A GRNN prediction method and system considering the spatial relationship of adjacent sample points

Abstract

The present invention discloses a GRNN prediction method and system that takes into account the spatial relationship of adjacent sample points, including: dividing the sampled data into test data and training data in proportion; improving the neuron transfer function of the pattern layer to construct a GRNN model that takes into account the spatial relationship of adjacent sample points; preprocessing the training data, training the GRNN model based on the preprocessed training data, and testing the trained GRNN model through the test data. The present invention considers the relationship between adjacent sampling points and greatly improves the accuracy of the valuation results. Applied to the field of ore grade valuation, achieving the effect of de-aggregation will make the grade valuation more accurate and reliable, reduce the gap between the predicted grade and the actual grade, facilitate the subsequent staff to formulate mining strategies, and avoid waste of resources.

Description

Technical Field

[0001] The present invention belongs to the technical field of artificial neural network prediction methods, and in particular relates to a GRNN prediction method and system that takes into account the spatial relationship of adjacent sample points. Background Art

[0002] Generalized Regression Neural Network (GRNN) is a type of radial basis neural network with strong nonlinear mapping capabilities and fault tolerance, fast convergence speed, and good prediction results even when there are fewer sampling points. Therefore, GRNN has been widely used in adaptive control, system identification, prediction and other fields.

[0003] The basic principle of GRNN neural network is: for random variables x and y, the joint probability density function is f(x,y), the conditional mean (predicted output) of variable y to variable x is the y (regression value) with the maximum probability value, and the regression of y to x is:

[0004]

[0005] The estimated density function is given by Parzen nonparametric estimation

[0006]

[0007] Among them, X and Y are the test data set sampling values ​​of variables x and y respectively, N is the training data capacity, p is the dimension of variable x, and σ is the Gaussian function width coefficient, also known as the smoothing factor, which is an undetermined parameter in the GRNN network.

[0008] The density function will be estimated Substitute the true density function f(x,y) into equation (1) and swap the order of integration and summation:

[0009]

[0010] because Formula (3) can be simplified as:

[0011]

[0012] Data clustering refers to the phenomenon that due to the limitations of the environment, cost, measurement technology and other conditions in reality, it is usually impossible to measure a batch of sample data evenly according to the geographical location, resulting in the sample data being very concentrated in some parts and very sparse in others. Ignoring this phenomenon will usually lead to a large deviation between the predicted results and the actual situation. Figure 1As shown in the figure, the data comes from some drilling data in a mining area, which only contains location information (x, y, z) and grade information. For the convenience of calculation and effect display, three drilling data are selected, among which drilling holes ZK-1 and ZK-2 are very close, and ZK-1 and ZK-3 are also very close. The midpoint X of drilling holes ZK-1 and ZK-3 is predicted. Using traditional GRNN for prediction, the smoothing factor σ is set to 0.5, and the values ​​of the neurons in the three drilling pattern layers are p1=

[0013] exp[-2*10 4 ],p2=exp[-2*10025],p3=exp[-2*10 4 ], it can be seen that the values ​​are relatively close, that is, p1=p3≈p2, then the predicted value is

[0014]

[0015] This result is quite different from the actual measured grade value.

[0016] As can be seen from the above, this method fails to account for the clustering effect of sampled data, and thus can easily lead to skewed estimates. For example, in the field of ore grade estimation, skewed estimates occur when the predicted grade for a particular area differs significantly from the actual grade. This can severely impact the development of mining strategies based on the predicted grade, resulting in a waste of human and material resources. This paper addresses this issue by proposing a solution to improve the accuracy of GRNN predictions. Summary of the Invention

[0017] To solve the above technical problems, the present invention proposes a GRNN prediction method and system that takes into account the spatial relationship between adjacent sample points, taking into account the relationship between adjacent sampling points, and greatly improving the accuracy of the valuation results.

