Tensor-kernel neural network for efficient prediction modeling and modeling method thereof

Abstract

The invention discloses a tensor-kernel neural network for efficient prediction modeling and a modeling method thereof, and the tensor-kernel neural network comprises a kernel function mapping module which is used for carrying out the nonlinear kernel mapping of input data to obtain high-dimensional data; the tensor decomposition module is used for performing low-rank reconstruction on high-dimensional data and extracting low-dimensional features; and the deep neural network is used for training and predicting the extracted data low-dimensional features and outputting a prediction result. The loss function can effectively balance the reconstruction error and the prediction error in the model training process, and the generalization ability of the model is improved. In combination with Gaussian radial basis kernel function nonlinear kernel mapping, nonlinear input data is mapped to a high-dimensional feature space, and low-rank reconstruction is performed on high-dimensional data through a CP decomposition method; and finally, training and predicting the extracted low-dimensional features through a deep neural network. According to the method, the calculation efficiency and the prediction precision can be remarkably improved in high-dimensional data modeling; and the calculation complexity is reduced, and meanwhile, accurate extraction of data features and efficient training of the model are ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of machine learning and deep learning, and specifically proposes an efficient prediction modeling method combining tensor decomposition, kernel function and neural network. Background Art

[0002] In the field of modern data science and machine learning, the processing and analysis of large-scale high-dimensional data is becoming a very challenging research problem. Especially in industries such as agriculture and finance, the data in these fields usually contain hundreds or even thousands of dimensions of features, and there are complex nonlinear relationships between different dimensions. How to extract effective features from these high-dimensional sparse data and make efficient and accurate predictions has become a major problem in existing technologies.

[0003] Existing machine learning and predictive modeling methods usually face the following two main problems when dealing with large-scale high-dimensional data:

[0004] 1) Dimensionality curse problem:

[0005] In high-dimensional data sets, the dimension of features increases significantly, resulting in an exponential increase in the computational complexity of the model. This not only increases the training time, but may also cause the model to overfit, that is, it performs well on the training set but cannot be generalized in actual applications. This problem is particularly prominent in traditional machine learning models, such as support vector machines (SVMs), logistic regression, decision trees, etc., as well as neural network models.

[0006] 2) Limited ability to handle nonlinear relationships:

[0007] For high-dimensional sparse data, there are often highly complex nonlinear relationships between the various feature dimensions. Although models such as neural networks and support vector machines have certain nonlinear processing capabilities, in high-dimensional data, the performance of these models is often limited by the sparsity and noise of the data. In addition, traditional neural networks are prone to falling into local optimal solutions and cannot effectively capture the complex relationships in the data.

[0008] In recent years, kernel methods and tensor decomposition techniques have shown excellent performance in nonlinear mapping and low-rank approximation of high-dimensional data, respectively. Kernel methods can transform low-dimensional data into high-dimensional space through nonlinear mapping in order to capture complex patterns in the original data. Tensor decomposition technology can decompose high-dimensional data into multiple low-rank matrices and extract the key features of the data. However, the combination of these two techniques has been less explored and applied in existing research and applications. Nevertheless, the respective advantages of tensor decomposition and kernel methods provide a theoretical basis for solving the problem of high-dimensional sparse data processing. Summary of the invention

[0009] In order to make up for the shortcomings of the prior art, the present invention proposes a tensor-kernel neural network (TKNN) for efficient prediction modeling and its modeling method. The network model combines kernel function mapping (RBF Kernel), tensor decomposition (CP decomposition) and deep neural network (DNN), which can significantly improve the computational efficiency and prediction accuracy in high-dimensional data modeling. The network model aims at the dimensionality curse problem in large-scale sparse data processing, adopts low-rank reconstruction and nonlinear feature extraction methods, and reduces the computational complexity while ensuring the accurate extraction of data features and efficient training of the model.

[0010] The technical solution adopted by the present invention is:

[0011] Tensor-kernel neural networks for efficient predictive modeling, including:

[0012] The kernel function mapping module is used to map the input data nonlinearly to obtain high-dimensional data, thereby capturing complex nonlinear features;

[0013] Tensor decomposition module, which reconstructs high-dimensional data into low-rank, extracts low-dimensional features, and reduces data dimension;

[0014] Deep neural network, trains and predicts the low-dimensional features of the extracted data and outputs the prediction results.

[0015] The loss function can effectively balance the reconstruction error and prediction error during model training and improve the generalization ability of the model.

[0016] The kernel function mapping module performs nonlinear mapping on the input data through a Gaussian radial basis kernel function (RBF Kernel) to obtain a high-dimensional feature Φ(X), which is expressed as follows:

[0017]

[0018] Among them, ||XX′|| 2 is the Euclidean distance between the input data and the center vector; X represents the original input data vector; X′ represents the center vector of the kernel function, which is usually a sample in the training data set; σ is the bandwidth parameter of the kernel function, which controls the amplitude of the kernel function and the distribution mapped to the high-dimensional space. By adjusting the σ value, the sensitivity of the model to different data can be controlled, thereby optimizing the high-dimensional feature extraction effect of the data; the larger the σ value, the slower the similarity decays, which is suitable for smoother data; when the value is small, local changes are more emphasized.

[0019] In the kernel function mapping module, the bandwidth parameter σ of the kernel function is adaptively adjusted according to the distribution of the input data, and the calculation formula is:

[0020]

[0021] Where μ is the mean of the input data set, n is the number of data points, and X i is the sample point of the input data.

[0022] Through the above, the parameter σ in the RBF kernel function is further refined. Through the adaptive adjustment method, the model can dynamically adapt to changes in data distribution, thereby improving the robustness of the kernel function mapping.

[0023] The tensor decomposition module performs CP decomposition (CANDECOMP / PARAFAC decomposition) on the high-dimensional feature data obtained by nonlinear mapping, and converts the high-dimensional tensor X∈R n1×n2×n3 Expressed as a decomposition form of a low-rank tensor:

[0024]

[0025] Among them, Y represents the mapped third-order tensor data; the factor matrix A (r) , B (r) , C (r) They represent the projection of the tensor on each dimension, respectively, and represent the characteristics of the data in different dimensions.

