Sparse multi-label feature selection method based on feature position

Abstract

The invention relates to the technical field of multi-label feature selection, in particular to a sparse multi-label feature selection method based on feature positions, which comprises the following steps of: decomposing an original feature space matrix by using a coupling matrix decomposition method; the basis matrix alignment of the feature space and the label space is realized through dynamic graph Laplacian; alternately optimizing to obtain a global optimal coefficient matrix; fusing information entropy and coefficient matrix score weighting to enhance double spaces; constructing an objective function through norms; and optimizing the objective function based on an alternating direction multiplier method and a norm threshold method to obtain a globally optimal solution. According to the method, a double-space interaction matrix is obtained through composite matrix decomposition and a dynamic graph Laplacian technology, interaction features and label weights are obtained through F-norm, and index normalization weighting is performed on the interaction weights by introducing information entropies of an original feature space and a label space, so that the label space and the feature space are enhanced; and high-dimensional structures among the data are captured to obtain valuable features.

Description

Technical Field

[0001] This invention relates to the field of multi-label feature selection technology, and in particular to a sparse multi-label feature selection method based on feature location. Background Technology

[0002] With the advent of the information age, the amount of data available has increased exponentially: the feature dimensionality of data is constantly increasing, and the semantic space is becoming increasingly rich. For example, in the field of image recognition, an image may simultaneously contain multiple target instances; in the field of emotion recognition, an expression or a piece of speech may express a variety of complex emotions. Because the feature space contains a large number of redundant and irrelevant features and is usually high-dimensional, it not only affects the response speed of machine learning models but also often leads to unsatisfactory performance. How to extract the most effective features for label recognition from the high-dimensional feature space to train machine learning models, thereby avoiding the negative impact of the dimensionality curse, is attracting increasing attention. Therefore, this invention explores the field of multi-label feature selection.

[0003] Feature selection methods can be mainly divided into embedding, filtering, and encapsulation methods. Compared to the first two methods, encapsulation methods require multiple selections of feature subsets for training and continuous feature selection, resulting in high time complexity. Embedding-based algorithms are independent of subsequent learning processes and generally use maximizing the correlation between the feature space and label space, and minimizing the redundancy between candidate and selected features as the benchmark for feature selection. Unlike the above two algorithms, embedding methods have attracted much attention from researchers due to their high efficiency and high accuracy. However, existing embedding methods have serious drawbacks. Existing embedded feature selection methods have several shortcomings: multi-focused latent space learning ignores information in the decomposition matrix that reflects the importance of features and labels; sparsity-based methods emphasize design norms to apply sparsity constraints, without fully considering label correlation and feature dependence; label enhancement-based methods emphasize converting logical labels to numerical values, ignoring feature redundancy; and coupled matrix factorization methods, although considering the interaction between the two spaces, still have redundancy problems or disrupt the inherent connections between the two spaces. Summary of the Invention

[0004] This invention provides a sparse multi-label feature selection method based on feature location. It obtains a dual-space interaction matrix (FPFS) through matrix factorization and dynamic graph Laplacian technique, uses F-norm to obtain the interaction features and label weights respectively, and enhances the label space and feature space by introducing the information entropy of the original feature space and label space into the interaction weights through exponential normalization weighting, so as to capture the high-dimensional structure between data and obtain valuable features.

[0005] To achieve the above objectives, this invention provides a sparse multi-label feature selection method based on feature location, comprising the following steps: S1. Use the coupled matrix decomposition method to decompose the original feature space matrix into a shared subspace matrix and the corresponding coefficient matrix; S2. Based on S1, the basis matrix alignment of the feature space and label space is achieved through dynamic graph Laplacian, realizing the interaction between the feature space and label space; S3. Use an alternating optimization strategy to optimize the variables of S1 and S2 to obtain the global optimal solution and the corresponding coefficient matrix. S4. Calculate the information entropy of the original feature space and label space respectively. Combine the feature and label scores obtained in S3 to perform exponential normalization weighting on the feature space and label space respectively to obtain the enhanced feature space matrix and label space matrix. S5, using robustness The norm is used as the distance function between the enhanced feature space and the label space, and is employed... The norm serves as a regularization term in the weight matrix; S6, Based on the alternating direction multiplier method and The norm thresholding method is used to optimize the objective function obtained from S5 to obtain the global optimal solution, thereby determining the importance of features and completing feature selection.

