Unbalanced data classification method based on optimization cost-sensitive weighted width network

Abstract

The application discloses an unbalanced data classification method based on an optimized cost-sensitive weighted width network, and comprises the following steps: obtaining an unbalanced classification data set and preprocessing; constructing an optimized cost-sensitive weighted width network, splicing feature nodes and enhanced nodes into a hidden layer after extraction; calculating a weighted matrix and a cost matrix based on a category sample distribution, and obtaining a cost information vector; taking minimization as an objective, adopting a backtracking search optimization algorithm to globally optimize the cost information vector, obtaining an optimal cost information vector and solving output weights, and obtaining a trained network; and classifying to-be-classified data by using the trained network. The application integrates a cost-sensitive weighting and a cost optimization framework into a width learning system, automatically searches an optimal cost information vector, significantly improves the recognition accuracy and generalization ability of a minority class, and is suitable for unbalanced category scenes such as fraud detection, medical diagnosis and fault detection.

Description

Technical Field

[0001] This invention relates to the technical field of imbalanced data classification and machine learning, and in particular to an imbalanced data classification method based on optimizing a cost-sensitive weighted width network. Background Technology

[0002] In the field of machine learning, class imbalance learning has always been a recognized challenge. In real-world problems, class distributions are often imbalanced, with the majority class dominating the dataset with a large number of samples, while the minority class has relatively few samples. This imbalance causes models to prioritize the majority class during training, often neglecting the minority class. However, in many practical applications, the minority class often contains more critical and valuable information. For example, in fraud detection, the minority class corresponds to fraudulent transactions; in medical diagnosis, the minority class may correspond to a rare but fatal disease; and in fault detection, the minority class may indicate potential equipment failure. Therefore, accurately identifying minority class data is crucial for improving model performance and practical application effectiveness.

[0003] Broad Learning Systems (BLS) have been widely applied in many fields due to their excellent classification performance, solid theoretical foundation, and efficient training speed. The main idea is to extract features from the input data to generate feature nodes, then map these feature nodes to generate augmentation nodes to extract nonlinear attributes, and finally connect the feature nodes and augmentation nodes to the output layer, solving for the optimal solution through a pseudo-inverse process. This flat network structure allows BLS to avoid the complex backpropagation process of deep networks, thus achieving fast training speed. However, within the standard framework of BLS, there is a fundamental assumption: the loss when each class is misclassified is considered equal. When the frequency of each class in the dataset is similar, this assumption holds and helps the algorithm provide better results; however, in imbalanced data scenarios, this assumption leads to insufficient attention to the minority class, resulting in a significant decrease in classification performance.

[0004] For imbalanced classification problems, existing algorithm-based improvements mainly involve constructing weight matrices and employing cost-sensitive strategies. For example, Weighted BLS (WBLS) provides a weighting scheme based on the number of samples for training samples of different classes to enhance the performance of the minority class; Class-Specific BLS (DKCSBLS) improves the model's ability to identify the minority class by assigning a unique penalty scheme to each class. However, these methods are usually based on empirical costs, focusing only on the class imbalance ratio while ignoring the individual characteristics of the data distribution. When the data distribution is uncertain, the relationship between the weighting scheme and generalization performance is unclear, increasing the possibility of overfitting. Furthermore, existing cost-sensitive learning methods may use a fixed cost matrix to reduce the overall loss, but in many cases, the optimal loss for misclassification between classes is unknown to the user, making it impossible to adaptively obtain the optimal weights from the data. Summary of the Invention

[0005] The purpose of this invention is to address the problems of uneven class distribution, difficulty in obtaining the loss for optimal misclassification, and unstable generalization performance of empirical weighting schemes in imbalanced data classification scenarios. It proposes an imbalanced data classification method based on an optimized cost-sensitive weighted width network, which can effectively solve the problem of insufficient minority class recognition accuracy caused by the equal weighting of misclassification costs, as well as the overfitting problem caused by relying on fixed empirical weighting. This effectively improves the recognition ability of minority classes and the generalization performance of the network.