[0026] R is the tensor decomposition rank, which indicates the number of features retained in the low-rank approximation; the decomposition rank R controls the complexity and computational efficiency of the model. A smaller R value can reduce the computational complexity, but may lose some feature information; a larger R value can retain more information, but the computational overhead increases.

[0027] Represents the outer product operation of vectors.

[0028] The rank R of the CP decomposition of the tensor decomposition module is adaptively set according to the dimension and complexity of the input data and is calculated by the following formula:

[0029] R=min(n1,n2,n3)×α

[0030] Among them, n1, n2, and n3 are the three dimensions of the tensor, and α is a hyperparameter that adjusts the decomposition accuracy and controls the complexity of the decomposition. The larger the value, the more complex the data pattern captured by the model; the smaller the value, the higher the computational efficiency.

[0031] The above specifically describes the rank of CP decomposition to ensure that a trade-off between computational efficiency and model accuracy is achieved by adaptively setting the size of the rank under different data sets.

[0032] The deep neural network trains and predicts the decomposed low-dimensional features, and the input features are the expanded low-dimensional tensors Use deep neural network to output prediction results;

[0033]

[0034] in, represents the output of the deep neural network; f DNN represents the forward propagation process of the deep neural network; vec(·) represents the vectorization operation of the tensor, which converts the tensor result after CP decomposition into a vector so as to serve as the input of the deep neural network.

[0035] The deep neural network trains and predicts low-rank features. The deep neural network adopts a multi-layer perceptron (MLP) structure, and the input is the low-dimensional features obtained by CP decomposition. Each layer of the deep neural network is calculated through linear transformation and nonlinear activation function, and its mathematical expression is as follows:

[0036] For layer l:

[0037] h (l) =f (l) (W (l) h (l-1) +b (l) )

[0038] Where: h (l) represents the output of the lth layer; W (l) represents the weight matrix of the lth layer; b (l) represents the bias vector of the lth layer; f (l) represents the activation function of the lth layer (such as ReLU or Sigmoid);

[0039] The low-dimensional tensor after tensor decomposition is flattened into a vector for input into a deep neural network.

[0040] Finally, the output layer of the deep neural network undergoes linear transformation and activation function to output the prediction result.

[0041]

[0042] Where: W (out) 、b (out) ) represent the weight and bias of the output layer respectively; f (out) Represents the activation function of the output layer, which is selected according to the type of prediction task, such as linear activation for regression tasks and Sigmoid or Softmax for classification tasks. The loss function consists of two parts: reconstruction error L recon and the prediction error L pred ;

[0043] Where: reconstruction error L recon:The difference between the data Φ(X) mapped by Gaussian radial basis kernel function (RBF Kernel) and the CP decomposition result is measured by Frobenius norm;

[0044]

[0045] Among them, ||·|| X is the Frobenius norm, which represents the sum of squares of reconstruction errors;

[0046] This ensures that the model can accurately reconstruct the features of high-dimensional data through CP decomposition.

[0047] Prediction error L pred :Measure the model prediction value through the mean square error (MSE) The difference between the true value y;

[0048]

[0049] Among them, λ is a regularization parameter used to balance the influence between reconstruction error and prediction error, and its range is set to 0.01≤λ≤0.1.

[0050] The model is optimized by minimizing the following combined loss function:

[0051]

[0052] Among them, L total is the total loss function.

[0053] The setting of the regularization parameter λ ensures that the reconstruction error and prediction error can be effectively weighed during the model training process, improves the generalization ability of the model, and is used to balance the reconstruction error and prediction error to avoid model overfitting.

[0054] A modeling method of tensor-kernel neural network for efficient predictive modeling, combining nonlinear kernel mapping of Gaussian radial basis kernel function, maps nonlinear input data to high-dimensional feature space, and then reconstructs high-dimensional data into low-rank through CP decomposition method; after high-dimensional data is mapped to feature space, CP decomposition is used to extract potential patterns and feature structures, achieving data dimensionality reduction while retaining important information. This process can reduce the computational burden without losing key features. Finally, the extracted low-dimensional features are trained and predicted through deep neural networks.

[0055] A tensor-kernel neural network for efficient predictive modeling, for use in potato farming or financial data analysis.

[0056] The present invention provides a tensor-kernel neural network (TKNN) for efficient predictive modeling, and the technical effects are as follows:

[0057] 1) The tensor-kernel neural network (TKNN) model combines RBF kernel mapping, tensor decomposition (CP decomposition) and deep neural network (DNN), which can significantly improve computational efficiency and prediction accuracy in high-dimensional data modeling. The tensor-kernel neural network (TKNN) model addresses the dimensionality curse problem in large-scale sparse data processing, and uses low-rank reconstruction and nonlinear feature extraction methods to reduce computational complexity while ensuring accurate extraction of data features and efficient model training.

[0058] 2) The tensor-kernel neural network (TKNN) model effectively solves the dimensionality curse and computational complexity problems in the existing technology when processing high-dimensional sparse data, and can significantly improve computational efficiency while maintaining prediction accuracy. The tensor-kernel neural network (TKNN) model is suitable for efficient prediction modeling tasks in a variety of large-scale data scenarios such as agricultural yield prediction and financial data analysis.

[0059] 3) The tensor-kernel neural network (TKNN) model integrates the advantages of kernel methods, CP decomposition and deep neural networks, and is suitable for data analysis in multiple fields. Whether it is corporate management, agricultural production or financial forecasting, the tensor-kernel neural network (TKNN) model can provide accurate decision support through efficient data processing and nonlinear pattern capture.

[0060] 4) Solve the dimensionality curse problem: Through CP decomposition, the computational complexity of high-dimensional data is effectively reduced; Improve nonlinear modeling capabilities: Kernel function mapping combined with DNN can effectively capture complex nonlinear relationships in data; Efficient prediction capabilities: Through the training and optimization of multi-layer neural networks, the prediction accuracy and efficiency are improved and the computational cost is reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 Schematic diagram of the overall structure of the tensor-kernel neural network (TKNN) model of the present invention.

