CN115049026A - Regression analysis method of space non-stationarity relation based on GSNNR - Google Patents

Abstract

The invention discloses a regression analysis method of spatial non-stationarity relation based on GSNNR, belonging to the technical field of combination of deep learning and spatial analysis. The method comprises the following steps: collecting spatial information data; inputting the spatial features and the attribute spatial features into a full-space adjacent nonlinear fusion neural network model, wherein the SAPDNN neural network model takes GNNWR as a basic model, and the attribute spatial features are added into an input layer; obtaining a full-space adjacent expression matrix through the SAPDNN neural network model; and inputting the full-space adjacent expression matrix into an SWNN module for processing, and outputting a weight matrix. The invention introduces the attribute space as an important characteristic for analyzing the non-stationarity process, provides the full-space expression of the fusion space and the attribute space, fuses the geographic space and the attribute space by using the deep neural network, and further improves the accuracy of the measurement of the non-stationarity.

Description

Regression Analysis Method of Spatial Nonstationarity Relationship Based on GSNNR

technical field

The invention belongs to the technical field of combining deep learning and spatial analysis, and in particular, particularly relates to a regression analysis method based on the spatial non-stationarity relationship of improved GSNNR.

Background technique

In the field of spatial analysis, the analysis of non-stationarity is very critical. Generally, mathematical models are needed to analyze the non-stationarity relationship of the corresponding space in analysis and prediction. The accuracy of measures of non-stationarity has become a core evaluation method for geospatial analysis models.

Geographic Neural Network Weighted Regression (GNNWR) is a relatively advanced model structure in the field of geospatial nonstationarity analysis. This model uses a deep neural network to replace the kernel function used for nonlinear fitting in the classical GWR model, which makes up for the disadvantage that the kernel function cannot fit complex nonlinear mapping. In the GNNWR model, the advanced deep neural network's powerful nonlinear fitting ability is used to construct a spatially weighted neural network (SWNN) to fit the nonlinear mapping process from original geospatial data to high-dimensional spatial hidden feature data. Firstly, the geographic space position distances between the multiple sample points and the points to be estimated are calculated, and the spatial distance matrix between the unknown points to be estimated and the multiple known sample points is obtained. Then the spatial distance matrix is input into the SWNN, and the deep neural network performs nonlinear mapping of the original data in the high-dimensional space, and obtains the corresponding spatial weight matrix by learning the data. Finally, the spatial weight matrix is used as the input of the linear regression model to obtain the final fitted value.

The mathematical modeling of GNNWR for non-stationary processes is limited to a single geographic space category, and only considers the distance characteristics between sample points and estimated points. In reality, spatial non-stationarity is also affected by attributes. GNNWR does not fully consider the spatial non-stationary data feature expression, resulting in unstable accuracy.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a regression analysis method based on the spatial non-stationarity relationship of GSNNR to make up for the deficiencies of the prior art.

In order to achieve the above object, the concrete technical scheme that the present invention takes is:

A regression analysis method of spatial non-stationarity relationship based on full spatial neural network regression (GSNNR), including the following steps:

S1: Collect spatial information data, which is divided into training set and test set, and the feature information obtained by data preprocessing includes spatial features and attribute spatial features;

S2: Input the spatial features and attribute spatial features obtained in S1 into the full-space adjacent nonlinear fusion neural network model (SAPDNN). The SAPDNN neural network model is based on GNNWR, and the attribute space features are added to the input layer; after the SAPDNN The neural network model obtains the full-space adjacent expression matrix;

S3: The full-space adjacent expression matrix is input into the SWNN module for processing, and a weight matrix W is output;

The weight matrix W is input to the linear regression model OLR to output the final prediction result y^;

S4: The GNNWR and SWNN constitute a GSNNR model, and the training set is used to train the GSNNR model to obtain a trained GSNNR model, and then the test data is input into the trained GSNNR model, and the result can be output.

Further, in S1: the spatial feature refers to the location information in the geographic space, such as information features such as longitude and latitude, altitude, and position coordinates; the attribute spatial feature refers to the own attribute owned by the geographic entity, such as Information features such as temperature, wind direction, vegetation type, tree diameter, etc.