[0006] To achieve the above objectives, the technical solution provided by this invention is: an imbalanced data classification method based on an optimized cost-sensitive weighted width network. This method achieves accurate classification of imbalanced data based on an optimized cost-sensitive weighted width network. The optimized cost-sensitive weighted width network incorporates a cost optimization framework into a weighted width learning system and improves the original weighting mechanism and output layer solution. The cost optimization framework aims to minimize... The optimization objective is to use a backtracking search optimization algorithm to globally optimize the cost information vector. The improvement to the weighting mechanism is to introduce an off-diagonal cost matrix on top of the original diagonal weighting matrix. Both matrices jointly determine the cost information vector, assigning differentiated misclassification penalty weights to each sample, replacing the original experience-based fixed weighting method. The improvement to the output layer solution is to embed the optimal cost information vector into the objective function to form a cost-sensitive regularized pseudo-inverse solution, replacing the original equally weighted pseudo-inverse solution method, thus giving minority class sample errors a greater penalty weight.

[0007] The specific implementation of this method includes the following steps:

[0008] Step 1: Obtain the imbalanced classification dataset and preprocess it to obtain clean feature data and class labels;

[0009] Step 2: The preprocessed feature data and class labels are fed into an optimized cost-sensitive weighted wide network for training. During training, the feature data is first transformed linearly with random weights and biases, and then mapped to feature nodes through an activation function. The feature nodes are then transformed linearly with random weights and biases, and then mapped to augmentation nodes through a non-linear activation function. The feature nodes and augmentation nodes are concatenated to form a hidden layer. A diagonal weighted matrix is ​​calculated based on the number of samples in each category. An off-diagonal cost matrix is ​​introduced to quantify the loss when each sample is misclassified to a different category. The cost information vector is represented as the vector value obtained by multiplying the diagonal weighted matrix and the off-diagonal cost matrix and summing them row by row. The goal is to minimize... The optimal cost information vector is obtained by using a backtracking search optimization algorithm to perform global optimization within the preset upper and lower bound constraints. The hidden layer and the optimal cost information vector are then embedded into the constrained output layer objective function. The cost-sensitive regularized pseudo-inverse solution is obtained by taking the derivative of the Lagrange multiplier method and KKT conditions, and the optimal output weight is obtained. Finally, the trained optimized cost-sensitive weighted width network is obtained.

[0010] Step 3: In the application stage, the data to be classified is input into the trained optimized cost-sensitive weighted wide network. After feature mapping and enhancement mapping are concatenated into a hidden layer, the classification prediction result is obtained by multiplying it with the optimal output weight.

[0011] Furthermore, in step 1, the preprocessing includes removing empty features, filling missing values, discretization, normalizing the feature data, and one-hot encoding the category labels.

[0012] Furthermore, in step 2, the process of concatenating the feature nodes and enhancement nodes to form the hidden layer is as follows: given input feature data... , Indicates size is A real matrix, where For the number of training samples, To input the feature dimension, use the formula Feature mapping generation Group feature nodes , , The number of feature node groups is denoted as , where and They are randomly generated respectively The weight matrix and bias matrix, For the feature layer activation function, Group feature nodes are concatenated as , Indicates by A feature node group consisting of a set of feature nodes; As input, through the formula Enhanced mapping generation Group Enhancement Nodes , , To increase the number of node groups, among which and Randomly generated The weight matrix and bias matrix, To enhance the nonlinear activation function of the layer, Group enhancement node splicing as , Indicates by A group of enhanced nodes; the final hidden layer is represented as .

[0013] Furthermore, in step 2, the diagonal weighting matrix is: Matrix, denoted as Its diagonal elements Calculated based on the number of samples in each category:

[0014] ;

[0015] in , Indicates the first The total number of samples belonging to the category of each sample. This represents the average number of samples across all categories;

[0016] The off-diagonal cost matrix is: Matrix, denoted as , The total number of categories, its elements Indicates the first The sample was misclassified as the first The loss during class, where , ,element A value of 0 indicates correct classification with no loss; the values ​​of other non-zero elements are generated through randomization; the cost information vector is labeled as... , its first Each component Depend on Calculated.