[0018] On the one hand, to achieve the above-mentioned object, the present invention provides a GRNN prediction method that takes into account the spatial relationship of adjacent sample points, comprising:

[0019] Divide the sampled data into test data and training data in proportion;

[0020] Improve the neuron transfer function of the pattern layer and construct a GRNN model; wherein the spatial relationship of adjacent sample points is combined in the construction process of the GRNN model;

[0021] The training data is preprocessed, the GRNN model is trained based on the preprocessed training data, and the trained GRNN model is tested using the test data.

[0022] Optionally, the neuron transfer function of the improved pattern layer includes:

[0023] Based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of the redundancy to obtain the DD weight of the sampling point, where the DD weight is used to represent the spatial relationship between adjacent sampling points;

[0024] The DD weight is combined with the neuron transfer function of the traditional pattern layer to obtain the neuron transfer function of the improved pattern layer.

[0025] Optionally, the DD weight is calculated as follows:

[0026]

[0027] Among them, λ i is the DD weight, X i and X j are the i-th sampling point and the j-th sampling point respectively, and σ2 is a parameter used to adjust the impact of distance on data redundancy.

[0028] Optionally, the neuron transfer function of the improved pattern layer is:

[0029]

[0030] Among them, X i is the characteristic vector of the i-th training data, σ1 is the smoothing factor, X is the input variable, p i is the value of the neuron in the traditional pattern layer, p′ i is the value of the improved pattern layer neuron.

[0031] Optionally, the constructed GRNN model includes: an input layer, a pattern layer, a summation layer, and an output layer; wherein the neurons in the summation layer are of two types, the first type adopts an arithmetic summation calculation method, and the second type adopts a weighted summation calculation method;

[0032] The arithmetic sum is calculated as follows:

[0033]

[0034] Among them, s0 is the arithmetic summation result, and m is the number of neurons in the improved pattern layer.

[0035] The weighted sum is calculated as follows:

[0036]

[0037] Among them, s nj is the value of the neuron in the summation layer, y ij is the jth output component of the i-th training sample, and k is the dimension of the output variable.

[0038] Optionally, the output layer is calculated as follows:

[0039]

[0040] Optionally, preprocessing the training data includes: first calculating a distance square matrix between the training data points;

[0041] The distance square moment is:

[0042]

[0043] On the other hand, to achieve the above-mentioned object, the present invention also provides a GRNN prediction method that takes into account the spatial relationship of adjacent sample points, including: a division module, a construction module and a training module;

[0044] The division module is used to divide the sampled data into test data and training data in proportion;

[0045] The construction module is used to improve the neuron transfer function of the pattern layer and construct a GRNN model that takes into account the spatial relationship of adjacent sample points;

[0046] The training module preprocesses the training data, trains the GRNN model based on the preprocessed training data, and tests the trained GRNN model using the test data.

[0047] Optionally, in the building module, improving the neuron transfer function of the pattern layer includes:

[0048] Based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of the redundancy to obtain the DD weight of the sampling point, where the DD weight is used to represent the spatial relationship between adjacent sampling points;

[0049] Combining the DD weight with the neuron transfer function of the traditional pattern layer to obtain the neuron transfer function of the improved pattern layer;

[0050] The DD weight is calculated as follows:

[0051]

[0052] Among them, λ i is the DD weight, X i and X j are the i-th sampling point and the j-th sampling point respectively, and σ2 is a parameter used to adjust the impact of distance on data redundancy;

[0053] The neuron transfer function of the improved pattern layer is:

[0054]

[0055] Among them, X i is the characteristic vector of the i-th training data, σ1 is the smoothing factor, X is the input variable, p i is the value of the neuron in the traditional pattern layer, p′ i is the value of the improved pattern layer neuron.