[0062] Figure 2 Schematic diagram of the high-dimensional feature extraction process after the input data is mapped by the kernel function.

[0063] Figure 3 Schematic diagram of the process of extracting low-rank tensor features after CP decomposition.

[0064] Figure 4 Schematic diagram of the process of training and predicting extracted features for the deep neural network module.

[0065] Figure 5 This is a graph of the loss value of the tensor kernel neural network (TKNN) model.

[0066] Figure 6This is a heat map of the correlation analysis results. DETAILED DESCRIPTION

[0067] A Tensor-Kernel Neural Network for Efficient Predictive Modeling (TKNN) for Efficient Predictive Modeling. The model combines Gaussian radial basis kernel function (RBFKernel), CP decomposition (CANDECOMP / PARAFAC decomposition) and deep neural network (DNN) to achieve nonlinear feature extraction and efficient prediction of high-dimensional data. The input data is mapped to a high-dimensional feature space through nonlinear kernel mapping by RBF Kernel to capture the complex nonlinear relationships in the data; then, CP decomposition is a tensor decomposition method that aims to decompose multidimensional data into several smaller low-rank tensors to identify potential patterns and structures in the data while reducing the dimensionality and retaining key features.

[0068] 1) The overall structure of the tensor-kernel neural network model consists of three main parts:

[0069] a: Kernel mapping module: used to map input data into high-dimensional space and capture complex nonlinear features.

[0070] b: Tensor decomposition module: performs CP decomposition on high-dimensional tensor data and extracts low-rank features to reduce data dimension.

[0071] c: Deep neural network: Use deep neural network to train and predict low-rank features and output prediction results.

[0072] 2) Kernel mapping module:

[0073] The kernel mapping module uses the radial basis kernel function (RBF Kernel) to perform nonlinear mapping on the input data. By calculating the distance between input samples, its similarity is mapped to a high-dimensional space to capture the nonlinear relationship between variables. The formula is:

[0074]

[0075] in:

[0076] Φ(X): Representation of input data X in high-dimensional feature space.

[0077] X: original input data vector.

[0078] X′: The center vector of the kernel function, usually a sample in the training data set.

[0079] ||XX′||2 : Euclidean distance between the input data and the center vector.

[0080] σ: The bandwidth parameter of the kernel function, which controls the amplitude of the kernel function and the distribution mapped to the high-dimensional space; by adjusting the σ value, the sensitivity of the model to different data can be controlled, thereby optimizing the high-dimensional feature extraction effect of the data.

[0081] 3) Tensor decomposition module:

[0082] The tensor decomposition module is responsible for low-rank reconstruction of the mapped high-dimensional feature data to reduce the data dimension and extract key features. The tensor-kernel neural network (TKNN) model uses CANDECOMP / PARAFAC (CP) decomposition to transform the third-order tensor data X∈R n1×n2×n3 It is expressed in a low-rank form. The specific decomposition expression is:

[0083]

[0084] in:

[0085] Y: The third-order tensor data after mapping.

[0086] R: The rank of the tensor decomposition, which indicates the number of features preserved in the low-rank approximation.

[0087] A (r) ∈R n1 , B (r) ∈R n2 , C (r) ∈R n3 : The rth factor matrix represents the decomposition results in three modes (dimensions).

[0088] : Outer product operation of vectors.

[0089] 4) Deep neural network: including multi-layer perceptron (MLP) structure, the input is the low-dimensional feature vector z obtained by tensor decomposition, the hierarchical structure is as follows:

[0090] ①. The first hidden layer: contains 128 neurons, the input is z, the output is h1, and its activation function is ReLU. The specific expression is:

[0091] h1=ReLU(W1z+b1)

[0092] Among them, W1 is the weight matrix, b1 is the bias vector, and the ReLU expression is:

[0093] ReLU(x)=max(0,x)

[0094] ②. The second hidden layer: contains 64 neurons, the input is h1, the output is h2, and its activation function is also ReLU. The specific expression is:

[0095] h2=ReLU(W2h1+b2)

[0096] Among them, W2 is the weight matrix and b2 is the bias vector.

[0097] ③. The second hidden layer: contains 32 neurons, the input is h2, the output is h3, and its activation function is also ReLU, expressed as:

[0098] h3=ReLU(W3h2+b3)

[0099] Among them, W3 is the weight matrix and b3 is the bias vector.

[0100] ④. Output layer: contains one neuron, the input is h3, and the output is the predicted value Its activation function is the Softmax function, and the specific expression is:

[0101]

[0102] Among them, W4 is the weight matrix and b4 is the bias vector.

[0103] The expression of the Sigmoid function is:

[0104]

[0105] The activation function ReLU of the first hidden layer is represented by the formula ReLU(x)=max(0,x), which maps the input z to the neuron output h1 of the first layer.

[0106] The activation function of subsequent layers is also ReLU, and similar formulas are used to describe the calculation process of different layers.

[0107] The activation function of the output layer is Sigmoid, formula Used to map the output of the last layer into a probability value This probability value is used in regression prediction tasks.

[0108] 5) Model loss function and optimization:

[0109] In order to train the model, the tensor-kernel neural network (TKNN) model uses a combined loss function to optimize the model performance. The total loss function L total It consists of two parts: reconstruction error L recon and the prediction error L pred .

[0110] The total loss function is defined as follows:

[0111] L total =L recon +λL pred

[0112] Where: reconstruction error L recon : Used to measure the difference between the reconstructed data and the original data of the tensor decomposition:

[0113]

[0114] Among them, ||·|| X is the Frobenius norm, which represents the sum of squares of the reconstruction error.

[0115] Prediction error L pred : Used to measure the predicted value The difference between the true value y is:

[0116]

[0117] Regularization parameter λ: used to balance the impact between reconstruction error and prediction error.