[0017] Furthermore, in step 2, to minimize The specific expression of the optimization objective is as follows:

[0018] ;

[0019] In the formula, This is the optimal cost information vector. Cost information vector The One portion, Indicates the sample number. This represents the variable that minimizes the objective function. The value of , The area under the ROC curve. For classification loss function, For the first Sample The label vector, and These are the preset lower and upper bounds of the cost information vector, respectively. To optimize the output function of the cost-sensitive weighted width network, it is obtained through the following process: for the input samples , by the final hidden layer Take the first The row obtains its corresponding hidden layer. , sample Corresponding hidden layer With cost information vector Corresponding output weights Multiplying them yields the network output, namely:

[0020] ;

[0021] in The result is obtained by solving the cost-sensitive regularized pseudoinverse:

[0022] ;

[0023] In the formula, For regularization parameters, For cost information vector The components form a diagonal matrix with diagonal elements. For the final hidden layer, It is the identity matrix. The label matrix is ​​formed by stacking the one-hot encoded label vectors of all training samples.

[0024] Furthermore, in step 2, the backtracking search optimization algorithm includes the following:

[0025] The cost information vector to be optimized Encoding as a population The individual within, the problem dimension is The population size is Individual serial number Dimension ;

[0026] The initial population is randomly generated within preset upper and lower boundaries according to a uniform distribution. ,in Indicates the first The first individual dimension, and The first The lower and upper bounds of a dimension, Indicates uniform distribution, and through Calculate each individual fitness value ,in The objective function to be minimized is the function corresponding to the individual. Value; after primary selection, recombination, and secondary selection iterations until the termination condition is met, the optimal individual is output, i.e., the optimal cost information vector. .

[0027] Furthermore, in step 2, the hidden layer and the optimal cost information vector are jointly embedded into the constrained output layer objective function, expressed as:

[0028] ;

[0029] In the formula, This represents the output weight matrix. For regularization parameters, For the first Sample The error vector, It is a diagonal matrix composed of the optimal cost information vectors. For the sample The label vector, For the sample Hidden layers generated by concatenating feature mapping and enhancement mapping;

[0030] The cost-sensitive regularized pseudo-inverse solution is obtained by using the Lagrange multiplier method and KKT conditions to differentiate the above objective function, thus obtaining the optimal output weights:

[0031] ;

[0032] In the formula, The optimal cost information vector The corresponding optimal output weight matrix, It is the identity matrix. To obtain the hidden layer, The label matrix is ​​formed by stacking the one-hot encoded label vectors of all training samples.

[0033] Further, in step 3, the classification prediction result is labeled as Through formula The calculation yielded, where The final hidden layer is formed by concatenating the data to be classified after feature mapping and augmentation mapping. To obtain the optimal output weights, take... The category corresponding to the dimension of the maximum value in each row is used as the final classification result.

[0034] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0035] 1. This invention introduces an off-diagonal cost matrix into the width learning system, which can distinguish the cost differences of different types of misclassification. Combined with a diagonal weighted matrix based on the number of class samples, a cost information vector that comprehensively reflects the importance of samples and the severity of misclassification is generated, so that the network pays more attention to minority class samples during training, effectively solving the problem of uneven class distribution.

[0036] 2. This invention is constructed to minimize The cost optimization framework for the objective directly optimizes the capabilities directly related to minority class identification. Compared to traditional methods that only optimize classification accuracy loss, this metric can more effectively guide the network to focus on minority class classification performance and improve generalization ability in imbalanced scenarios.

[0037] 3. This invention employs a backtracking search optimization algorithm to globally optimize the cost information vector, automatically searching for the optimal cost information vector within preset upper and lower bounds. This avoids the problem of unstable generalization performance of traditional experience-weighted methods when the data distribution is unknown, and achieves adaptive, non-empirical cost-sensitive learning.

[0038] 4. This invention maintains the efficient training characteristics of the width learning system, which does not require backpropagation and only solves the optimal solution through pseudo-inverse. While introducing cost-sensitive weighting and cost optimization framework, it does not significantly increase the training time overhead, making it suitable for practical application scenarios with real-time requirements. Attached Figure Description

[0039] Figure 1 This is a flowchart illustrating the method of the present invention.