[0006] Preferably, in step S1, the expression for minimizing the correlation error between the feature space and label space and the shared subspace and corresponding coefficient matrix through coupled matrix decomposition is: ; in, This represents the feature matrix of n instances with d feature dimensions; Represents a label matrix containing n instances with l label dimensions; It is a shared subspace matrix, where k is the dimension of the shared subspace; It is the eigenvalue matrix; It is the label coefficient matrix; For hyperparameters; and All are Phoenician norms.

[0007] Preferably, in step S2, the expression for the dynamic graph Laplace is: ; in, For hyperparameters, Represents the trace of the matrix. The characteristic coefficient matrix transpose, For label coefficient matrix The graph Laplace matrix, Calculate using the following steps: S21. Calculate the label coefficient correlation weight matrix using the heat kernel function combined with the KNN algorithm. : ; in, Represents the similarity matrix of label coefficients The Line 1 Column elements, Represents the label coefficient matrix The row vectors Represents the label coefficient matrix The row vectors express and The 2-norm square, For hyperparameters, Represents the label coefficient matrix The Middle Before the journey A set consisting of nearest neighbors; S22. Construct a diagonal matrix Its diagonal elements are the label coefficient similarity matrix. The sum of the elements in the corresponding row, i.e. ; in, For the first Line 1 One element; S23. Calculate using the definition of the Laplace matrix. : ; ; in, Represents the eigencoefficient matrix The row vectors Represents the eigencoefficient matrix The Row vectors.

[0008] Preferably, in step S3, an alternating optimization strategy is used to optimize the variables of S1 and S2 to obtain the global optimal solution and the corresponding coefficient matrix. The steps are as follows: S31. Determine the objective function for optimization: ; in, The target loss function; S32. Find the optimization function with respect to... , , First-order partial derivative: ; ; ; S33. Setting the partial derivative to 0, we get , , The closed-form update formula, with alternating iterative updates: ; ; ; .

[0009] Preferably, in step S4, the exponent normalization weighting steps are as follows: S41. Calculate the information entropy of the original feature space and label space column-wise using the histogram method to obtain the information entropy score: ; ; in, This is the function for calculating information entropy. The information entropy score of the original feature space is used to filter out densely distributed redundant features; The information entropy score of the original label space is used to filter labels with low information content; S42. The eigencoefficient matrix obtained from S3 and label coefficient matrix Calculating the 2-norm for each column yields the feature scores and label scores under the coupled decomposition: ; ; in, For the first The coupling decomposition score of each feature, For the first The coupling decomposition score of each label; the higher the score, the richer the reconstruction information of the corresponding feature or label. S43. Calculate feature weights and label weights using the exponential normalization formula: ; ; in, For the first The weighting factors of each feature, For the first The weighting factor for each label, and the exponential function are used to amplify the difference in importance between features and labels, ensuring that the weights of key features and labels are more prominent; S44. Apply the calculated weights to the original feature matrix. and label matrix Weighting is performed to generate the enhanced matrix: ; ; in, For the enhanced feature space matrix, This is the enhanced label space matrix.

[0010] Preferably, in step S5, the objective function is: ; in, The feature weight matrix, For hyperparameters; for The norm distance term is used to reduce the impact of outliers on feature-label mapping learning, thereby achieving robust mapping of the augmented space. for Norm regularization terms cause the feature weight matrix to... The rows are sparse, thus filtering out the feature subset that contributes significantly to label prediction.

[0011] Preferably, in step S6, the method is based on alternating direction multipliers and The norm thresholding method optimizes the objective function, including the following steps: S61. Define the loss function: ; S62. Introducing the residual matrix This transforms the objective function into a constrained optimization problem: ; in, This is used to separate feature-label mapping error from the sparsity constraint of the weight matrix, reducing the optimization difficulty; S63. Use the augmented Lagrange method to introduce constraints into the objective function and construct the augmented Lagrange function: ; in, It is a Lagrange multiplier. For penalty parameters; S64, Alternating Iterative Update , and : fixed and Regarding the augmented Lagrange function with respect to Taking the derivative and setting it to zero, we get Closed-form update formula: ; in for An identity matrix of order 1 ensures the effectiveness of matrix inversion operations; fixed and ,pass Norm soft threshold operator update : ; in, for The norm soft thresholding operator is defined as: ; in, For the input matrix, For threshold parameters; fixed and Update the Lagrange multiplier : ; S65, Repeat S64 until the loss function is defined. If the change is less than the preset convergence threshold, calculate the feature weight matrix. For each row, sort the 2-norms by norm and select the top ones. The features are selected as the optimal feature subset.