[0056] Compared with the prior art, the present invention has the following advantages and technical effects:

[0057] This paper improves the neuronal transfer function of the pattern layer and proposes a metric to indicate the importance of sampling points: the DD weight. This metric is then incorporated into the traditional GRNN method. This metric considers the relationship between adjacent sampling points, significantly improving the accuracy of the valuation results. Applied to the field of ore grade estimation, the declustering effect achieves more accurate and reliable grade estimates, reducing the gap between predicted and actual grades, facilitating the formulation of mining strategies, and avoiding waste of resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0059] Figure 1 Schematic diagram of a flow chart of a GRNN prediction method taking into account the spatial relationship of adjacent sample points according to embodiment 1 of the present invention;

[0060] Figure 2 Schematic diagram of the network structure of the GRNN model taking into account the spatial relationship between adjacent sample points according to Example 1 of the present invention;

[0061] Figure 3 This is a schematic diagram of aggregated data according to Example 1 of the present invention;

[0062] Figure 4 Schematic diagram of the structure of a GRNN prediction system that takes into account the spatial relationship of adjacent sample points according to Example 2 of the present invention. DETAILED DESCRIPTION

[0063] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0064] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0065] Example

[0066] like Figure 1 As shown, this embodiment provides a GRNN prediction method that takes into account the spatial relationship of adjacent sample points, including:

[0067] Divide the sampled data into test data and training data in proportion;

[0068] Improve the neuron transfer function of the pattern layer and construct a GRNN model; wherein the spatial relationship of adjacent sample points is combined in the construction process of the GRNN model;

[0069] The training data is preprocessed, the GRNN model is trained based on the preprocessed training data, and the trained GRNN model is tested using the test data.

[0070] In this embodiment, the test data is input. For the sampled data, it is divided according to a certain ratio (such as 8:2), with one part used as training data (more data) and the other part used as test data.

[0071] Furthermore, the neuron transfer function of the improved pattern layer includes:

[0072] Based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of the redundancy to obtain the DD weight of the sampling point, where the DD weight is used to represent the spatial relationship between adjacent sampling points;

[0073] The DD weight is combined with the neuron transfer function of the traditional pattern layer to obtain the neuron transfer function of the improved pattern layer.

[0074] Furthermore, in the constructed GRNN model, there are two types of neurons in the summation layer, the first type adopts an arithmetic summation calculation method, and the second type adopts a weighted summation calculation method;

[0075] In this embodiment, a GRNN model is constructed that takes into account the spatial relationship between adjacent sample points:

[0076] The network structure of the GRNN model that takes into account the spatial relationship of adjacent sample points is as follows: Figure 2 As shown in the figure, it consists of four layers: input layer, pattern layer, summation layer and output layer.

[0077] Input layer:

[0078] where X=[x1,x2,...,x n ] represents the characteristics of the data to be tested (input vector). The number of neurons in the input layer is the number of characteristics of the input data. This layer does not process the data and directly passes the data to the pattern layer.

[0079] Pattern layer:

[0080] The number of neurons in the pattern layer is the number of training data. Each neuron corresponds to different training data. The traditional neuron transfer function of the pattern layer is shown in formula (5):

[0081]

[0082] where X i is the eigenvector of the i-th training data, σ1 is the width coefficient (smooth factor) of the Gaussian function, and neuron p i The output is the input variable X and the i-th training data X i The exponential form of the square of the Euclid distance between them.

[0083] The model used in the GRNN method that takes into account the spatial relationship of adjacent sample points adopted in the present invention does not change the four-layer network structure of the GRNN model, but only changes the neuron transfer function of the pattern layer, while other parts remain unchanged.

[0084] Taking into account the spatial relationship between neighboring sample points means taking the relationship between the sample points into account. When clustered data appears, the results will perform better than traditional methods. A characteristic of clustered data is that various redundancies will appear in the estimation process. According to Tobler's first geographical law, the greater the average or cumulative distance between a sampling point and other sampling points, the less redundancy the sampling point has, and vice versa. Therefore, based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of redundancy, and an additional indicator indicating the importance of the sampling point is proposed: DD weight λ = [λ1,λ2,...,λ n ], DD weight λ of the i-th sampling point i is calculated as follows:

[0085]

[0086] where X i and X j Represents the i-th sampling point and the j-th sampling point. To ensure consistency with the traditional calculation method, the exponential form of the square of the Euclid distance between the two sampling points is used for calculation, where σ2 is a parameter used to adjust the impact of distance on data redundancy.