Further, in the S1: the Euclidean distance is used to measure the spatial features:

For the measurement of attribute space features, it refers to the absolute difference distance of the specified attribute value of the geographic attribute in the vector space or the weighted difference distance of multiple attribute values; the mathematical expression of the attribute distance is as follows:

表示第i与j个样本点之间的属性距离，上标A是属性特征的标识，n为样本点参与计算的属性类别个数，

是第k个属性值的加权系数，且满足

；in,

Indicates the attribute distance between the i-th and jth sample points, the superscript A is the identification of the attribute feature, n is the number of attribute categories that the sample points participate in the calculation,

is the weighting coefficient of the kth attribute value, and satisfies

;

与属性距离

进行融合，构建“位置-属性”统一距离表达

，表示如下：In order to eliminate the difference in the measurement scale between the position distance and the attribute distance in the vector space, the scale weight parameter is introduced, and the position distance is

distance from property

Fusion to build a "position-attribute" unified distance expression

, expressed as follows:

Among them, λ and φ are the location distance scale weight parameter and the attribute distance scale weight parameter, respectively.

的非线性融合函数，其数学表达如下：Further, in S2: for the two sample points 𝑖 and 𝑗 in the space, it is assumed that there is a unified distance expression that takes into account both the position distance and the attribute distance

The nonlinear fusion function of , its mathematical expression is as follows:

的非线性融合函数，构建两个样本点之间的“位置-属性”融合神经网络（Spatial-attribute Proximities NeuralNetwork，SAPNN）；以位置距离

与属性距离

作为输入，通过若干全连接层，得到𝑖与𝑗两个样本点之间的统一距离表征量：以位置距离

与属性距离

作为输入，通过若干全连接层，得到𝑖与𝑗两个样本点之间的统一距离表征量，如下公式表示：Using Neural Networks to Fit the "Location-Attribute" Unified Distance Expression

The nonlinear fusion function of , constructs a "position-attribute" fusion neural network (Spatial-attribute Proximities Neural Network, SAPNN) between two sample points;

distance from property

As input, through several fully connected layers, the uniform distance representation between the two sample points 𝑖 and 𝑗 is obtained: the position distance

distance from property

As input, through several fully connected layers, the uniform distance representation between the two sample points 𝑖 and 𝑗 is obtained, which is expressed by the following formula:

SAPNN is used to fuse the spatial features and attribute features of two sample points; considering the interaction of the "space-attribute" unified distance relationship between any two sample points in the point set, a "space-attribute" fusion deep neural network is constructed. (Spatial-attribute Proximities Deep Neural Network, SAPDNN);

与属性距离表征向量

，其中n为样本点总数；为简单起见，以上两种距离表征向量分别简化为

与

；以样本点i与其他所有样本点的位置距离

与属性距离

作为输入，对样本点

与每一个样本点两点之间的位置距离

与属性距离

都采用SAPNN网络进行“位置-属性”的统一距离融合计算，可以得到该样本点

与所有样本点的融合位置距离与属性距离的统一距离表征向量

，再经过若干全连接层进行非线性融合，获得可以表征空间中样本点

的与其他所有样本点之间“位置-属性”统一距离度量

，其公式如下表示：For any sample point i, the position distance representation vector of the point and other points in the point set in the sample space can be obtained

and attribute distance representation vector

, where n is the total number of sample points; for simplicity, the above two distance representation vectors are simplified as

and

; the distance between sample point i and all other sample points

distance from property

As input, for sample points

The position distance between the two points from each sample point

distance from property

Both use the SAPNN network to perform the unified distance fusion calculation of "position-attribute", and the sample point can be obtained.

Uniform distance representation vector with fused location distances and attribute distances to all sample points

, and then go through several fully connected layers for nonlinear fusion to obtain sample points that can represent the space.

The unified distance metric of "location-attribute" between all other sample points

, the formula is as follows:

。

.

Further, the SAPDNN neural network model adopts a three-layer neural network architecture of input layer, hidden layer and output layer, and uses He parameter initialization, PReLU activation function, batch normalization, variable learning rate and other technologies to improve the model during training. generalizability.

Further, the He parameter initialization, PReLU activation function, batch normalization, and variable learning rate are as follows:

The initialization of the He parameter: avoid the exponential enlargement or shrinkage of the signal when the pre-propagation and back-propagation are performed in the network, thereby avoiding the disappearance or explosion of the gradient;

The PReLU activation function, ai is a learnable parameter,

The PReLU activation function improves the fitting performance of the model with almost no increase in parameters, reducing the risk of overfitting;

The batch normalization: the output of each layer of the model is normalized before passing through the activation function to ensure that the value remains stable when it propagates in the middle of the network, making the network easier to converge and reducing the risk of overfitting;

The variable learning rate: In model training, it is usually desirable to have a larger initial learning rate and a smaller later learning rate. Using a variable learning rate can adapt the learning rate to the extent of the model training, and as the model becomes more and more accurate, the learning rate becomes smaller and smaller.