[0118] The total loss function L of the tensor kernel neural network (TKNN) model total It can be expressed as:

[0119]

[0120] Where: Φ(X) represents the result of mapping the input data X to a high-dimensional space through an RBF Kernel (radial basis kernel function).

[0121]

[0122] Among them, σ is the hyperparameter of the RBF kernel function, which controls the kernel width in high-dimensional mapping.

[0123] Represents the low-rank tensor decomposition by CP decomposition (CANDECOMP / PARAFAC decomposition), where R is the rank of the tensor decomposition, which is used to reconstruct the data Φ(X) after RBF mapping.

[0124] A(:,r): represents the rth column of matrix A, which is one of the factor matrices of CP decomposition and is used to represent a pattern (dimension) in the data.

[0125] B(:,r): represents the rth column of matrix B, which is one of the factor matrices of CP decomposition.

[0126] C(:,r): represents the rth column of matrix C, which is one of the factor matrices of CP decomposition.

[0127] Vector outer product operation.

[0128] : represents the square of the Frobenius norm, which is used to calculate the error between the original data and the reconstructed data through CP decomposition.

[0129] : Indicates that the features after CP decomposition are predicted through DNN (deep neural network). It is the output of DNN. The features input to DNN are the results of CP decomposition, which enter the neural network for training and prediction after Flatten (vectorization) operation.

[0130] f DNN : Represents the function representation of a deep neural network, and the output is obtained through forward propagation of multiple layers of neurons.

[0131] vec(·): represents the vectorization operation of the tensor, which converts the tensor result after CP decomposition into a vector so that it can be used as the input of the DNN.

[0132] y: represents the true target value (label), such as the yield per acre in agricultural data.

[0133] : is the mean square error (MSE) term used to measure the prediction error, and λ is the regularization parameter that controls the model's sensitivity to the prediction error. It determines the regularization strength of the model and prevents the model from overfitting.

[0134] Figure 1 It is a schematic diagram of the overall structure of the tensor-kernel neural network (TKNN) of the present invention, showing the specific workflow of the kernel mapping module, CP decomposition module and deep neural network module.

[0135] Figure 2 The figure is a schematic diagram of the high-dimensional feature extraction process after the input data is mapped by the kernel function. The process represents the high-dimensional feature extraction process after the input data is mapped by the kernel function. The kernel function is calculated through the Euclidean distance between the data, and the input data is mapped to a high-dimensional space to capture the complex relationships in the data.

[0136] Figure 3 Schematic diagram of the process of extracting low-rank tensor features after CP decomposition. Each step of this process has a clear function and role, showing how to extract low-rank features from high-dimensional tensor data through CP decomposition and provide a simplified feature representation for subsequent feature analysis or model training.

[0137] Figure 4 Schematic diagram of the process of training and predicting extracted features for the deep neural network module. Figure 4 The process shows how to train and predict the extracted features through the deep neural network module. The whole process includes feature data input, hidden layer step-by-step feature extraction, output layer generation of prediction results, loss calculation and weight update through back propagation to optimize the training effect of the model.

[0138] Example:

[0139] 1. Implementation background:

[0140] The tensor-kernel neural network (TKNN) model of the present invention is for large-scale data analysis and predictive modeling tasks in the fields of agriculture, finance, etc., and has important applications in nonlinear feature extraction and efficient prediction of multidimensional data. Taking potato growth data as an example, the tensor-kernel neural network (TKNN) model can realize the correlation analysis and efficient prediction of potato growth environment, yield and quality by combining Gaussian radial basis kernel function mapping, tensor decomposition (CP decomposition) and deep neural network (DNN). This model overcomes the defect that traditional linear models cannot effectively handle complex nonlinear relationships in high-dimensional data, can accurately predict potato yield, and optimize agricultural production strategies through analysis of growth conditions.

[0141] (II) Data preparation and feature representation:

[0142] When analyzing potato growth data, the tensor-kernel neural network (TKNN) model first integrates the actual data into tensor form for kernel mapping and tensor decomposition.

[0143] a. Growth environment data:

[0144] Regional characteristic data: including minimum temperature and maximum temperature, regional characteristic data is expressed as Among them, 6 is the number of regions, and 26 is the environmental characteristic variable of each region;

[0145] Irrigation data: includes irrigation amounts for four growing seasons, expressed as a tensor Corresponding to irrigation conditions in 4 different growing seasons;

[0146] Nutritional composition data: including 21 kinds of mineral test data, the nutritional composition data is expressed as Each column represents the amount of a specific mineral or nutrient.

[0147] b. Potato quality and yield data:

[0148] Nutritional composition data: including 15 nutrients of potatoes, such as protein, carbohydrates, etc., represented as a 6×15 tensor;

[0149] Yield data: includes yield data per acre, represented as a 6×1 tensor, as the prediction target.

[0150] c. Tensor representation:

[0151] Regional characteristic data, irrigation data, and nutrient composition data are expressed as: env ∈R 6×26 , and X nutr ∈R 6×21 , used to predict yield and optimize quality respectively.

[0152] (III) Model implementation steps:

[0153] a). Kernel function mapping:

[0154] In order to capture the complex nonlinear relationship between potato growth environment, nutritional components and yield, the present invention uses a Gaussian radial basis kernel function to map the input tensor to a high-dimensional feature space.

[0155] Kernel mapping formula:

[0156]

[0157] Among them, X represents the input tensor and σ is the width parameter of the kernel function. This step can capture the complex nonlinear relationship in the input data and provide support for subsequent tensor decomposition and feature extraction.

[0158] b). Tensor decomposition (CP decomposition):

[0159] The present invention uses CP decomposition to reduce the dimension of the tensor data after kernel mapping to extract the core features and remove redundant information. CP decomposition can approximate high-dimensional tensors as a combination of multiple low-rank tensors, thereby effectively reducing data complexity. CP decomposition formula:

[0160]

[0161] Among them, A (r) ,B (r) ,C (r) is a factor matrix of tensors, representing the pattern matrix of potato growth environment, nutrients and regional characteristics, and R is the rank number. CP decomposition can extract the key influencing factors of temperature, irrigation, mineral content and nutrients on yield.