[0040] Figure 2 The overall architecture diagram for optimizing cost-sensitive weighted width networks. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0042] like Figure 1 and Figure 2As shown, this embodiment discloses an imbalanced data classification method based on an optimized cost-sensitive weighted width network. This method achieves accurate classification of imbalanced data based on the optimized cost-sensitive weighted width network. The optimized cost-sensitive weighted width network incorporates a cost optimization framework into the weighted width learning system and improves the original weighting mechanism and output layer solution. The cost optimization framework aims to minimize... The optimization objective is to use a backtracking search optimization algorithm to globally optimize the cost information vector. The improvement to the weighting mechanism is to introduce an off-diagonal cost matrix on top of the original diagonal weighting matrix. Both matrices jointly determine the cost information vector, assigning differentiated misclassification penalty weights to each sample, replacing the original experience-based fixed weighting method. The improvement to the output layer solution is to embed the optimal cost information vector into the objective function to form a cost-sensitive regularized pseudo-inverse solution, replacing the original equally weighted pseudo-inverse solution method, thus giving minority class sample errors a greater penalty weight.

[0043] The specific implementation of this method includes the following steps:

[0044] Step 1: Obtain the imbalanced classification dataset and preprocess it to obtain clean feature data and class labels, as follows:

[0045] The imbalanced classification dataset is processed by removing empty features and filling missing values; the feature data is normalized; and the class labels are one-hot encoded. The preprocessed dataset is denoted as . ,in Indicates the sample number. Indicates the first The feature vector of each sample has a feature dimension of . , Indicates the first The label vector of each sample, with dimension . , indicating shared ownership Categories Given the total number of samples, the feature data is composed of the feature vectors and label vectors of all samples obtained after preprocessing. and category labels , This is a matrix where the rows represent the feature vectors of each sample, and the columns represent the feature dimensions of the samples. It is a matrix composed of stacked one-hot encoded label vectors of all training samples.

[0046] Step 2: The preprocessed feature data and class labels are fed into an optimized cost-sensitive weighted wide network for training. During training, the feature data is first transformed linearly with random weights and biases, and then mapped to feature nodes through an activation function. The feature nodes are then transformed linearly with random weights and biases, and then mapped to augmentation nodes through a non-linear activation function. The feature nodes and augmentation nodes are concatenated to form a hidden layer. A diagonal weighted matrix is ​​calculated based on the number of samples in each category. An off-diagonal cost matrix is ​​introduced to quantify the loss when each sample is misclassified to a different category. The cost information vector is represented as the vector value obtained by multiplying the diagonal weighted matrix and the off-diagonal cost matrix and summing them row by row. The goal is to minimize... With the target value as the optimization objective, a backtracking search optimization algorithm is used to globally optimize the cost information vector within preset upper and lower bound constraints to obtain the optimal cost information vector. The hidden layer and the optimal cost information vector are then jointly embedded into the constrained output layer objective function. The cost-sensitive regularized pseudo-inverse solution is obtained through Lagrange multiplier method and KKT conditional differentiation to obtain the optimal output weights, ultimately resulting in a trained optimized cost-sensitive weighted width network. The details are as follows:

[0047] Given input feature data , Indicates size is A real matrix, where For the number of training samples, To input the feature dimension, use the formula Feature mapping generation Group feature nodes , , The number of feature node groups is denoted as , where and They are randomly generated respectively The weight matrix and bias matrix, For the feature layer activation function, Group feature nodes are concatenated as , Indicates by A feature node group consisting of a set of feature nodes; As input, through the formula Enhanced mapping generation Group Enhancement Nodes , , To increase the number of node groups, among which and Randomly generated The weight matrix and bias matrix, To enhance the nonlinear activation function of the layer, Group enhancement node splicing as , Indicates by A group of enhanced nodes; the final hidden layer is represented as ;

[0048] The specific steps for constructing a diagonal weighted matrix and an off-diagonal cost matrix, and calculating the cost information vector, are as follows: First, construct the diagonal weighted matrix. , for A matrix whose diagonal elements Calculated based on the number of samples in each category:

[0049] ;

[0050] In the formula, , Indicates the first The total number of samples belonging to the category of each sample. This represents the average number of samples across all categories;

[0051] Then construct the off-diagonal cost matrix. , for matrix, For the sample size, The total number of categories, its elements Indicates the first The sample was misclassified as the first The loss during class time , ,element A value of 0 indicates correct classification with no loss; the values ​​of the other non-zero elements are generated through randomization; finally, the cost information vector... The Each component Depend on The calculation yielded, where and As before, these represent the sample number and category number.

