slope, x i Let ξ be the i-th independent variable, ρ be the constant term, F be the set of positive rational numbers, R be the set of real numbers, and ξ be the variable. i Let be the i-th slack variable.

[0028] Furthermore, the decision function is:

[0029]

[0030] Where, α i For Lagrange multipliers, w(x i ,x) is the kernel function, and ρ is the constant term.

[0031] Furthermore, the formula for constructing new samples is:

[0032] x nev = x + rand(0,1) × (xn - x)

[0033] Where x represents the original sample, x nev This indicates a new sample.

[0034] The beneficial effects of the technical solution provided by this invention are:

[0035] (1) Compared with the traditional undersampling algorithm, the hybrid sampling algorithm of the present invention can fully retain representative data, without losing important information, and the selected data has complete features, making the samples more pure.

[0036] (2) Compared with the traditional oversampling algorithm, the hybrid sampling algorithm of the present invention does not simply increase the number of sample points by copying data, but generates new samples after learning the features of existing data. It fully considers the differences of existing data and is not prone to data redundancy problems. Attached Figure Description

[0037] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0038] Figure 1 This is a flowchart of a landslide susceptibility assessment and modeling sample selection method based on hybrid sampling, as described in an embodiment of the present invention.

[0039] Figure 2 This is a graph showing the accuracy of LR susceptibility evaluation using OCSVM-SMOTE sampling and without OCSVM-SMOTE sampling in this embodiment of the invention.

[0040] Figure 3 This is a graph showing the accuracy of RF susceptibility evaluation using OCSVM-SMOTE sampling and without OCSVM-SMOTE sampling in this embodiment of the invention.

[0041] Figure 4 This is a graph showing the accuracy of GBDT susceptibility evaluation using OCSVM-SMOTE sampling and without OCSVM-SMOTE sampling in this embodiment of the invention. Detailed Implementation

[0042] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0043] The embodiments of the present invention provide a method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling.

[0044] Please refer to Figure 1 , Figure 1 This is a flowchart of a landslide susceptibility assessment modeling sample selection method based on hybrid sampling, as described in an embodiment of the present invention, specifically including:

[0045] A method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling first performs single-class support vector machine model calculation (steps 1-10), and then performs synthetic minority class oversampling calculation (steps 11-12), specifically as follows:

[0046] Step 1: Load the original total index dataset, which includes landslide data and non-landslide data. Each dataset consists of an independent variable x = (x1, x2, ..., x...) composed of multiple index factors (elevation, aspect, slope, etc.). 10 And the corresponding dependent variable y (whether a landslide occurs). A hyperplane is constructed between the data and the origin; let's assume this hyperplane is:

[0047] w·Φ(x)-ρ=0

[0048] Where w is the slope, x i Let be the i-th independent variable, ρ be the constant term, F be the set of positive rational numbers, and R be the set of real numbers.

[0049] Step 2: Maximize the distance between the hyperplane and the origin, based on correct classification:

[0050]

[0051] (w·Φ(x i ))≥ρ

[0052] Where, x i Let be the i-th independent variable.

[0053] Step 3: According to the definition of a hyperplane, adjusting the sign of ρ and the signs of the elements in the w vector simultaneously will not affect the hyperplane. Therefore, if ρ > 0, the problem of maximizing the distance between the hyperplane and the origin can be rewritten as:

[0054]

[0055] Step 4: Process the problem of maximizing the distance between the hyperplane and the origin solved in Step 2 by decomposing it into:

[0056]

[0057]

[0058] Step 5: When solving the problem, since the overall sign of the elements in vector w does not affect ||w|| 2 The value of ρ is such that as long as the final value of ρ is positive, the assumption in step 3 is satisfied. Meanwhile, to facilitate gradient calculation, ||w|| is used. 2 Adding a 1 / 2, the final optimization objective can be written as:

[0059]

[0060] (w·Φ(x i ))≥ρ

[0061] Where w is the slope, x i Let ξ be the i-th independent variable, ρ be the constant term, F be the set of positive rational numbers, R be the set of real numbers, and ξ be the variable. i Let be the i-th slack variable.

[0062] Step 6: Generally, for a straight line with a fixed slope, the larger the absolute value of its offset, the further it is from the zero point. Taking w*xb = 0 as an example, when w is fixed, the larger |b| is, the further the line is from the origin. Therefore, after adding the slack variable ξ to the function, its optimization objective function can be written as:

[0063]

[0064] (w·Φ(x i ))≥ρ-ξ i ,ξ i ≥0

[0065] Where v∈(0,1) is used to adjust the degree of relaxation. After optimizing and solving according to the objective function to obtain w and ρ, for multiple samples, the output of its decision function f(x)=sgn((w*Φ(x))-ρ) is positive.

[0066] Step 7: To solve the dual problem, we use the kernel trick, specifically the Lagrange multiplier α. i ,β i The Lagrange equation can be written as follows:

[0067]

[0068] Step 8: Then, by taking the partial derivatives with respect to the parameters w, ξ, and ρ, we can write out some of the Karush-Kuhn-Tucker (KKT) conditions:

[0069]

[0070]

[0071] Step 9: By deriving the dual problem and using the kernel trick, it is possible to achieve the solution through the support vectors {x}. i :i∈[l],α i The decision function is obtained by finding the value of 0.

[0072]

[0073] Where, α i For Lagrange multipliers, w(x i ,x) is the kernel function, and ρ is the constant term.