[0162] c). Deep Neural Network (DNN) training and prediction:

[0163] The low-rank tensor after CP decomposition is input into the DNN model for training to achieve yield and quality prediction. DNN extracts features layer by layer through multiple hidden layers and generates the final prediction output.

[0164] d). Deep Neural Network (DNN) model structure:

[0165] The multi-layer perceptron structure (MLP) contains 128, 64, and 32 neurons in each layer, and the activation function is the ReLU function. The output layer uses the Sigmoid function or the Softmax function to predict yield and quality.

[0166] DNN calculation formula:

[0167] h (l) =f (l) (W (l) h (l-1) +b (l) )

[0168] Among them, W (l) is the weight matrix, b (l) is the bias, f (l) is the activation function. The final output prediction value is the yield and quality of potatoes.

[0169] e). Loss function and model optimization:

[0170] In order to ensure dual optimization of yield prediction and quality prediction, the tensor-kernel neural network (TKNN) model uses a weighted loss function to measure the prediction errors of yield and nutritional components respectively.

[0171] Total loss function:

[0172] L total =L recon +λ1L pred +λ2L nutr

[0173] Among them, L recon is the reconstruction error of tensor decomposition, L pred is the output forecast error, L nutr is the prediction error of nutrient composition. By adjusting the weight coefficients λ1 and λ2, the balance between yield and quality can be optimized.

[0174] Optimization method: The Adam optimization algorithm is used to train the model, calculate the gradient through back propagation, and update the weight parameters in the DNN model to gradually reduce the total loss function.

[0175] (IV): Correlation analysis and application scenarios:

[0176] By analyzing potato growth environment and nutrient data using a tensor-kernel neural network (TKNN) model, the present invention can effectively reveal the impact of environmental factors (such as temperature, irrigation volume, and mineral content) on yield and nutrient content. This model can not only accurately predict yield, but also provide quality optimization suggestions under different environmental conditions.

[0177] ①. Correlation analysis between growth environment and yield: The low-dimensional features extracted by kernel mapping and tensor decomposition can analyze the impact of different temperatures, irrigation and mineral content on yield, and help optimize production strategies.

[0178] ②. Balanced optimization of nutrients and yield: The present invention can help farmers find the best growing environment and irrigation strategy by simultaneously predicting the yield and nutrients of potatoes, thereby achieving a balance between high yield and high quality.

[0179] ③. Optimizing agricultural production: By analyzing data from different regions and growth conditions, the present invention can provide optimization strategies for agricultural production, especially in terms of irrigation amount, fertilization amount, temperature control, etc., to help improve potato yield and quality.

[0180] By extending the tensor-kernel neural network (TKNN) model and incorporating the potato nutrient content data and growth environment data into the analysis, not only can the accuracy of yield prediction be improved, but also the nutritional quality of potatoes can be optimized. This implementation method fully utilizes the advantages of the tensor-kernel neural network (TKNN) model in processing high-dimensional complex data, providing more comprehensive decision support for agricultural production.

[0181] (V): Implementation effect

[0182] By applying the potato growth environment and yield data, the efficient prediction ability of the tensor-kernel neural network (TKNN) model in agricultural big data analysis was verified. The model maps multidimensional features such as regional characteristics, irrigation data, mineral content, and nutrients to kernel functions, extracts key low-rank features through the tensor decomposition module, and combines the deep neural network (DNN) for nonlinear regression analysis, ultimately achieving high-precision prediction of potato yield per acre. The following data uses the relevant data of potatoes grown in different regions as an example for example research.

[0183] 1: Data source and data:

[0184] ①. Weather forecast big data platform (website: http: / / data.cma.cn / );

[0185] ②. Data collected by sensors installed on site;

[0186] ③. Average yield per mu of potato growers in central Inner Mongolia over the past three years;

[0187] ④.Data test report, testing unit: Beijing Institute of Optical Science and Technology.

[0188] a) Regional characteristic data:

[0189] Table 1 Growth environment temperature data of 6 regions

[0190]

[0191]

[0192] b) Irrigation data:

[0193] Table 2 Irrigation data

[0194]

[0195] c) Potato mineral content test data:

[0196] Table 3 Potassium and sodium content

[0197]

[0198] Table 4 Calcium and magnesium content

[0199]

[0200]

[0201] Table 5 Iron and zinc content

[0202]

[0203] Table 6 Phosphorus content

[0204] Region Name P1 P2 P3 Zone 1 1639.66 1663.13 1626.92 Zone 2 1649.03 1678.72 1607.76 Zone 3 1710.7 1738.33 1690.7 Zone 4 1735.22 1779.4 1701.1 Zone 5 1626.04 1668.59 1684.94 Zone 6 1617.99 1647.07 1688.15

[0205] Note: Three samples were provided for testing in the same area, and the test results are as follows:

[0206] K1: Potassium content of the first sample tested in the same area, in mg / kg

[0207] K2: Potassium content of the second sample tested in the same area, in mg / kg

[0208] K3: Potassium content of the third sample tested in the same area, in mg / kg.

[0209] Table 7 Correspondence table of sample test items

[0210]

[0211]

[0212] d) Data on nutritional content of potatoes:

[0213] Table 8 Vitamin C and cellulose content

[0214]

[0215] Table 9 Protein and starch content

[0216]

[0217] Table 10 Reducing sugar content

[0218]

[0219]

[0220] Note: Three samples were provided for testing in the same area, and the test results are as follows:

[0221] Vc1: Vitamin C content of the first sample tested in the same area, in mg / 100g.

[0222] Vc2: Vitamin C content of the second sample tested in the same area, in mg / 100g.

[0223] Vc3: Vitamin C content of the third sample tested in the same area, in mg / 100g.