[0052] The cost information vector is optimized using the backtracking search (BSA) algorithm. To perform global optimization, the specific steps are as follows: explicitly define minimizing... The value is the optimization objective, specifically expressed as:

[0053] ;

[0054] In the formula, This is the optimal cost information vector. Cost information vector The One portion, Indicates the sample number. This represents the variable that minimizes the objective function. The value of , The area under the ROC curve. For classification loss function, For the first Sample The label vector, and These are the preset lower and upper bounds of the cost information vector, respectively. To optimize the output function of the cost-sensitive weighted width network, it is obtained through the following process: for the input samples , by the final hidden layer Take the first The row obtains its corresponding hidden layer. , sample Corresponding hidden layer With cost information vector Corresponding output weights Multiplying them yields the network output, namely:

[0055] ;

[0056] in The result is obtained by solving the cost-sensitive regularized pseudoinverse:

[0057] ;

[0058] In the formula, For regularization parameters, For cost information vector The components form a diagonal matrix with diagonal elements. For the final hidden layer, It is the identity matrix. The category labels are obtained from the preprocessing in step 1.

[0059] Solving the above objective using BSA can be divided into four stages:

[0060] During the initialization phase, the cost information vector to be optimized is... Encoding as individuals within a population, problem dimension , The sample size is [number], and the population size is [number]. Individual serial number Dimension The initial population is randomly generated within a preset upper and lower bound, evenly distributed. ,satisfy ,in Indicates population The Middle The first individual dimension, and The first The lower and upper bounds of a dimension, Indicates uniform distribution, and through calculate The Middle individual fitness value ,in The objective function to be minimized is the function corresponding to the individual. value;

[0061] During the main selection phase, the historical population is regenerated in a uniform distribution. ,satisfy ,in Indicates population The Middle The first individual Dimension. By comparing two that follow a uniform distribution random numbers and ,when season The historical population was then randomly shuffled to obtain a shuffled historical population. ,in This is a random permutation function that randomly shuffles and rearranges each row of the input matrix before outputting the result.

[0062] During the reorganization phase, a binary mapping matrix is ​​constructed. , It is composed of 0 or 1. OK Column matrices are used to selectively control the direction of mutation. This is achieved through formulas. A new population is generated, in which Indicates a new population. It indicates that it follows a standard normal distribution. random scalar, This represents the dot product. This mutation operation uses the difference between the historical and current populations to generate search directions, enhancing the algorithm's global exploration capability. For new populations exceeding the upper and lower bounds... Individual values ​​are corrected according to the boundary correction rule, as shown in the following formula:

[0063] ;

[0064] In the formula, Indicates the new population after correction No. The first individual dimension, This indicates the original new population No. The first individual dimension, , and All follow a uniform distribution The generated random numbers, after correction, form a new population. Other elements that do not exceed the upper and lower bounds and Consistent.

[0065] In the next selection phase, a greedy strategy is used to compare the fitness of individuals in the new population with that of individuals in the original population, retaining individuals with better fitness for the next generation:

[0066] ;

[0067] In the formula, To select a better population, For the revised new population The Individual, This is an indicator function that takes the value 1 when the condition is true and 0 otherwise. for The Middle The fitness value of each individual. A better population is obtained after selection. Then, calculate The fitness values ​​of each individual are calculated, the global minimum and the corresponding optimal individual are updated, and the primary selection, recombination, and secondary selection stages are repeated until the preset maximum number of iterations is reached. Finally, the global optimal cost information vector is output. .