[0074] Step 10: By deriving the dual problem, we can remove samples similar to landslide data from non-landslide data, thus purifying the landslide and non-landslide samples and performing a sample underfitting process.

[0075] Step 11: For each sample x in the landslide, calculate its distance to all samples in the original total sample set using Euclidean distance as the standard, and obtain its k nearest neighbors.

[0076] Step 12: Set a sampling ratio based on the sample imbalance ratio to determine the sampling multiplier N. For each minority landslide data sample, randomly select several samples from its k nearest neighbors, assuming the selected nearest neighbors are xn. For each randomly selected nearest neighbor xn, construct a new sample with the original total sample according to the following formula.

[0077] x nev = x + rand(0,1) × (xn - x)

[0078] Where x represents the original sample, x nev This indicates a new sample.

[0079] Using the above methods can effectively optimize the sample selection problem, and enable the selected model to be effectively used for training in different models, thereby improving the accuracy of landslide susceptibility assessment.

[0080] In this embodiment, the original data is input into a single-class support vector machine model to determine the similarity between non-slope data and slope data. Similar non-slope data is marked as 1, and dissimilar non-slope data is marked as -1. During this training process, the kernel function of OCSVM is set to rbf, and the training error is 0.1. 70% of the similar slope data is selected as training data, and the same number of samples are selected from the dissimilar non-slope data. The remaining slope and non-slope data are used as validation data Xtest and Ytest to remove invalid and redundant data, achieving the purpose of undersampling while retaining the effective information in the samples. The training data is input into a synthetic minority class oversampling technique model to perform oversampling processing on the sample data, obtaining new training data Xsmo and Ysmo. The mixed-sampled data Xsmo and Ysmo are then input into the machine learning model to perform modeling operations corresponding to independent and dependent variables. Xtest and Ytest are used to verify the model accuracy.

[0081] The following are specific examples:

[0082] Taking Zouma Town and Longju Town in Wanzhou District, Chongqing as examples, ArcGIS was used to extract indicator factors (slope, elevation, slope structure, land use, strata, distance from road, slope aspect, slope morphology, topographic humidity index, and vegetation normalized index) for the study area, and corresponding landslide data were obtained to form a sample dataset, totaling 200,601 samples, including 629 landslide datasets and 199,972 non-landslide datasets.

[0083] The data was first undersampled using OCSVM to separate non-landslides with similar characteristics to landslides. Then, the landslide data was oversampled using SMOTE. Finally, 70% of the landslides and the same number of non-landslides were randomly selected for modeling, and the remaining data were used for validation.

[0084] To demonstrate the superiority and adaptability of the mixed sampling model, three models were used for modeling, and the predictive accuracy was verified using Receiver Operating Characteristic Curve (ROC). The predictive accuracies are as follows: Figure 2-4 As shown.

[0085] As can be seen, our proposed OCSVM-SMOTE hybrid sampling method has achieved good optimization results in all three models, which means that hybrid sampling can effectively improve the prediction accuracy of the model and has good adaptability.

[0086] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling, characterized in that: include: S1: Load the original total index dataset and construct a hyperplane between all data points in the dataset and the origin; S2: Input the raw data obtained in step S1 into the OCSVM model to perform undersampling processing to obtain landslide data and non-landslide data; S3: Select a portion of similar landslide data and dissimilar non-landslide data as training data and input it into the SMOTE model to perform oversampling processing on the training data to obtain a new landslide dataset; S4: For each sample x in the new landslide, calculate its distance to all samples in the new landslide dataset using Euclidean distance as the standard, and obtain its k nearest neighbors; S5: Set a sampling ratio based on the sample imbalance ratio to determine the sampling multiplier N. For each sample... x Randomly select several samples from its k nearest neighbors, assuming the selected nearest neighbors are... xn For each randomly selected nearest neighbor xn The selected sample is obtained by combining the original sample with the new sample. Step S2 specifically includes the following steps: S21: Based on correct classification, maximize the distance between the hyperplane and the origin; S22: By handling the coupling problem and adding the slack variable ξ, the problem of maximizing the distance between the hyperplane and the origin is transformed into solving the objective function of optimization; S23: By deriving the dual problem and using the kernel trick, the objective function of the above optimization is solved using support vectors to obtain the decision function; S24: By using the decision function, the dual problem is derived, and samples similar to landslide data in non-landslide data are removed to obtain purer landslide and non-landslide data; The formula for maximizing the distance between the hyperplane and the origin is: Where w is the slope and xi is the i-th independent variable. Let F be a constant term, F be the set of positive rational numbers, and R be the set of real numbers; The objective function to be optimized is: Where w is the slope and xi is the i-th independent variable. Let F be a constant term, F be the set of positive rational numbers, and R be the set of real numbers. Let i be the slack variable; The decision function is: in, For Lagrange multipliers, , For kernel function, This is a constant term.

2. The method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling as described in claim 1, characterized in that: In step S1, each data point in the dataset contains an independent variable x consisting of multiple indicator factors and a corresponding dependent variable y. The independent variable x includes elevation, aspect and slope, and the dependent variable y is whether a landslide has occurred.

3. The method for selecting samples for landslide susceptibility assessment modeling based on hybrid sampling as described in claim 1, characterized in that: The formula for constructing a new sample is: Where x represents the original sample, This indicates a new sample.

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