[0224] Table 11 Correspondence table of sample test items

[0225] symbol name unit V Vitamin C mg / 100g F Cellulose g / 100g P protein g / 100g S starch g / 100g RS Reducing sugar g / 100g

[0226] Table 12 Correspondence table of sample test items

[0227]

[0228]

[0229] e) Yield per acre

[0230] Table 13 Yield per acre data

[0231]

[0232] 2: Implementation of the key steps of the Tensor-Kernel Neural Network (TKNN) algorithm:

[0233]

[0234] a) Kernel Mapping:

[0235] The second part of the code, rbf_kernel function, implements kernel function mapping, which maps the input multi-dimensional feature data (including regional characteristics, irrigation data, mineral content, nutrient composition, etc.) to RBF kernel function to generate a high-dimensional nonlinear feature space.

[0236] This part corresponds to the RBF Kernel Mapping module in the Tensor-Kernel Neural Network (TKNN), which captures complex nonlinear relationships.

[0237] b) Feature splicing and standardization:

[0238] The np.hstack function stitches together all the data from different sources (regional features region_data, irrigation data irrigation_data, mineral content mineral_data, and nutrient composition nutrition_data) to form a complete feature matrix.

[0239] After that, StandardScaler() is used to standardize the data to ensure that the data distribution input to the neural network is consistent.

[0240] This part is related to data preprocessing and feature processing after tensor decomposition.

[0241] c) Tensor Decomposition:

[0242] Although there is no code that directly implements tensor decomposition (such as CP decomposition or PARAFAC decomposition) in the screenshot, the use of StandardScaler to normalize the data can be understood as standardizing the data after tensor decomposition so that the neural network can better process the input data.

[0243] In tensor-kernel neural network (TKNN), tensor decomposition is used to extract core low-rank features and use them as data representation for subsequent DNN input.

[0244] d) Deep Neural Network (DNN) Module:

[0245] Starting from part #4 in the code, a fully connected neural network consisting of 3 hidden layers is constructed. The activation function of each layer is relu, and the last layer is a linear activation function, which is used to predict the output continuous value (potato yield per acre).

[0246] This corresponds to the deep neural network module in the tensor-kernel neural network (TKNN), which is responsible for training low-rank features and performing yield prediction.

[0247] e) Model compilation and training:

[0248] Sections #5 and #6 of the code show how to optimize a neural network using the Adam optimizer and the mean squared error (MSE) as the loss function.

[0249] This corresponds to the optimization process in the Tensor Kernel Neural Network (TKNN), where gradient descent and the Adam algorithm are used to update the network parameters to minimize the prediction error.

[0250] In summary, the code in the screenshot mainly implements the process of kernel mapping, feature processing and deep neural network training, reflecting the core steps of tensor kernel neural network (TKNN).

[0251] 3: Implementation effect of efficient potato yield prediction based on tensor-kernel neural network (TKNN) model:

[0252] The tensor-kernel neural network (TKNN) model of the present invention is combined with potato growth data to carry out a prediction experiment of yield per mu. The experimental results show that the tensor-kernel neural network (TKNN) model has extremely high prediction accuracy and fast convergence speed.

[0253]

[0254] (I) Efficient convergence performance:

[0255] like Figure 5 As shown, Figure 5 middle,

[0256]

[0257] In the early stage of training, the model loss function value dropped rapidly, indicating that the model can converge to a lower loss value in fewer training cycles, greatly reducing the model training time. After 500 training cycles, the model loss value almost stabilized, proving the high efficiency of the model.

[0258] (II) Accurate prediction results:

[0259] The final prediction results of the tensor-kernel neural network (TKNN) for potato yield per acre show that the predicted value is highly consistent with the true value, and the mean square error (MSE) is 4.14911185941909e-09, which is almost negligible. This shows that the tensor-kernel neural network (TKNN) model can effectively capture the complex nonlinear relationship between the growth environment and potato yield, and provide high-precision prediction results.

[0260] (III) Applicability and scalability:

[0261] Through kernel function mapping and tensor decomposition, the tensor-kernel neural network (TKNN) model of the present invention can efficiently process multidimensional feature data and successfully establish a close relationship between regional characteristics, irrigation data, mineral content, nutrients and potato yield. The model is suitable for agricultural data analysis scenarios and can provide an accurate and reliable basis for crop yield prediction and optimization.

[0262] In summary, it shows excellent prediction ability and fast convergence performance in practical applications, and can significantly improve the efficiency of data analysis in agricultural production.

[0263] (1): Correlation analysis between growth environment and potato yield:

[0264] By using the tensor-kernel neural network (TKNN) model, kernel mapping is performed on multi-dimensional features such as regional characteristics, irrigation data, mineral content and nutritional components of potatoes, low-rank tensor features are extracted by combining CP decomposition, and model training and prediction are performed through deep neural networks. The tensor-kernel neural network (TKNN) effectively captures the nonlinear correlation between complex growth environment characteristics and potato yield, achieving efficient and accurate yield prediction.

[0265] a) Program code:

[0266]

[0267] b) Heat map of correlation analysis results, such as Figure 6 As shown:

[0268] c) Correlation analysis between growth environment and yield:

[0269] a. Feature construction and kernel mapping:

[0270] In the tensor-kernel neural network (TKNN), regional characteristics, irrigation data, mineral content, and nutrient content are spliced ​​into a multidimensional feature tensor, and the RBF kernel function is used for kernel mapping, ensuring that the input data can capture complex nonlinear relationships in high-dimensional space. The program code implements kernel mapping of multidimensional data, and maps regional characteristics, irrigation, minerals, and nutrients to high-dimensional feature space through the RBF kernel function, thereby providing richer feature interaction information. This step provides refined input features for the yield prediction model;

[0271] b. Low-rank tensor decomposition: The data after kernel mapping uses CP decomposition to extract low-rank tensor features, which further reduces the data dimension while maintaining important feature information and reducing the impact of noise on the model. Through this process, the tensor-kernel neural network (TKNN) model can extract key low-rank tensor features from high-dimensional features for subsequent training and prediction of deep neural network models;

[0272] c. Deep neural network training and prediction: During the training process of the tensor-kernel neural network (TKNN), the deep neural network (DNN) is trained on the extracted features through forward propagation, back propagation and Adam optimization algorithm. The mean square error (MSE) between the final predicted value and the actual potato yield data is extremely small, indicating that the prediction accuracy of the model is extremely high;

