LS-SVM algorithm sample thinning method based on sample Euclidean distance

Abstract

The invention relates to a method for training sample thinning by using a sample Euclidean distance, in the process of constructing a seabed trend surface by using an LS-SVM algorithm, a sounding training sample is thinned by using the Euclidean distance of the sample to obtain an LS-SVM algorithm with sparsity, and a robust seabed trend surface model function is obtained by adjusting kernel parameters. According to the method for thinning the training sample based on the sample Euclidean distance, the defect that the selected training sample does not have sparsity is overcome, and the seabed trend surface function constructed on the basis is more reasonable.

Description

Technical Field

[0001] This invention belongs to the field of marine measurement technology. It is a patented method specifically applied to constructing seabed trend surfaces using the LS-SVM algorithm and effectively thinning training samples. Background Technology

[0002] The LS-SVM algorithm transforms the process of constructing the seabed trend surface into solving a high-dimensional linear least squares problem, simplifying the computational complexity compared to the standard support vector machine. However, constructing the seabed trend surface using LS-SVM still presents the following problems: During the construction of the model function using the LS-SVM algorithm, the selected bathymetry training samples all influence the construction of the seabed trend surface function. As the number of bathymetry training samples increases, the construction of the trend surface function becomes extremely complex, and the computational and storage requirements for model building also increase accordingly. This significantly limits the application of the LS-SVM algorithm.

[0003] The validity of the seabed trend surface constructed using the LS-SVM algorithm depends on whether the selected training samples and kernel function truly reflect the actual changes in seabed topography. To effectively compensate for the lack of sparsity in the selected training samples, and while ensuring the accuracy of the function model, the model function is obtained by adjusting the combination parameters. Summary of the Invention

[0004] The purpose of this invention is to thin out the selected depth sounding training samples using Euclidean distance, thereby effectively improving the construction efficiency of the seabed trend surface function while ensuring the accuracy of the function model.

[0005] The present invention solves its technical problem by adopting the following technical solution: The method for thinning training samples for the LS-SVM algorithm based on sample Euclidean distance includes the following steps: Step 1: Using each selected training sample as the center, calculate and sum the Euclidean distances from other training samples to that center. The sample with the smallest sum of Euclidean distances is the training sample whose center is [the center of the training sample]. ; Step 2: Calculate the training samples one by one. Relative to the sample center Euclidean distance ; Step 3: By comparing the mean squared errors of the samples before and after the first and second thinning, the accuracy index of the function model is judged, and the threshold of Euclidean distance is determined while ensuring the accuracy of the function model. Step 4: Thin out the training samples using the Euclidean distance threshold, and reconstruct the model function using the LS-SVM algorithm.

[0006] Furthermore, the specific implementation method of step 1 is as follows: the selected depth measurement training samples are... , , Given the total number of samples, the planar coordinates of the sounding points are... As input information for the LS-SVM algorithm; depth sounding value As output values, the optimization objective and constraints of the optimal trend surface model function are as follows: (1) (2) In the formula, nonlinear mapping For the plane coordinate function of the sounding point, For weight vectors, It is a real constant; For error variables; As a penalty factor; Introducing the Lagrange function Solve the optimization problem of the above equation: (3) In the formula, For Lagrange multipliers, the corresponding multiplier is called the Lagrange multiplier. The sample points are support vectors, and the KKT optimization conditions are applied. ,get: (4) The Lagrange multipliers are all proportional to the error vector, and in reality, the error vector is not zero. Therefore, the solution of the LS-SVM algorithm is non-sparse. Let the kernel function be... This yields the following system of linear equations: (5) By solving the real constants and Lagrange multipliers Then, the seabed trend surface constructed using LS-SVM is: (6) When the support vector solution is not sparse, all the training data contributes to the final trend surface constructor, increasing the computational load and storage space of the algorithm. As the number of samples increases, the construction of the function model becomes extremely complex.