[0068] Obtain the optimal cost information vector Then, the final hidden layer With the optimal cost information vector The objective function of the constrained output layer is co-embedded, and a cost-sensitive regularized pseudo-inverse is solved. The specific steps are as follows: The optimization objective function of the cost-sensitive weighted width network is defined as:

[0069] ;

[0070] In the formula, This represents the output weight matrix. For regularization parameters, For the first The error vector of each sample. It is a diagonal matrix composed of the optimal cost information vectors. For the sample The label vector, For the sample Hidden layers generated by concatenating feature mapping and enhancement mapping;

[0071] Constructing the Lagrange function:

[0072] ;

[0073] In the formula, These are Lagrange multipliers. Based on the KKT conditions, respectively... , and Find the partial derivative and set it to zero:

[0074] ;

[0075] ;

[0076] ;

[0077] Combining the above three equations, we can eliminate... and The optimal output weights are obtained by solving the problem.

[0078] ;

[0079] In the formula, The optimal cost information vector The corresponding optimal output weight matrix, It is the identity matrix. To obtain the hidden layer, The label matrix is ​​formed by stacking the one-hot encoded label vectors of all training samples.

[0080] Step 3: In the application phase, the data to be classified is input into the trained, optimized cost-sensitive weighted wide network. After feature mapping and enhancement mapping are concatenated into a hidden layer, the classification prediction result is obtained by multiplying it with the optimal output weights, as follows:

[0081] For data to be classified The final hidden layer is formed by concatenating the random weight matrix and bias matrix determined in step 2 after feature mapping and enhancement mapping. Through the formula Calculate the predicted output ,Pick The category corresponding to the dimension of the maximum value in each row is used as the final classification result.

[0082] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. An imbalanced data classification method based on an optimized cost-sensitive weighted width network, characterized in that, This method achieves accurate classification of imbalanced data based on an optimized cost-sensitive weighted width network. This optimized cost-sensitive weighted width network incorporates a cost optimization framework into a weighted width learning system, and improves the original weighting mechanism and output layer solution. The cost optimization framework aims to minimize... The optimization objective is to use a backtracking search optimization algorithm to globally optimize the cost information vector. The improvement to the weighting mechanism is to introduce an off-diagonal cost matrix on top of the original diagonal weighting matrix. Both matrices jointly determine the cost information vector, assigning differentiated misclassification penalty weights to each sample, replacing the original experience-based fixed weighting method. The improvement to the output layer solution is to embed the optimal cost information vector into the objective function to form a cost-sensitive regularized pseudo-inverse solution, replacing the original equally weighted pseudo-inverse solution method, thus giving minority class sample errors a greater penalty weight. The specific implementation of this method includes the following steps: Step 1: Obtain the imbalanced classification dataset and preprocess it to obtain clean feature data and class labels; Step 2: The preprocessed feature data and class labels are fed into an optimized cost-sensitive weighted wide network for training. During training, the feature data is first transformed linearly with random weights and biases, and then mapped to feature nodes through an activation function. The feature nodes are then transformed linearly with random weights and biases, and then mapped to augmentation nodes through a non-linear activation function. The feature nodes and augmentation nodes are concatenated to form a hidden layer. A diagonal weighted matrix is ​​calculated based on the number of samples in each category. An off-diagonal cost matrix is ​​introduced to quantify the loss when each sample is misclassified to a different category. The cost information vector is represented as the vector value obtained by multiplying the diagonal weighted matrix and the off-diagonal cost matrix and summing them row by row. The goal is to minimize... The optimal cost information vector is obtained by using a backtracking search optimization algorithm to perform global optimization within the preset upper and lower bound constraints. The hidden layer and the optimal cost information vector are then embedded into the constrained output layer objective function. The cost-sensitive regularized pseudo-inverse solution is obtained by taking the derivative of the Lagrange multiplier method and KKT conditions, and the optimal output weight is obtained. Finally, the trained optimized cost-sensitive weighted width network is obtained. Step 3: In the application stage, the data to be classified is input into the trained optimized cost-sensitive weighted wide network. After feature mapping and enhancement mapping are concatenated into a hidden layer, the classification prediction result is obtained by multiplying it with the optimal output weight.

2. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 1, characterized in that, In step 1, the preprocessing includes removing empty features, filling missing values, discretization, normalizing the feature data, and one-hot encoding the class labels.

3. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 1, characterized in that, In step 2, the process of concatenating the feature nodes and enhancement nodes to form the hidden layer is as follows: given input feature data , Indicates size is A real matrix, where For the number of training samples, To input the feature dimension, use the formula Feature mapping generation Group feature nodes , , The number of feature node groups is denoted as , where and They are randomly generated respectively The weight matrix and bias matrix, For the feature layer activation function, Group feature nodes are concatenated as , Indicates by A feature node group consisting of a set of feature nodes; As input, through the formula Enhanced mapping generation Group Enhancement Nodes , , To increase the number of node groups, among which and Randomly generated The weight matrix and bias matrix, To enhance the nonlinear activation function of the layer, Group enhancement node splicing as , Indicates by A group of enhanced nodes; the final hidden layer is represented as .

4. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 3, characterized in that, In step 2, the diagonal weighting matrix is Matrix, denoted as Its diagonal elements Calculated based on the number of samples in each category: ； in , Indicates the first The total number of samples belonging to the category of each sample. This represents the average number of samples across all categories; The off-diagonal cost matrix is: Matrix, denoted as , The total number of categories, its elements Indicates the first The sample was misclassified as the first The loss during class, where , ,element A value of 0 indicates correct classification with no loss; the values ​​of other non-zero elements are generated through randomization; the cost information vector is labeled as... , its first Each component Depend on Calculated.

5. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 4, characterized in that, In step 2, to minimize The specific expression of the optimization objective is as follows: ； In the formula, This is the optimal cost information vector. Cost information vector The One portion, Indicates the sample number. This represents the variable that minimizes the objective function. The value of , The area under the ROC curve. For classification loss function, For the first Sample The label vector, and These are the preset lower and upper bounds of the cost information vector, respectively. To optimize the output function of the cost-sensitive weighted width network, it is obtained through the following process: for the input samples , by the final hidden layer Take the first The row obtains its corresponding hidden layer. , sample Corresponding hidden layer With cost information vector Corresponding output weights Multiplying them yields the network output, namely: ； in The result is obtained by solving the cost-sensitive regularized pseudoinverse: ； In the formula, For regularization parameters, For cost information vector The components form a diagonal matrix with diagonal elements. For the final hidden layer, It is the identity matrix. The label matrix is ​​formed by stacking the one-hot encoded label vectors of all training samples.

6. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 5, characterized in that, In step 2, the backtracking search optimization algorithm includes the following: The cost information vector to be optimized Encoding as a population The individual within, the problem dimension is The population size is Individual serial number Dimension ; The initial population is randomly generated within preset upper and lower bounds according to a uniform distribution. ,in Indicates the first The first individual dimension, and The first The lower and upper bounds of a dimension, Indicates uniform distribution, and through Calculate each individual fitness value ,in The objective function to be minimized is the function corresponding to the individual. Value; after primary selection, recombination, and secondary selection iterations until the termination condition is met, the optimal individual is output, i.e., the optimal cost information vector. .

7. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 6, characterized in that, In step 2, the hidden layer and the optimal cost information vector are jointly embedded into the constrained output layer objective function, as follows: ； In the formula, This represents the output weight matrix. For regularization parameters, For the first Sample The error vector, It is a diagonal matrix composed of the optimal cost information vectors. For the sample The label vector, For the sample Hidden layers generated by concatenating feature mapping and enhancement mapping; The cost-sensitive regularized pseudo-inverse solution is obtained by using the Lagrange multiplier method and KKT conditions to differentiate the above objective function, thus obtaining the optimal output weights: ； In the formula, The optimal cost information vector The corresponding optimal output weight matrix, It is the identity matrix. To obtain the hidden layer, The label matrix is ​​formed by stacking the one-hot encoded label vectors of all training samples.

8. The imbalanced data classification method based on an optimized cost-sensitive weighted width network according to claim 7, characterized in that, In step 3, the classification prediction result is labeled as Through formula The calculation yielded, where The final hidden layer is formed by concatenating the data to be classified after feature mapping and augmentation mapping. To obtain the optimal output weights, take... The category corresponding to the dimension of the maximum value in each row is used as the final classification result.

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