[0273] d. Correlation analysis between growth environment and yield: After model training, the correlation heat map generated by the program was used to analyze the correlation between growth environment characteristics and potato yield. The heat map clearly shows the correlation between various characteristics and potato yield, among which the correlation between irrigation data and mineral content such as potassium (K), calcium (Ca), zinc (Zn) and other elements is high, especially in some areas, the increase in mineral content and the increase in yield show a positive correlation;

[0274] e. Result verification: Through correlation analysis, the tensor-kernel neural network (TKNN) can help determine which factors have the greatest impact on potato yield under different growth conditions. The analysis results show that the content of certain specific minerals such as potassium (K) and calcium (Ca) has a high positive correlation with yield, indicating that optimizing these factors can help increase potato yield. The high correlation between irrigation data and yield also further verifies the effective capture of environmental conditions by the tensor-kernel neural network (TKNN) model;

[0275] f. Conclusion of heat map analysis: Figure 6It can be observed from the heat map that some environmental characteristics and mineral elements have a strong positive correlation with yield, such as potassium (K) and calcium (Ca). This indicates that higher potato yields can be obtained under the conditions of optimizing these elements. In addition, some characteristics such as fat content in nutrients have little effect on yield or are negatively correlated, so optimization adjustments should be made based on this information in yield prediction.

[0276] (VII): Summary of implementation effects:

[0277] In summary, the correlation analysis between the growth environment and potato yield based on the tensor-kernel neural network (TKNN) model clearly shows the contribution of various growth environment factors (regional characteristics, irrigation, minerals and nutrients) to yield. Through the prediction of deep neural networks, the model performs well in practical applications with high prediction accuracy, which can effectively guide agricultural production, optimize planting plans and increase crop yields.

[0278] (VIII): The innovation of the present invention is mainly reflected in the following aspects:

[0279] The innovativeness of the tensor-kernel neural network (TKNN) model for efficient predictive modeling can be summarized as follows in conjunction with the potato agriculture and finance fields:

[0280] (1) Combining kernel mapping and tensor decomposition of multidimensional data: Improving the ability to process complex environment data:

[0281] In potato agriculture: Potato growth environment data includes multi-dimensional heterogeneous data such as regional characteristics, irrigation data, mineral content, and nutrient composition. The tensor-kernel neural network (TKNN) model maps these complex environmental features to high-dimensional space through kernel mapping to better capture nonlinear relationships, and combines CP tensor decomposition to extract low-rank tensor features from high-dimensional features. This innovation enables the model to maintain efficient calculation and reduce dimensions when facing complex and multi-dimensional growth environments, while retaining key influencing factors.

[0282] In the financial field: Similarly, financial market data usually contains multiple dimensions such as trading volume, price fluctuations, interest rates, economic indicators, etc. Through kernel mapping and tensor decomposition, the tensor-kernel neural network (TKNN) model can efficiently reduce the dimension of multi-dimensional financial features and extract low-rank features for financial market prediction and risk management, thereby improving the accuracy of prediction. (2) Combination of deep neural networks and tensor features: Accurate prediction and feature interaction analysis:

[0283] In potato agriculture: Deep neural networks can make full use of low-rank features obtained through tensor decomposition and further learn the complex interactions between features, thereby achieving accurate prediction of potato yields. This innovative combination enables the model to not only provide accurate yield predictions, but also learn the contribution of various growth factors through the back-propagation algorithm, providing data support for optimizing crop management such as irrigation and fertilization.

[0284] In the financial field: Deep neural networks combined with tensor-decomposed financial market feature data can help identify complex market fluctuation patterns, thereby better performing asset allocation, risk prediction, and investment decisions. In addition, the model can also help decision makers optimize investment portfolios or reduce market risks by analyzing the interactions between different financial indicators.

[0285] (3) Correlation analysis between complex environmental factors and output (or market):

[0286] In potato agriculture: Through the tensor-kernel neural network (TKNN), the correlation between multidimensional environmental factors such as regional characteristics, irrigation data, mineral content, and nutrient composition and potato yield can be deeply analyzed. The generation of heat maps shows the degree of influence of various environmental factors on yield, which provides a scientific basis for agricultural planting management and helps farmers or agricultural experts optimize planting strategies according to different environmental conditions to improve potato yield and quality.

[0287] In the financial field: Tensor-kernel neural network (TKNN) can help analyze the correlation between different indicators in the financial market and reveal the relationship between market behavior and external economic factors. This is of great significance for financial investment decision-making, risk control and market forecasting, and can provide investors with more accurate market information and reduce investment risks.

[0288] (4) Efficient prediction and modeling capabilities:

[0289] In potato agriculture: Tensor-kernel neural network (TKNN) can efficiently process multi-dimensional agricultural environmental data and generate accurate yield forecasts in a short time through the combination of kernel mapping, tensor decomposition and deep neural network. This allows farmers to quickly adjust management strategies according to environmental changes, thereby improving agricultural production efficiency.

[0290] In the financial field: Tensor-kernel neural network (TKNN) can quickly process massive amounts of financial data and provide traders and investors with real-time market forecasts and risk assessments. Especially in high-frequency trading or real-time market analysis, the efficiency and predictive power of the tensor-kernel neural network (TKNN) model can help financial institutions respond faster and gain a competitive advantage.

[0291] (5) Strong fusion and scalability of multiple data sources:

[0292] In potato agriculture: Tensor-kernel neural network (TKNN) can integrate multiple data sources, such as climate data, soil nutrients, irrigation information, etc., to form a comprehensive growth environment analysis framework. This innovation enables the model to handle multi-dimensional heterogeneous data sources and provide comprehensive prediction and decision support for the agricultural field.

[0293] In the financial field: Tensor-kernel neural network (TKNN) can also integrate financial data from different markets, such as stock market, futures market, bond market and other data sources, and conduct joint analysis and prediction on this basis. This multi-source data fusion makes the model highly scalable and can be applied in different financial fields.