[0007] Furthermore, the specific implementation method of step 2 is as follows: The training samples are first thinned using a Euclidean distance threshold, and the coordinate information of the first thinned training samples is obtained. Substitute into the expression: (7) Obtain the predicted value based on the optimal function model , compared with the actual water depth By comparison, the residual values ​​are obtained. Calculate the mean square error of the residual value sequence. , where n is the number of training samples after the first thinning; The Euclidean distance threshold is increased again (0.7 * Euclidean distance) to perform a second round of thinning on the training samples, and the coordinate information of the thinned training samples is then recorded. Substitute into the expression: (8) Obtain the predicted value based on the optimal function model , compared with the actual water depth By comparison, the residual values ​​can be obtained. Calculate the mean square error of the residual value sequence. , This is the number of samples after the second dilution.

[0008] Furthermore, the specific implementation method of step 3 is as follows: A seabed trend surface function is constructed using the LS-SVM algorithm. A mean squared error limit of 0.001 is used, and it is considered that if the mean squared error exceeds 0.001, the model accuracy index decreases. The accuracy index of the function model is judged by comparing the mean squared errors before and after the first and second thinning of the samples. Under the premise of ensuring the accuracy of the function model, a threshold for the Euclidean distance is determined.

[0009] The advantages and positive effects of this invention are: by using Euclidean distance to thin the selected depth measurement training samples, not only is the construction speed of the function model accelerated, but the rationality and accuracy of the function model construction are also improved. Attached Figure Description

[0010] Figure 1 This is a schematic diagram illustrating how the Euclidean distance threshold is used to thin out training samples according to the present invention. Detailed Implementation

[0011] The method for thinning training samples for the LS-SVM algorithm based on sample Euclidean distance includes the following steps: (1) In the process of constructing the seabed trend surface function using the LS-SVM algorithm, all training sample points are support vectors, which all affect the construction of the seabed trend surface.

[0012] Assume the selected depth measurement training samples are , , This represents the total number of samples. The planar coordinates of the sounding points are... As input information for the LS-SVM algorithm; depth sounding value As output values, the optimization objective and constraints of the optimal trend surface model function are as follows: (1) (2) In the formula, nonlinear mapping For the plane coordinate function of the sounding point, For weight vectors, It is a real constant; For error variables; This is a penalty factor.

[0013] Introducing the Lagrange function Solve the optimization problem of the above equation: (3) In the formula, For Lagrange multipliers, the corresponding multiplier is called the Lagrange multiplier. The sample points are the support vectors. Based on the KKT optimization conditions... This yields the following expression: (4) As can be seen from expression (4), the Lagrange multipliers are all proportional to the error vector, and in reality, the error vector is not zero. Therefore, the solution of the LS-SVM algorithm is non-sparse.

[0014] Define the kernel function as This yields the following system of linear equations: (5) By solving the real constants and Lagrange multipliers Then, the seabed trend surface constructed using LS-SVM is: (6) As can be seen from expression (6), when the support vector solution is not sparse, all the training data will affect the final trend surface constructor, which increases the computational load and storage space of the algorithm. As the number of samples increases, the construction of the function model will become extremely complex.

[0015] (2) In principle, the depth measurement training samples should have a gradual change relative to the sample center, therefore the Euclidean distance This reflects the reasonableness of the sample's contribution to the function model construction. To ensure the reasonableness of the seabed trend surface construction, and while maintaining the accuracy of the function model, an Euclidean distance threshold is determined, and the bathymetry training samples are selected accordingly.

[0016] like Figure 1As shown, the training samples are first thinned using a Euclidean distance threshold (0.8 * Euclidean distance), and the coordinate information of the first thinned training samples is obtained. Substitute into the expression: (7) Obtain the predicted value based on the optimal function model , compared with the actual water depth By comparison, the residual values ​​can be obtained. Calculate the mean square error of the residual value sequence. , where n is the number of training samples after the first thinning.

[0017] The Euclidean distance threshold is increased again (0.7 * Euclidean distance) to perform a second round of thinning on the training samples, and the coordinate information of the thinned training samples is then recorded. Substitute into the expression: (8) Obtain the predicted value based on the optimal function model , compared with the actual water depth By comparison, the residual values ​​can be obtained. Calculate the mean square error of the residual value sequence. , This is the number of samples after the second dilution.