[0087] For the neuron p in the pattern layeri , its output value is actually the weight of the i-th training data. Considering the above-mentioned spatial relationship of adjacent sample points, combined with the DD weight λ in formula (6) i , and incorporate it into the weight of formula (5) to obtain a new weight calculation formula (pattern layer neuron transfer function), as shown in formula (7):

[0088]

[0089] Among them, X i is the characteristic vector of the i-th training data, σ1 is the smoothing factor, X is the input variable, p i is the value of the neuron in the traditional pattern layer, p′ i is the value of the improved pattern layer neuron.

[0090] Summation layer:

[0091] There are two types of neurons in the summation layer, each using a different method for calculation.

[0092]

[0093] In fact, it is the arithmetic sum of all neurons in the pattern layer. The connection weight between it and each neuron in the pattern layer is 1, which can be simplified to formula (9):

[0094]

[0095] Among them, s0 is the arithmetic summation result, and m is the number of neurons in the improved pattern layer.

[0096] The calculation method of the second type is shown in formula (10):

[0097]

[0098] where Y i The label vector representing the i-th training data is actually the weighted sum of all neurons in the pattern layer, which can be simplified as formula (11):

[0099]

[0100] Among them, s nj is the value of the neuron in the summation layer, y ij is the jth output component of the i-th training sample, and k is the dimension of the output variable.

[0101] Output layer:

[0102] The number of neurons in the output layer is the dimension k of the label vector in the training data. Each neuron divides the output value of the summation layer to obtain the output vector The output y of the jth neuron j Corresponding estimation results The j-th element of is calculated as shown in formula (12):

[0103]

[0104] Furthermore, the training data is preprocessed by first calculating the distance square matrix between the training data points.

[0105] In this embodiment, for the training data {[X1, Y1], [X2, Y2], ..., [X m ,Y m ]}, where m represents the number of training data, X i ,i=1,2,...,m represents the feature vector of the i-th training data. Assuming that the number of features is n, then X i is a vector of length n. Similarly, if the sampling point label dimension is k, then Y i , i=1,2,...,m is a vector of length k. For the DD weight mentioned in formula (6), the distance square matrix D between the training data points can be calculated in the training data preprocessing stage, that is,

[0106]

[0107] Furthermore, training the GRNN model includes: training the model using a cross-validation method, determining the values ​​of parameters σ1 and σ2, and performing prediction and output.

[0108] In this embodiment, the GRNN model that takes into account the spatial relationship of neighboring sample points used in this embodiment only includes the smoothing factor σ1 of the Gaussian function and the parameter σ2 used to control the influence of distance on data redundancy. For the smoothing factor σ1 of the Gaussian function, the larger σ1 is, the closer the predicted value of the model is to the actual mean of the training data, and the smaller σ1 is, the closer it is to the actual value of the training data. The parameter σ2 is used to control the influence of distance on data redundancy. Selecting a suitable value can avoid the phenomenon of excessive aggregation. In specific applications, sampled data is usually used to use methods such as cross-validation to determine the parameters that are most suitable for this area. According to the distance square matrix D in step three, the DD weight λ of each training data can be calculated, and its calculation formula is as follows:

[0109]

[0110] The model can be trained using methods such as cross-validation to determine the appropriate parameters σ1 and σ2. Finally, the neurons in the output layer are the prediction results of the test data (generally referring to the physical quantity that needs to be predicted, such as the grade value in the field of ore grade valuation).