[0012] Therefore, this invention provides a sparse multi-label feature selection method based on feature location, which has the following advantages: FPFS first utilizes dynamic graph Laplacian technique and coupled matrix factorization technique to obtain the importance matrix corresponding to the features and labels; secondly, FPFS calculates the mutual information matrix of the original feature space correlation matrix and the original label space correlation matrix, and combines it with the importance matrix obtained in the first step to enhance the feature space and label space respectively, capturing the high-dimensional structure of the data; finally, it uses sparse... The norm learns the mapping from the feature space to the label space. Extensive experiments on multiple real-world multi-label datasets demonstrate that FPFS achieves superior results compared to state-of-the-art methods. Attached Figure Description

[0013] Figure 1The figures show the performance curves of the present invention and the comparison algorithm on six datasets with varying feature selection ratios under Micro-F1 and Macro-F1 metrics for linear SVM classifiers. (a1), (a2), (a3), (a4), (a5), and (a6) represent the experimental results of FPFS and seven multi-label feature selection methods on the Artworks, Leisure, Safety, Entertainment, Health, and Science datasets under Micro-F1, respectively; (b1), (b2), (b3), (b4), (b5), and (b6) represent the experimental results of FPFS and seven multi-label feature selection methods on the Artworks, Leisure, Safety, Entertainment, Health, and Science datasets under Macro-F1, respectively. Figure 2 The figures show the performance curves of each algorithm under the HL and ZOL metrics for the MLKNN classifier. Among them, (a1), (a2), (a3), (a4), (a5), and (a6) are the experimental results of FPFS and seven multi-label feature selection methods for the Artworks, Leisure, Safety, Entertainment, Health, and Science datasets under the HL metric, respectively; (b1), (b2), (b3), (b4), (b5), and (b6) are the experimental results of FPFS and seven multi-label feature selection methods for the Artworks, Leisure, Safety, Entertainment, Health, and Science datasets under the ZOL metric, respectively. Figure 3 The figure shows the results of the Bonferroni-Dunn test for detecting differences between methods at a significance level of α=0.05; where (a), (b), (c), and (d) are the results for the indices Micro (SVM), Macro (SVM), HL (ML-KNN), and ZOL (ML-KNN), respectively. Figure 4 For parameter sensitivity analysis in the Health dataset; (a) and (b) are respectively Sensitivity analysis results under Micro-F1 and Macro-F1, (c) and (d) are respectively Sensitivity analysis results under Micro-F1 and Macro-F1, (e) and (f) are respectively Sensitivity analysis results under Micro-F1 and Macro-F1; Figure 5 The graph shows the convergence analysis of the algorithm; where (a), (b), (c), (d), (e), and (f) are the convergence curves on the Enron, Science, Sentiment, Flag, Entertainment, and Art datasets, respectively. Detailed Implementation

[0014] The following detailed description of embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0015] Example 1 This invention provides a sparse multi-label feature selection method based on feature location, comprising the following steps: S1. Use the coupled matrix decomposition method to decompose the original feature space matrix into a shared subspace matrix and the corresponding coefficient matrix; S2. Based on S1, the basis matrix alignment of the feature space and label space is achieved through dynamic graph Laplacian, realizing the interaction between the feature space and label space; S3. Use an alternating optimization strategy to optimize the variables of S1 and S2 to obtain the global optimal solution and the corresponding coefficient matrix. S4. Calculate the information entropy of the original feature space and label space respectively. Combine the feature and label scores obtained in S3 to perform exponential normalization weighting on the feature space and label space respectively to obtain the enhanced feature space matrix and label space matrix. S5, using robustness The norm is used as the distance function between the enhanced feature space and the label space, and is employed... The norm serves as a regularization term in the weight matrix; S6, Based on the alternating direction multiplier method and The norm thresholding method is used to optimize the objective function obtained from S5 to obtain the global optimal solution, thereby determining the importance of features and completing feature selection.