Further, the SWNN module is a neural network architecture of an input layer, two hidden layers (can be more than two layers) and an output layer; the weights are calculated for the input pair full-space adjacent expression matrix; The same training optimization technique for SAPDNN.

Compared with the prior art, the advantages and beneficial effects of the present invention are:

(1) The present invention introduces attribute space as an important feature of the analytical non-stationarity process, and the attribute space incorporates the input of the spatial non-stationarity detection model; Attribute Space refers to the attributes possessed within the scope of geographic space. The spatial differences of geographical attributes combined with the spatial and temporal distribution of geography are of great significance for revealing complex geographical phenomena.

(2) The present invention proposes a full-space representation of fusion space and attribute space, and uses deep neural network to fuse geographic space and attribute space. Compared with a single geographic space feature, the composite feature after fusion can more accurately represent the actual spatial feature. Stationarity process, thereby further improving the accuracy of the measure of non-stationarity.

(3) The present invention also proposes a full-space adjacent nonlinear fusion neural network (SAPDNN). The neural network model is based on GNNWR and adds attribute space features to improve the accuracy of prediction. The network is used to integrate geographic spatial features and geographic attribute features to obtain a full spatial representation of geographic features.

Description of drawings

Figure 1 is the basic frame diagram of the SAPDNN neural network model.

Figure 2 is a process diagram of the SAPNN neural network model.

Figure 3 is a process diagram of the SAPDNN neural network model.

Figure 4 is the basic frame diagram of the SWNN module.

Figure 5 is a flow chart of the output weight matrix of the SWNN module.

Figure 6 is the input and output structure diagram of the GSNNWR model.

FIG. 7 is a flow chart of cross-training and verification of the present invention.

Detailed ways

The technical solutions of the present invention will be further described below with reference to the embodiments.

Example 1:

A regression analysis method of spatial non-stationarity relationship based on full spatial neural network regression (GSNNR), including the following steps:

S1: Collect spatial information data, which is divided into training set and test set. The feature information obtained by data preprocessing includes spatial features and attribute spatial features; the spatial features refer to location information in geographic space, such as latitude and longitude, altitude , location coordinates and other information features; the attribute space features refer to the own attributes possessed by geographic entities, such as information features such as temperature, wind direction, vegetation type, tree diameter, etc.

For spatial features, Euclidean distance is used to measure:

For the measurement of attribute space features, it refers to the absolute difference distance of the specified attribute value of the geographic attribute in the vector space or the weighted difference distance of multiple attribute values; the mathematical expression of the attribute distance is as follows:

表示第i与j个样本点之间的属性距离，上标A是属性特征的标识，n为样本点参与计算的属性类别个数，

是第k个属性值的加权系数，且满足

；in,

Indicates the attribute distance between the i-th and jth sample points, the superscript A is the identification of the attribute feature, n is the number of attribute categories that the sample points participate in the calculation,

is the weighting coefficient of the kth attribute value, and satisfies

;

与属性距离

进行融合，构建“位置-属性”统一距离表达

，表示如下：In order to eliminate the difference in the measurement scale between the position distance and the attribute distance in the vector space, the scale weight parameter is introduced, and the position distance is

distance from property

Fusion to build a "position-attribute" unified distance expression

, expressed as follows:

Among them, λ and φ are the location distance scale weight parameter and the attribute distance scale weight parameter, respectively.

S2: Input the spatial features and attribute spatial features obtained by S1 into the full-space adjacent nonlinear fusion neural network model (SAPDNN), as shown in Figure 1, the SAPDNN neural network model is based on GNNWR, and attributes are added to the input layer. Spatial features; the full-space adjacent expression matrix is obtained through the SAPDNN neural network model;

的非线性融合函数，其数学表达如下：For the two sample points 𝑖 and 𝑗 in the space, it is assumed that there is a uniform distance expression that takes into account both the location distance and the attribute distance.