[0111] By using the GRNN prediction method of the present invention that takes into account the spatial relationship of adjacent sample points, a set of declustering effect mechanisms can be embedded in the original GRNN model, thereby improving the credibility of the prediction results. Figure 3 For prediction, the value of the smoothing factor σ1 is 0.5, the value of the smoothing factor σ2 is 2, and the DD weights of the three sampling points are:

[0112]

[0113] because Much smaller than Removing it has little effect on the results. The predicted value Compared to traditional GRNNs, the error is reduced, achieving a de-aggregation effect. For example, in the field of ore grade estimation, achieving de-aggregation makes grade estimation more accurate and reliable, narrowing the gap between predicted and actual grades, facilitating subsequent mining strategy development and avoiding resource waste.

[0114] Example 2

[0115] like Figure 4 As shown, this embodiment provides a GRNN prediction system that takes into account the spatial relationship of adjacent sample points, including: a partitioning module, a construction module and a training module;

[0116] The division module is used to divide the sampled data into test data and training data in proportion;

[0117] The construction module is used to improve the neuron transfer function of the pattern layer and construct a GRNN model that takes into account the spatial relationship of adjacent sample points;

[0118] The training module preprocesses the training data, trains the GRNN model based on the preprocessed training data, and tests the trained GRNN model using the test data.

[0119] In the partitioning module, input the test data. For the sampled data, divide it according to a certain ratio (such as 8:2), with one part used as training data (more data) and the other part used as test data.

[0120] Furthermore, in the building module, the neuron transfer function of the improved pattern layer includes:

[0121] Based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of the redundancy to obtain the DD weight of the sampling point, where the DD weight is used to represent the spatial relationship between adjacent sampling points;

[0122] Combining the DD weight with the neuron transfer function of the traditional pattern layer to obtain the neuron transfer function of the improved pattern layer;

[0123] In this embodiment, the network structure of the GRNN model taking into account the spatial relationship of adjacent sample points is as follows: Figure 2 As shown in the figure, it consists of four layers: input layer, pattern layer, summation layer and output layer.

[0124] Input layer:

[0125] where X=[x1,x2,...,x n ] represents the characteristics of the data to be tested (input vector). The number of neurons in the input layer is the number of characteristics of the input data. This layer does not process the data and directly passes the data to the pattern layer.

[0126] Pattern layer:

[0127] The number of neurons in the pattern layer is the number of training data. Each neuron corresponds to different training data. The traditional neuron transfer function of the pattern layer is shown in formula (5):

[0128]

[0129] where X i is the eigenvector of the i-th training data, σ1 is the width coefficient (smooth factor) of the Gaussian function, and neuron p i The output is the input variable X and the i-th training data X i The exponential form of the square of the Euclid distance between them.

[0130] The model used in the GRNN method that takes into account the spatial relationship of adjacent sample points adopted in the present invention does not change the four-layer network structure of the GRNN model, but only changes the neuron transfer function of the pattern layer, while other parts remain unchanged.

[0131] Taking into account the spatial relationship between neighboring sample points means taking the relationship between the sample points into account. When clustered data appears, the results will perform better than traditional methods. A characteristic of clustered data is that various redundancies will appear in the estimation process. According to Tobler's first geographical law, the greater the average or cumulative distance between a sampling point and other sampling points, the less redundancy the sampling point has, and vice versa. Therefore, based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of redundancy, and an additional indicator indicating the importance of the sampling point is proposed: DD weight λ = [λ1,λ2,...,λ n ], DD weight λ of the i-th sampling point i is calculated as follows:

[0132]

[0133] where X i and X j Represents the i-th sampling point and the j-th sampling point. To ensure consistency with the traditional calculation method, the exponential form of the square of the Euclid distance between the two sampling points is used for calculation, where σ2 is a parameter used to adjust the impact of distance on data redundancy.

[0134] For the neuron p in the pattern layer i , its output value is actually the weight of the i-th training data. Considering the above-mentioned spatial relationship of adjacent sample points, combined with the DD weight λ in formula (6) i , and incorporate it into the weight of formula (5) to obtain a new weight calculation formula (pattern layer neuron transfer function), as shown in formula (7):

[0135]

[0136] Among them, X i is the characteristic vector of the i-th training data, σ1 is the smoothing factor, X is the input variable, p i is the value of the neuron in the traditional pattern layer, p′ i is the value of the improved pattern layer neuron.