[0016] In step S1, the expression for minimizing the correlation error between the feature space and label space and the shared subspace and the corresponding coefficient matrix through coupled matrix decomposition is as follows: ; in, This represents the feature matrix of n instances with d feature dimensions; Represents a label matrix containing n instances with l label dimensions; It is a shared subspace matrix, where k is the dimension of the shared subspace; It is the eigenvalue matrix; It is the label coefficient matrix; For hyperparameters; and All are Phoenician norms.

[0017] In step S2, the expression for the dynamic graph Laplace is: ; in, For hyperparameters, Represents the trace of the matrix. The characteristic coefficient matrix transpose, For label coefficient matrix The graph Laplace matrix, Calculate using the following steps: S21. Calculate the label coefficient correlation weight matrix using the heat kernel function combined with the KNN algorithm. : ; in, Represents the similarity matrix of label coefficients The Line 1 Column elements, Represents the label coefficient matrix The row vectors Represents the label coefficient matrix The row vectors express and The 2-norm square, For hyperparameters, Represents the label coefficient matrix The Middle Before the journey A set consisting of nearest neighbors; S22. Construct a diagonal matrix Its diagonal elements are the label coefficient similarity matrix. The sum of the elements in the corresponding row, i.e. ; in, For the first Line 1 One element; S23. Calculate using the definition of the Laplace matrix. : ; ; in, Represents the eigencoefficient matrix The row vectors Represents the eigencoefficient matrix The Row vectors.

[0018] In step S3, an alternating optimization strategy is used to optimize the variables in S1 and S2 to obtain the global optimal solution and the corresponding coefficient matrix. The steps are as follows: S31. Determine the objective function for optimization: ; in, The target loss function; S32. Find the optimization function with respect to... , , First-order partial derivative: ; ; ; S33. Setting the partial derivative to 0, we get , , The closed-form update formula, with alternating iterative updates: ; ; ; .

[0019] In step S4, the steps for exponential normalization weighting are as follows: S41. Calculate the information entropy of the original feature space and label space column-wise using the histogram method to obtain the information entropy score: ; ; in, This is the function for calculating information entropy. The information entropy score of the original feature space is used to filter out densely distributed redundant features; The information entropy score of the original label space is used to filter labels with low information content; S42. The eigencoefficient matrix obtained from S3 and label coefficient matrix Calculating the 2-norm for each column yields the feature scores and label scores under the coupled decomposition: ; ; in, For the first The coupling decomposition score of each feature, For the first The coupling decomposition score of each label; the higher the score, the richer the reconstruction information of the corresponding feature or label. S43. Calculate feature weights and label weights using the exponential normalization formula: ; ; in, For the first The weighting factors of each feature, For the first The weighting factor for each label, and the exponential function are used to amplify the difference in importance between features and labels, ensuring that the weights of key features and labels are more prominent; S44. Apply the calculated weights to the original feature matrix. and label matrix Weighting is performed to generate the enhanced matrix: ; ; in, For the enhanced feature space matrix, This is the enhanced label space matrix.

[0020] In step S5, the objective function is: ; in, The feature weight matrix, For hyperparameters; for The norm distance term is used to reduce the impact of outliers on feature-label mapping learning, thereby achieving robust mapping of the augmented space. for Norm regularization terms cause the feature weight matrix to... The rows are sparse, thus filtering out the feature subset that contributes significantly to label prediction.

[0021] In step S6, based on the alternating direction multiplier method and The norm thresholding method optimizes the objective function, including the following steps: S61. Define the loss function: ; S62. Introducing the residual matrix This transforms the objective function into a constrained optimization problem: ; in, This is used to separate feature-label mapping error from the sparsity constraint of the weight matrix, reducing the optimization difficulty; S63. Use the augmented Lagrange method to introduce constraints into the objective function and construct the augmented Lagrange function: ; in, It is a Lagrange multiplier. For penalty parameters; S64, Alternating Iterative Update , and : fixed and Regarding the augmented Lagrange function with respect to Taking the derivative and setting it to zero, we get Closed-form update formula: ; in for An identity matrix of order 1 ensures the effectiveness of matrix inversion operations; fixed and ,pass Norm soft threshold operator update : ; in, for The norm soft thresholding operator is defined as: ; in, For the input matrix, For threshold parameters; fixed and Update the Lagrange multiplier : ; S65, Repeat S64 until the loss function is defined. If the change is less than the preset convergence threshold, calculate the feature weight matrix. For each row, sort the 2-norms by norm and select the top ones. The features are selected as the optimal feature subset.