The nonlinear fusion function of , its mathematical expression is as follows:

的非线性融合函数，构建两个样本点之间的“位置-属性”融合神经网络（Spatial-attribute Proximities NeuralNetwork，SAPNN），如图2所示；以位置距离

与属性距离

作为输入，通过若干全连接层，得到𝑖与𝑗两个样本点之间的统一距离表征量：以位置距离

与属性距离

作为输入，通过若干全连接层，得到𝑖与𝑗两个样本点之间的统一距离表征量，如下公式表示：Using Neural Networks to Fit the "Location-Attribute" Unified Distance Expression

The nonlinear fusion function of the

distance from property

As input, through several fully connected layers, the uniform distance representation between the two sample points 𝑖 and 𝑗 is obtained: the position distance

distance from property

As input, through several fully connected layers, the uniform distance representation between the two sample points 𝑖 and 𝑗 is obtained, which is expressed by the following formula:

SAPNN is used to fuse the spatial features and attribute features of two sample points; considering the interaction of the "space-attribute" unified distance relationship between any two sample points in the point set, a "space-attribute" fusion deep neural network is constructed. (Spatial-attribute Proximities Deep Neural Network, SAPDNN), as shown in Figure 3;

，均可获得该点与样本空间内点集中其他点的位置距离表征向量

与属性距离表征向量

，其中

为样本点总数；为简单起见，以上两种距离表征向量分别简化为

与

；以样本点i与其他所有样本点的位置距离

与属性距离

作为输入，对样本点

与每一个样本点两点之间的位置距离

与属性距离

都采用SAPNN网络进行“位置-属性”的统一距离融合计算，可以得到该样本点

与所有样本点的融合位置距离与属性距离的统一距离表征向量

，再经过若干全连接层进行非线性融合，获得可以表征空间中样本点的与其他所有样本点之间“位置-属性”统一距离度量

，其公式如下表示：for any sample point

, the position distance representation vector of the point and other points in the point set in the sample space can be obtained

and attribute distance representation vector

,in

is the total number of sample points; for simplicity, the above two distance representation vectors are simplified as

and

; the distance between sample point i and all other sample points

distance from property

As input, for sample points

The position distance between the two points from each sample point

distance from property

Both use the SAPNN network to perform the unified distance fusion calculation of "position-attribute", and the sample point can be obtained.

Uniform distance representation vector with fused location distances and attribute distances to all sample points

, and then perform nonlinear fusion through several fully connected layers to obtain a unified distance metric of "position-attribute" between the sample point and all other sample points in the space.

, the formula is as follows:

。

.

The SAPDNN neural network model adopts a three-layer neural network architecture of input layer, hidden layer and output layer, and uses He parameter initialization, PReLU activation function, batch normalization, variable learning rate and other technologies in training to improve the generalization of the model. sex.

The He parameter initialization, PReLU activation function, batch normalization, and variable learning rate are as follows:

The initialization of the He parameter: avoid the exponential enlargement or shrinkage of the signal when the pre-propagation and back-propagation are performed in the network, thereby avoiding the disappearance or explosion of the gradient;

The PReLU activation function, ai is a learnable parameter,

The PReLU activation function improves the fitting performance of the model with almost no increase in parameters, reducing the risk of overfitting;

The batch normalization: the output of each layer of the model is normalized before passing through the activation function to ensure that the value remains stable when it propagates in the middle of the network, making the network easier to converge and reducing the risk of overfitting;

The variable learning rate: In model training, it is usually desirable to have a larger initial learning rate and a smaller later learning rate. Using a variable learning rate can adapt the learning rate to the extent of the model training, and as the model becomes more and more accurate, the learning rate becomes smaller and smaller.

S3: The full-space adjacent expression matrix is input into the SWNN module for processing, as shown in Figure 5, a weight matrix W is output;

The weight matrix W is input to the linear regression model OLR to output the final prediction result y^;

As shown in Figure 4, the SWNN module is a neural network architecture with an input layer, two hidden layers (can be more than two layers) and an output layer with four layers; the weights are calculated for the input pair full-space adjacent expression matrix; The same training optimization technique as SAPDNN is used in training.

S4: The GNNWR and SWNN constitute a GSNNR model, and the GSNNR model is trained by using the training set to obtain a trained GSNNR model, and then the test data is input into the trained GSNNR model, and the output result can be, as shown in the figure 6 shown.