[0294] (6) The universality and cross-domain applicability of the model:

[0295] In potato agriculture: Tensor-kernel neural network (TKNN) can not only be applied to potato yield prediction, but also be extended to yield prediction and growth management of other crops. Its kernel mapping and tensor decomposition technology can be applied to various agricultural production scenarios and has wide applicability.

[0296] In the financial field: The versatility of the tensor-kernel neural network (TKNN) is reflected in its ability to handle multidimensional data problems in the financial market, including asset price prediction, risk management, investment strategy optimization, etc. Its multidimensional data processing capabilities and complex feature learning capabilities can well meet the needs in the financial market.

[0297] The innovation of the tensor-kernel neural network (TKNN) for efficient prediction modeling is reflected in its ability to effectively integrate kernel mapping, tensor decomposition and deep neural network, and is particularly suitable for processing and predicting multidimensional complex data. Whether in potato agriculture, optimizing agricultural production through accurate yield prediction and environmental feature correlation analysis, or in the financial field, helping financial decision makers better predict market behavior and assess risks, the tensor-kernel neural network (TKNN) has strong innovation and broad application prospects.

Claims

1. Tensor-kernel neural network for efficient predictive modeling, characterized by include: Kernel function mapping module, used to perform nonlinear kernel mapping of input data to obtain high-dimensional data; Tensor decomposition module, which reconstructs high-dimensional data into low-rank and extracts low-dimensional features; Deep neural network, which trains and predicts the extracted low-dimensional features of the data and outputs the prediction results; The loss function effectively weighs the reconstruction error and prediction error during model training.

2. The tensor-kernel neural network for efficient predictive modeling according to claim 1, characterized in that: The kernel function mapping module performs nonlinear mapping on the input data through a Gaussian radial basis kernel function (RBF Kernel) to obtain a high-dimensional feature Φ(X), which is expressed as follows: Among them, ||XX′|| 2 is the Euclidean distance between the input data and the center vector; X represents the original input data vector; X′ represents the center vector of the kernel function; σ is the bandwidth parameter of the kernel function, which controls the amplitude of the kernel function and its distribution mapped to the high-dimensional space.

3. The tensor-kernel neural network for efficient predictive modeling according to claim 2, characterized in that: The bandwidth parameter σ of the kernel function is adaptively adjusted according to the distribution of the input data, and the calculation formula is: Where μ is the mean of the input data set, n is the number of data points, and X i is the sample point of the input data.

4. The tensor-kernel neural network for efficient predictive modeling according to claim 1, characterized in that: The tensor decomposition module performs CP decomposition on the high-dimensional feature data obtained by nonlinear mapping, and converts the high-dimensional tensor X∈R n1×n2×n3 Expressed as a decomposition form of a low-rank tensor: Among them, Y represents the third-order tensor data after mapping; Factor Matrix A (r) , B (r) , C (r) Respectively represent the projection of the tensor on each dimension, indicating the characteristics of the data in different dimensions; R is the tensor decomposition rank, which indicates the number of features retained in the low-rank approximation; Represents the outer product operation of vectors.

5. The tensor-kernel neural network for efficient predictive modeling according to claim 4, characterized in that: The rank R of the CP decomposition of the tensor decomposition module is adaptively set according to the dimension and complexity of the input data and is calculated by the following formula: R=min(n1,n2,n3)×α Among them, n1, n2, n3 are the three dimensions of the tensor, and α is a hyperparameter that controls the decomposition accuracy.

6. The tensor-kernel neural network for efficient predictive modeling according to claim 1, characterized in that: The deep neural network trains and predicts the decomposed low-dimensional features, and the input features are the expanded low-dimensional tensors Use deep neural network to output prediction results; in, represents the output of the deep neural network; f DNN represents the forward propagation process of the deep neural network; vec(·) represents the vectorization operation of the tensor, which converts the tensor result after CP decomposition into a vector so as to serve as the input of the deep neural network.

7. The tensor-kernel neural network for efficient predictive modeling according to claim 1, characterized in that: The deep neural network trains and predicts low-rank features. The deep neural network adopts a multi-layer perceptron (MLP) structure, and the input is the low-dimensional features obtained by CP decomposition; each layer of the deep neural network is calculated through linear transformation and nonlinear activation function, and its mathematical expression is as follows: For layer l: h (l) =f (l) (W (l) h (l-1) +b (l) ) Where: h (l) represents the output of the lth layer; W (l) represents the weight matrix of the lth layer; b (l) represents the bias vector of the lth layer; f (l) represents the activation function of the lth layer; Flatten the low-dimensional tensor after tensor decomposition into a vector for input into a deep neural network; Finally, the output layer of the deep neural network undergoes linear transformation and activation function to output the prediction result. Where: W (out) 、b (out) ) represent the weight and bias of the output layer respectively; f (out) represents the activation function of the output layer.

8. The tensor-kernel neural network for efficient predictive modeling according to claim 1, characterized in that: The loss function consists of two parts: reconstruction error L recon and the prediction error L pred ; Where: reconstruction error L recon :The difference between the data Φ(X) mapped by Gaussian radial basis kernel function (RBF Kernel) and the CP decomposition result is measured by Frobenius norm; Among them, ||·|| T is the Frobenius norm, which represents the sum of squares of reconstruction errors; Prediction error L pred :Measure the model prediction value through the mean square error (MSE) The difference between the true value y; Among them, λ is the regularization parameter, which is used to balance the influence between reconstruction error and prediction error; The model is optimized by minimizing the following combined loss function: Among them, L total is the total loss function.

9. A modeling method of a tensor-kernel neural network according to any one of claims 1 to 8, characterized in that: Combined with the nonlinear kernel mapping of Gaussian radial basis kernel function, the nonlinear input data is mapped to the high-dimensional feature space, and then the high-dimensional data is reconstructed into low-rank through the CP decomposition method; finally, the extracted low-dimensional features are trained and predicted through a deep neural network.

10. A tensor-kernel neural network according to any one of claims 1 to 8, characterized in that: Used in potato farming or in financial data analysis.

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