[0022] To verify the effectiveness of the sparse multi-label feature selection method based on feature location proposed in this invention, experiments were conducted using eight widely used multi-label datasets from the Mulan Library, covering multiple domains such as image, text, and music. For example, the image dataset `flags` contains 194 images and 19 features, while the music emotion classification dataset `emotions` contains 593 songs, each with a subset of 6 labels, such as: happy-pleased, amazed-surprised, etc. Detailed dataset information is summarized in Table 1.

[0023] Table 1 Information about the experimental dataset

[0024] Four commonly used multi-label classification evaluation criteria are used to evaluate the performance of feature selection methods from different dimensions. Micro-F1 and Macro-F1 are based on linear SVM classifiers. The larger the value, the better the classification performance, reflecting the model's overall ability to recognize labels and the average recognition ability of labels in each category. Hamming Loss and Zero One Loss are based on the commonly used MLKNN classifier. The smaller the value, the lower the model's classification error. They respectively measure the average misclassification rate of sample labels and the error rate of the overall prediction results.

[0025] To highlight the superiority of this invention, seven baseline methods were compared, including four sparse learning-based embedding methods, two information theory-based filtering methods, and one problem transformation algorithm. The regularization parameters of all compared methods were searched within the range recommended in their respective literatures. The hyperparameters of this invention were adjusted and selected in a grid {0.1, 0.3, 0.5, 0.7, 0.9, 1, 10}. The number of selected features was increased from 1% to 20% of the dataset's features, with a step size of 1%. Since the Flags dataset contains only 19 features, all features were used in the experiments.

[0026] Table 2. Results of different methods on various datasets for Micro-F1, Macro-F1, Hamming Loss (HL), and ZeroOne Loss (ZOL) metrics (mean ± standard deviation)

[0027] Table 2 presents the global experimental performance of different comparison methods on the dataset, covering four evaluation metrics: Micro-F1, Macro-F1, Hamming Loss (HL), and Zero One Loss (ZOL). The ranking of each method on the corresponding dataset is indicated in parentheses after the result; if multiple methods have the same ranking, the average ranking is used. The last row of the table shows the average ranking of each method under each metric. Analysis of the data in the table shows that the method proposed in this invention significantly outperforms all other comparison methods across all evaluation criteria.

[0028] To further validate the classification performance of FPFS, the Friedman test and Bonferroni-Dunn test were used for observation. Clearly, from Table 2 and... Figure 3 It can be seen that the features selected by FPFS are highly valuable, and FPFS consistently ranks first in all situations, exhibiting significant statistical differentiation from other methods. Furthermore, in Figure 1 and Figure 2 The paper illustrates the performance trends of all methods using the standard. The first two SVM-based classifier metrics initially show improved performance, then stabilized or even declined. The latter two MLKNN-based metrics exhibit greater fluctuations due to the characteristics of their criteria. However, overall, the method presented in this invention remains superior. In summary, FPFS in this invention significantly outperforms other methods. Research shows that FPFS, by utilizing coupled matrix decomposition based on dynamic graph Laplacian constraints to obtain the interaction weight coefficients between the feature space and label space, and by weighting the relationships between original labels and the relationships between feature spaces, followed by sparse mapping, can effectively explore the high-dimensional structure of data and filter out valuable features.

[0029] Table 3. Friedman test statistics and critical values ​​for each evaluation index.

[0030] Parameter sensitivity analysis and convergence analysis: The FPFS algorithm includes three parameters, namely , and This invention studies the sensitivity of parameters through experiments, specifically presenting the results of the Arts dataset from the perspective of a support vector machine classifier. The specific rule is: adjust one parameter within a grid range {0.1, 0.3, 0.5, 0.7, 0.9, 1, 10}, while keeping other parameters fixed at 1 for easy comparison. Figure 4In the results, FPFS's sensitivity to all parameter values ​​is within an acceptable range, indicating that the algorithm has a large safe parameter selection range. Furthermore, to verify whether the proposed algorithm can converge quickly, convergence experiments were conducted on six benchmark datasets, and the results are as follows: Figure 5 As shown, the loss function value of FPFS can converge quickly and tend to stabilize in a small number of iterations, which once again proves the feasibility of the algorithm design.