The technical features of this embodiment include the following:

(1) "Space-attribute" feature fusion. The spatial features and geographic attribute features corresponding to each sample point are input into SAPDNN, and the "spatial-attribute" full proximity feature expression matrix is obtained after operation. Combine the outputs of multiple sample points into a large matrix as the input to the next module.

(2) "Space-attribute" feature weight matrix calculation. For the fusion feature matrix output by the previous module, a deep neural network is used to extract features, and the neural network adopts a multi-layer perceptron structure. In training, optimization techniques such as Dropout, He parameter initialization, and PReLU activation function are used to enhance the generalization ability of the model.

(3) Calculation of prediction results. The non-stationary coefficients are obtained by multiplying the non-stationary weights by the least squares coefficients. The fitted value y ̂_i of the final output of the model is the result of the multiplicative summation of all non-stationary coefficients and their corresponding independent variables. The least squares coefficients are obtained from the training set.

(4) Verification test. To verify the effectiveness of the algorithm design in the future, the data set is divided into training set and test set according to the ratio of 3:1, and 10-fold cross-validation is carried out within the training set according to the ratio of 9:1. The process of cross-validation is shown in Figure 7.

Example 2

This example is based on Example 1, takes the spatial non-stationarity relationship of PM2.5 concentration in the atmosphere as the research object, and uses the algorithm model to predict the actual PM2.5 concentration value.

In order to ensure the representativeness of the data, the present invention selects the nationwide monitoring point data in 2018 as the research data, and focuses on comparing the full-spatial proximity expression after the fusion of "space-attribute" features. influences. For data processing, wind direction (WD) is selected as the geographical attribute feature related to PM2.5 concentration, and PM2.5 concentration is used as the prediction object. The input features of the model also include elevation (DEM), relative humidity (r), 10m wind speed ( WS), aerosol (AOD), precipitation (TP), temperature at 2 m (TEMP).

In the training set and test set, all data samples are randomly divided into training cross-validation set and test set according to the ratio of 3:1. In the cross-validation set, the ratio of 9:1 is used for 10-fold cross-validation to ensure the generalization ability of the model. . The data used were randomly sampled from monitoring points across the country, and the data presented a random distribution within the geographic space of the country, ensuring that the conclusions of this case were generally representative.

Compared with the GWR and GNNWR models, the improvement of the present invention mainly lies in the following two points:

1. Introduce geographic attribute space as one of the input features of the algorithm, and use SAPDNN to fuse the "space-attribute" features to obtain a full spatial representation. The new scheme proposed by the present invention is more representative at the basic data level than the original scheme that only considers the geospatial position relationship, and the feature processing method combining "space-attribute" can better characterize the actual geospatial non-stationarity relation.

2. The calculation accuracy is improved after the introduction of a new feature representation method. Comparing the GNNWR model without considering the spatial characteristics of geographic attributes and the GWR model with different kernel functions, the accuracy is improved by about 10% on average.

1. Introducing geographic attribute space

The existing model scheme only mines the spatial non-stationarity relationship between samples from the two-dimensional distance in the geographic spatial position relationship. However, in fact, this relationship between samples is affected by many factors. After introducing geographic attribute features , the expression of the sample in the data is closer to the actual situation and contains more semantic information.

Second, the use of deep neural network fusion of two features

After introducing a new feature expression, a deep neural network is used to fuse the processing of two different features, and a full-space expression matrix of "space-attribute" is obtained as the input data for the subsequent calculation. Since the data itself contains more semantic information, the calculation accuracy of the model is improved.

On the basis of the above embodiments, the present invention continues to describe in detail the technical features involved and the functions and functions of the technical features in the present invention, so as to help those skilled in the art to fully understand the features of the present invention. technical solutions and reproduce them.

Finally, although this specification is described in terms of implementations, not each implementation only includes an independent technical solution. This description in the specification is only for the sake of clarity. Those skilled in the art should take the specification as a whole, and each implementation The technical solutions in the examples can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims (7)

1. a regression analysis method based on the spatial non-stationarity relation of GSNNR, is characterized in that, this method may further comprise the steps: S1: Collect spatial information data, which is divided into training set and test set, and the feature information obtained by data preprocessing includes spatial features and attribute spatial features; S2: Input the spatial features and attribute spatial features obtained in S1 into the full-space adjacent nonlinear fusion neural network model SAPDNN. The SAPDNN uses GNNWR as the basic model, and attribute space features are added to the input layer; expression matrix; S3: The full-space adjacent expression matrix is input into the SWNN module for processing, and a weight matrix W is output;