[0018] (3) The seabed trend surface function was constructed using the LS-SVM algorithm. 0.001 was taken as the mean squared error limit. It was considered that if the mean squared error was greater than 0.001, the model accuracy index would decrease. The accuracy index of the function model was judged by comparing the mean squared errors of the samples before and after the first and second thinning. Under the premise of ensuring the accuracy of the function model, the threshold of the Euclidean distance was determined.

[0019] It should be emphasized that the embodiments described in this invention are illustrative rather than limiting. Therefore, this invention is not limited to the embodiments described in the specific implementation. Any other implementation methods derived by those skilled in the art based on the technical solutions of this invention also fall within the scope of protection of this invention.

Claims

1. A method for thinning training samples of the LS-SVM algorithm based on sample Euclidean distance, characterized in that, Includes the following steps: Step 1: Using each selected training sample as the center, calculate and sum the Euclidean distances from other training samples to that center. The sample with the smallest sum of Euclidean distances is the training sample whose center is [the center of the training sample]. ; Step 2: Calculate the training samples one by one. Relative to the sample center Euclidean distance ; Step 3: By comparing the mean squared errors of the samples before and after the first and second thinning, the accuracy index of the function model is judged, and the threshold of Euclidean distance is determined while ensuring the accuracy of the function model. Step 4: Thin out the training samples using the Euclidean distance threshold, and reconstruct the model function using the LS-SVM algorithm.

2. The method for thinning training samples of the LS-SVM algorithm based on sample Euclidean distance according to claim 1, characterized in that, The specific implementation method of step 1 is as follows: the selected depth measurement training samples are... , , Given the total number of samples, the planar coordinates of the sounding points are... As input information for the LS-SVM algorithm; depth sounding value As output values, the optimization objective and constraints of the optimal trend surface model function are as follows: (1) (2) In the formula, nonlinear mapping For the plane coordinate function of the sounding point, For weight vectors, It is a real constant; For error variables; As a penalty factor; Introducing the Lagrange function Solve the optimization problem of the above equation: (3) In the formula, For Lagrange multipliers, the corresponding multiplier is called the Lagrange multiplier. The sample points are support vectors, and the KKT optimization conditions are applied. ,get: (4) The Lagrange multipliers are all proportional to the error vector, and in reality, the error vector is not zero. Therefore, the solution of the LS-SVM algorithm is non-sparse. Let the kernel function be... This yields the following system of linear equations: (5) By solving the real constants and Lagrange multipliers Then, the seabed trend surface constructed using LS-SVM is: (6) When the support vector solution is not sparse, all the training data contributes to the final trend surface constructor, increasing the computational load and storage space of the algorithm. As the number of samples increases, the construction of the function model becomes extremely complex.

3. The method for thinning training samples of the LS-SVM algorithm based on sample Euclidean distance according to claim 1, characterized in that, The specific implementation method of step 2 is as follows: The training samples are first thinned using a Euclidean distance threshold, and the coordinate information of the first thinned training samples is obtained. Substitute into the expression: （7） Obtain the predicted value based on the optimal function model , compared with the actual water depth By comparison, the residual values ​​are obtained. Calculate the mean square error of the residual value sequence. , where n is the number of training samples after the first thinning; The Euclidean distance threshold is increased again (0.7 * Euclidean distance) to perform a second round of thinning on the training samples, and the coordinate information of the thinned training samples is then recorded. Substitute into the expression: （8） Obtain the predicted value based on the optimal function model , compared with the actual water depth By comparison, the residual values ​​can be obtained. Calculate the mean square error of the residual value sequence. , This is the number of samples after the second dilution.

4. The method for thinning training samples of the LS-SVM algorithm based on sample Euclidean distance according to claim 1, characterized in that, The specific implementation method of step 3 is as follows: construct the seabed trend surface function using the LS-SVM algorithm, take 0.001 as the mean square error limit, and consider that if the mean square error is greater than 0.001, the model accuracy index will decrease. The accuracy index of the function model is judged by comparing the mean square error of the sample before and after the first and second thinning. Under the premise of ensuring the accuracy of the function model, the threshold of Euclidean distance is determined.

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