[0031] Ablation experiment: This invention uses ablation studies to illustrate the impact of weighting mechanisms from the perspective of Support Vector Machine (SVM) classifiers. Tables 4 and 5 use several representative datasets from different fields for validation, comparing three methods: RFS (the baseline method without weighting the feature and label spaces), FPFS-X (without weighting the feature space), and FPFS-Y (without weighting the label space). It can be seen that, considering the influence of feature location on feature selection, and through the interaction weights between the feature and label spaces and the weighting of the original space, FPFS achieves better classification performance than unweighted methods or those considering only a single space augmentation scheme.

[0032] Table 4 Results of ablation studies using the Micro index dataset

[0033] Table 5. Results of ablation studies using the Macro index on the dataset.

[0034] Explainability: This invention reveals the influence of causal mechanisms on feature selection results by showcasing the features selected in the representative dataset Flags. The Flags dataset is used for predicting the color of a flag based on features, specifically red, green, blue, yellow, white, black, and orange. In this dataset application scenario, this invention uses a feature selection matrix that considers feature location information. The top three features with the best discriminative power were selected through experiments for comparative verification. Experimental results show that the top three features selected in this invention are features A, B, and C. In comparison, the features selected by the LCIFS method are features A, B, and D; the features selected by the SSFS method are features A, E, and F; the features selected by the FPFS-X ablation method are features G, F, and B; the features selected by the FPFS-Y method are features H, F, and D; and the features selected by the RFS method are features A, F, and C. The above comparison results show that the features selected by the feature selection scheme (FPFS) adopted in this invention have better predictive suitability for flag colors. To further verify the rationality and effectiveness of the selected top three features, this invention uses the classic causal analysis method HITON-PC to search the parent-child nodes (PCs) of the tags. The search results show that the PC nodes corresponding to the target variable completely match the top three features selected in this invention. This proves that the features selected in this invention possess both strong causal correlation and feature relevance, providing a reliable feature foundation for subsequent prediction tasks.

[0035] Therefore, this invention employs the aforementioned method for exploring sparse multi-label feature selection. FPFS first utilizes dynamic graph Laplacian technique and coupled matrix factorization to obtain the importance matrix corresponding to the features and labels. Secondly, FPFS calculates the mutual information matrix of the original feature space correlation matrix and the original label space correlation matrix, and combines this with the importance matrix obtained in the first step to enhance both the feature space and label space, capturing the high-dimensional structure of the data. Finally, it uses sparse... The norm learns the mapping from the feature space to the label space. Extensive experiments on multiple real-world multi-label datasets demonstrate that FPFS achieves superior results compared to state-of-the-art methods.

[0036] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A sparse multi-label feature selection method based on feature location, characterized in that, Includes the following steps: S1. Use the coupled matrix decomposition method to decompose the original feature space matrix into a shared subspace matrix and the corresponding coefficient matrix; S2. Based on S1, the basis matrix alignment of the feature space and label space is achieved through dynamic graph Laplacian, realizing the interaction between the feature space and label space; S3. Use an alternating optimization strategy to optimize the variables of S1 and S2 to obtain the global optimal solution and the corresponding coefficient matrix. S4. Calculate the information entropy of the original feature space and label space respectively. Combine the feature and label scores obtained in S3 to perform exponential normalization weighting on the feature space and label space respectively to obtain the enhanced feature space matrix and label space matrix. S5, using robust l 2,1 The norm is used as the distance function between the enhanced feature space and the label space, and l is employed. 2,1 The norm serves as a regularization term in the weight matrix; S6, Based on the alternating direction multiplier method and The norm thresholding method is used to optimize the objective function obtained from S5 to obtain the global optimal solution, thereby determining the importance of features and completing feature selection.

2. The sparse multi-label feature selection method based on feature location according to claim 1, characterized in that, In step S1, the expression for minimizing the correlation error between the feature space and label space and the shared subspace and the corresponding coefficient matrix through coupled matrix decomposition is as follows: ； in, This represents the feature matrix of n instances with d feature dimensions; Represents a label matrix containing n instances with l label dimensions; It is a shared subspace matrix, where k is the dimension of the shared subspace; It is the eigenvalue matrix; It is the label coefficient matrix; For hyperparameters; and All are Phoenician norms.