The weight matrix W is input to the linear regression model OLR to output the final prediction result y^; S4: The GNNWR and SWNN constitute a GSNNR model, and the training set is used to train the GSNNR model to obtain a trained GSNNR model, and then the test data is input into the trained GSNNR model, and the result can be output. 2. The regression analysis method according to claim 1, wherein in S1: the spatial feature refers to location information in geographic space, including latitude and longitude, altitude, and position coordinates; the attribute spatial feature Refers to the own attributes of geographic entities, including temperature, wind direction, vegetation type, and tree diameter. 3. regression analysis method as claimed in claim 1, is characterized in that, in described S1: described spatial feature adopts Euclidean distance to measure:

; The measure of the attribute space feature is the absolute difference distance of the specified attribute value of the geographic attribute in the vector space or the weighted difference distance of multiple attribute values; the mathematical expression of the attribute distance is as follows:

in,

Indicates the attribute distance between the i-th and jth sample points, the superscript A is the identification of the attribute feature, n is the number of attribute categories that the sample points participate in the calculation,

is the weighting coefficient of the kth attribute value, and satisfies

; Introduce the scale weight parameter, the position distance

distance from property

Fusion to build a "position-attribute" unified distance expression

, expressed as follows:

Among them, λ and φ are the location distance scale weight parameter and the attribute distance scale weight parameter, respectively. 4. The regression analysis method according to claim 1, characterized in that, in S2: for two sample points 𝑖 and 𝑗 in the space, it is assumed that there is a uniform distance expression that takes into account the position distance and the attribute distance

The nonlinear fusion function of , its mathematical expression is as follows:

Using Neural Networks to Fit the "Location-Attribute" Unified Distance Expression

The nonlinear fusion function of , constructs the "position-attribute" fusion neural network SAPNN between two sample points;

distance from property

As input, through several fully connected layers, the uniform distance representation between the two sample points 𝑖 and 𝑗 is obtained: the position distance

distance from property

As input, through several fully connected layers, the uniform distance representation between the two sample points 𝑖 and 𝑗 is obtained, which is expressed by the following formula:

SAPNN is used to fuse the spatial features and attribute features of two sample points; considering the interaction of the "space-attribute" unified distance relationship between any two sample points in the point set, a "space-attribute" fusion deep neural network is constructed. SAPDNN; For any sample point i, the position distance representation vector of the point and other points in the point set in the sample space can be obtained

and attribute distance representation vector

, where n is the total number of sample points; for simplicity, the above two distance representation vectors are simplified as

and

; the distance between sample point i and all other sample points

distance from property

As input, for sample points

The position distance between the two points from each sample point

distance from property

Both use the SAPNN network to perform the unified distance fusion calculation of "position-attribute", and the sample point can be obtained.

Uniform distance representation vector with fused location distances and attribute distances to all sample points

, and then go through several fully connected layers for nonlinear fusion to obtain sample points that can represent the space.

The unified distance metric of "location-attribute" between all other sample points

, the formula is as follows:

. 5. regression analysis method as claimed in claim 1 is characterized in that, in described S2, described SAPDNN adopts the neural network architecture of input layer, hidden layer and output layer three layers, uses He parameter initialization in training, PReLU activation function, batch normalization, and variable learning rate to improve the generalization of the model. 6. regression analysis method as claimed in claim 5, is characterized in that, described He parameter initialization, PReLU activation function, batch normalization, variable learning rate are as follows: The initialization of the He parameter: avoid the exponential enlargement or shrinkage of the signal when the pre-propagation and back-propagation are performed in the network, thereby avoiding the disappearance or explosion of the gradient; The PReLU activation function, ai is a learnable parameter,

The PReLU activation function improves the fitting performance of the model with almost no increase in parameters; The batch normalization: normalize the output of each layer of the model before passing through the activation function; The variable learning rate: Using the variable learning rate can make the learning rate adapt to the degree of model training. When the model becomes more and more accurate, the learning rate becomes smaller and smaller. 7. regression analysis method as claimed in claim 1, is characterized in that, described SWNN module is the neural network architecture of input layer, two layers and above hidden layer and output layer; For the paired group full-space adjacent expression matrix of input Perform weight calculation; use the same training optimization technique as the SAPDNN in training.

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