[0137] Summation layer:

[0138] There are two types of neurons in the summation layer, each using a different method for calculation.

[0139]

[0140] In fact, it is the arithmetic sum of all neurons in the pattern layer. The connection weight between it and each neuron in the pattern layer is 1, which can be simplified to formula (9):

[0141]

[0142] Among them, s0 is the arithmetic summation result, and m is the number of neurons in the improved pattern layer.

[0143] The calculation method of the second type is shown in formula (10):

[0144]

[0145] where Y i The label vector representing the i-th training data is actually the weighted sum of all neurons in the pattern layer, which can be simplified as formula (11):

[0146]

[0147] Among them, snj is the value of the neuron in the summation layer, y ij is the jth output component of the i-th training sample, and k is the dimension of the output variable.

[0148] Output layer:

[0149] The number of neurons in the output layer is the dimension k of the label vector in the training data. Each neuron divides the output value of the summation layer to obtain the output vector The output y of the jth neuron j Corresponding estimation results The j-th element of is calculated as shown in formula (12):

[0150]

[0151] In the training module, the training data is pre-processed as follows: firstly, the distance square matrix between the training data points is calculated.

[0152] In this embodiment, for the training data {[X1, Y1], [X2, Y2], ..., [X m ,Y m ]}, where m represents the number of training data, X i ,i=1,2,...,m represents the feature vector of the i-th training data. Assuming that the number of features is n, then X i is a vector of length n. Similarly, if the sampling point label dimension is k, then Y i , i=1,2,...,m is a vector of length k. For the DD weight mentioned in formula (6), the distance square matrix D between the training data points can be calculated in the training data preprocessing stage, that is,

[0153]

[0154] Training the GRNN model includes: training the model in a cross-validation manner, determining the values ​​of parameters σ1 and σ2, and performing prediction and output.

[0155] In this embodiment, the GRNN model that takes into account the spatial relationship of neighboring sample points used in this embodiment only includes the smoothing factor σ1 of the Gaussian function and the parameter σ2 used to control the influence of distance on data redundancy. For the smoothing factor σ1 of the Gaussian function, the larger σ1 is, the closer the predicted value of the model is to the actual mean of the training data, and the smaller σ1 is, the closer it is to the actual value of the training data. The parameter σ2 is used to control the influence of distance on data redundancy. Selecting a suitable value can avoid the phenomenon of excessive aggregation. In specific applications, sampled data is usually used to use methods such as cross-validation to determine the parameters that are most suitable for this area. According to the distance square matrix D in step three, the DD weight λ of each training data can be calculated, and its calculation formula is as follows:

[0156]

[0157] The model can be trained using methods such as cross-validation to determine the appropriate parameters σ1 and σ2. Finally, the neurons in the output layer are the prediction results of the test data (generally referring to the physical quantity that needs to be predicted, such as the grade value in the field of ore grade valuation).

[0158] By using the GRNN prediction system of the present invention that takes into account the spatial relationship of adjacent sample points, a set of declustering effect mechanisms can be embedded in the original GRNN model, thereby improving the credibility of the prediction results. Figure 3 For prediction, the value of the smoothing factor σ1 is 0.5, the value of the smoothing factor σ2 is 2, and the DD weights of the three sampling points are:

[0159]

[0160] because Much smaller than Removing it has little effect on the results. The predicted value Compared to traditional GRNNs, the error is reduced, achieving a de-aggregation effect. For example, in the field of ore grade estimation mentioned above, achieving de-aggregation makes grade estimation more accurate and reliable, narrowing the gap between predicted and actual grades, facilitating subsequent mining strategy development and avoiding resource waste.