3. The sparse multi-label feature selection method based on feature location according to claim 2, characterized in that, In step S2, the expression for the dynamic graph Laplace is: ； in, For hyperparameters, Represents the trace of the matrix. The characteristic coefficient matrix transpose, For label coefficient matrix The graph Laplace matrix, Calculate using the following steps: S21. Calculate the label coefficient correlation weight matrix using the heat kernel function combined with the KNN algorithm. : ； in, Represents the similarity matrix of label coefficients The Line 1 Column elements, Represents the label coefficient matrix The row vectors Represents the label coefficient matrix The row vectors express and The 2-norm square, For hyperparameters, Represents the label coefficient matrix The Middle Before the journey A set consisting of nearest neighbors; S22. Construct a diagonal matrix Its diagonal elements are the label coefficient similarity matrix. The sum of the elements in the corresponding row, i.e. ; in, For the first Line 1 One element; S23. Calculate using the definition of the Laplace matrix. : ； ； in, Represents the eigencoefficient matrix The row vectors Represents the eigencoefficient matrix The Row vectors.

4. The sparse multi-label feature selection method based on feature location according to claim 3, characterized in that, In step S3, an alternating optimization strategy is used to optimize the variables in S1 and S2 to obtain the global optimal solution and the corresponding coefficient matrix. The steps are as follows: S31. Determine the objective function for optimization: ； in, The target loss function; S32. Find the optimization function with respect to... , , First-order partial derivative: ； ； ； S33. Setting the partial derivative to 0, we get , , The closed-form update formula, with alternating iterative updates: ； ； ； 。 5. The sparse multi-label feature selection method based on feature location according to claim 4, characterized in that, In step S4, the steps for exponential normalization weighting are as follows: S41. Calculate the information entropy of the original feature space and label space column-wise using the histogram method to obtain the information entropy score: ； ； in, This is the function for calculating information entropy. The information entropy score of the original feature space is used to filter out densely distributed redundant features; The information entropy score of the original label space is used to filter labels with low information content; S42. The eigencoefficient matrix obtained from S3 and label coefficient matrix Calculating the 2-norm for each column yields the feature scores and label scores under the coupled decomposition: ； ； in, For the first The coupling decomposition score of each feature, For the first The coupling decomposition score of each label; the higher the score, the richer the reconstruction information of the corresponding feature or label. S43. Calculate feature weights and label weights using the exponential normalization formula: ； ； in, For the first The weighting factors of each feature, For the first The weighting factor for each label, and the exponential function are used to amplify the difference in importance between features and labels, ensuring that the weights of key features and labels are more prominent; S44. Apply the calculated weights to the original feature matrix. and label matrix Weighting is performed to generate the enhanced matrix: ； ； in, For the enhanced feature space matrix, This is the enhanced label space matrix.

6. The sparse multi-label feature selection method based on feature location according to claim 5, characterized in that, In step S5, the objective function is: ； in, The feature weight matrix, For hyperparameters; for The norm distance term is used to reduce the impact of outliers on feature-label mapping learning, thereby achieving robust mapping of the augmented space. for Norm regularization terms cause the feature weight matrix to... The rows are sparse, thus filtering out the feature subset that contributes significantly to label prediction.

7. The sparse multi-label feature selection method based on feature location according to claim 6, characterized in that, In step S6, based on the alternating direction multiplier method and The norm thresholding method optimizes the objective function, including the following steps: S61. Define the loss function: ； S62. Introducing the residual matrix This transforms the objective function into a constrained optimization problem: ； in, This is used to separate feature-label mapping error from the sparsity constraint of the weight matrix, reducing the optimization difficulty; S63. Use the augmented Lagrange method to introduce constraints into the objective function and construct the augmented Lagrange function: ； in, It is a Lagrange multiplier. For penalty parameters; S64, Alternating Iterative Update , and : fixed and Regarding the augmented Lagrange function with respect to Taking the derivative and setting it to zero, we get Closed-form update formula: ； in for An identity matrix of order 1 ensures the effectiveness of matrix inversion operations; fixed and ,pass Norm soft threshold operator update : ； in, for The norm soft thresholding operator is defined as: ； in, For the input matrix, For threshold parameters; fixed and Update the Lagrange multiplier : ； S65, Repeat S64 until the loss function is defined. If the change is less than the preset convergence threshold, calculate the feature weight matrix. For each row, sort the 2-norms by norm and select the top ones. The features are selected as the optimal feature subset.

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