[0161] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A GRNN prediction method that takes into account the spatial relationship of adjacent sample points, characterized in that: include: Divide the sampled data into test data and training data in proportion; wherein the sampled data refers to drilling data of the mining area, including ore location information and ore grade information; Improve the neuron transfer function of the pattern layer and construct a GRNN model; wherein the spatial relationship of adjacent sample points is combined in the construction process of the GRNN model; Preprocessing the training data, training the GRNN model based on the preprocessed training data, testing the trained GRNN model using the test data, and predicting ore grade information based on the tested GRNN model; The neuron transfer functions of the improved pattern layer include: Based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of the redundancy to obtain the DD weight of the sampling point, where the DD weight is used to represent the spatial relationship between adjacent sampling points; Combining the DD weight with the neuron transfer function of the traditional pattern layer to obtain the neuron transfer function of the improved pattern layer; The calculation method of the DD weight is: Among them, λ i is the DD weight, X i and X j are the i-th sampling point and the j-th sampling point respectively, and σ2 is a parameter used to adjust the impact of distance on data redundancy; The neuron transfer function of the improved pattern layer is: Among them, X i is the characteristic vector of the i-th training data, σ1 is the smoothing factor, X is the input variable, p i is the value of the neuron in the traditional pattern layer, p′ i is the value of the improved pattern layer neuron.

2. The GRNN prediction method taking into account the spatial relationship of adjacent sample points according to claim 1, characterized in that The constructed GRNN model includes: an input layer, a pattern layer, a summation layer, and an output layer; wherein, there are two types of neurons in the summation layer, the first type adopts an arithmetic summation calculation method, and the second type adopts a weighted summation calculation method; The arithmetic sum is calculated as follows: Among them, s0 is the arithmetic summation result, and m is the number of neurons in the improved pattern layer; The weighted sum is calculated as follows: Among them, s nj is the value of the neuron in the summation layer, y ij is the jth output component of the i-th training sample, and k is the dimension of the output variable.

3. The GRNN prediction method taking into account the spatial relationship of adjacent sample points according to claim 2, characterized in that: The output layer is calculated as:

4. The GRNN prediction method taking into account the spatial relationship of adjacent sample points according to claim 1, characterized in that The training data is preprocessed as follows: firstly calculating the distance square matrix between the training data points; The distance square moment is:

5. The GRNN prediction method taking into account the spatial relationship of adjacent sample points according to claim 1, characterized in that Training the GRNN model includes: training the model in a cross-validation manner, determining the values ​​of parameters σ1 and σ2, and performing prediction and output.

6. A GRNN prediction system that takes into account the spatial relationship of adjacent sample points, characterized in that: include: Divide modules, build modules and train modules; The partitioning module is used to divide the sampled data into test data and training data in proportion; wherein the sampled data refers to drilling data of the mining area, including ore location information and ore grade information; The construction module is used to improve the neuron transfer function of the pattern layer and construct a GRNN model that takes into account the spatial relationship of adjacent sample points; The training module preprocesses the training data, trains the GRNN model based on the preprocessed training data, tests the trained GRNN model using the test data, and predicts ore grade information based on the tested GRNN model; In the building block, the neuron transfer function of the improved pattern layer includes: Based on the redundancy of the data, the cumulative distance between each sampling point and other sampling points is used as a measure of the redundancy to obtain the DD weight of the sampling point, where the DD weight is used to represent the spatial relationship between adjacent sampling points; Combining the DD weight with the neuron transfer function of the traditional pattern layer to obtain the neuron transfer function of the improved pattern layer; The DD weight is calculated as follows: Among them, λ i is the DD weight, X i and X j are the i-th sampling point and the j-th sampling point respectively, and σ2 is a parameter used to adjust the impact of distance on data redundancy; The neuron transfer function of the improved pattern layer is: Among them, X i is the characteristic vector of the i-th training data, σ1 is the smoothing factor, X is the input variable, p i is the value of the neuron in the traditional pattern layer, p′ i is the value of the improved pattern layer neuron.

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