Beach sediment data analysis method for feature selection based on fuzzy elastic network

Abstract

The invention discloses a beach sediment data analysis method for feature selection based on a fuzzy elastic network. The method comprises the following steps: S1, converting original beach sediment data into a data matrix; s2, setting the dimensionality after dimensionality reduction, the hyper-parameter, the sum, the convergence threshold, the value of the LP norm and the maximum number of iterations; and S3, decoupling the projection matrix into a decoding matrix and an encoding matrix, and the like. According to the method, a new model combining PCA and a fuzzy elastic network enhances sparsity or promotes group sparsity through parameter adjustment, a projection matrix in PCA is decomposed into a coding matrix and a decoding matrix, orthogonality constraint and regularization effectiveness are reserved, and a learned row sparse decoding matrix retains PCA dominant characteristics and can be used for feature selection.

Description

Technical Field

[0001] This invention relates to the field of data analysis technology, and in particular to a method for analyzing beach sediment data based on feature selection using fuzzy elastic networks. Background Technology

[0002] With the continuous development of marine science, the importance of collecting and analyzing marine data is becoming increasingly prominent. Data analysis of beach sediments is of paramount importance for understanding marine ecosystems, predicting natural disasters, and conducting environmental assessments. However, the sheer volume and high dimensionality of marine data pose significant challenges to traditional analytical methods, making the development of new algorithms for processing and analyzing marine data an urgent priority. In high-dimensional data processing, dimensionality reduction techniques are particularly crucial, as they can extract key information and reduce computational costs and storage requirements. Meanwhile, feature selection techniques can directly extract discriminative subsets from the raw data, which is essential for the monitoring and assessment of the marine environment.

[0003] Currently, dimensionality reduction techniques are mainly divided into two categories: feature extraction and feature selection. Feature extraction is achieved by mapping high-dimensional data to a low-dimensional subspace. Principal Component Analysis (PCA), a classic method, compresses data by finding the direction that maximizes variance, retaining more information, but may generate new features that are difficult to interpret intuitively. In contrast, feature selection directly selects a discriminative subset from the original features, maintaining data interpretability, and has been widely used in many fields, such as text mining, visual classification, and bioinformatics. Feature selection methods are divided into supervised and unsupervised methods based on whether they rely on data labels. While supervised methods can utilize the association between features and labels to identify key features, label acquisition is costly, while unsupervised methods are more favored because they do not rely on labels.

[0004] Unsupervised feature selection methods include filtering, wrapping, and embedding. Filtering methods, such as Laplacian score (LS), evaluate based solely on the data features themselves, offering high computational efficiency but potentially failing to guarantee improved performance in mining tasks. Wrapping methods find the optimal feature subset through trial and error, achieving high accuracy but incurring high computational costs and limited generalization ability. To address these challenges and improve the effectiveness of unsupervised feature selection algorithms, regularization techniques, especially... L Regularization is receiving increasing attention. Algorithms like Multi-Cluster Feature Selection (MCFS) utilize spectral analysis and... L 1. Regularization identifies key features, while the Local Linear Embedding (RNE) algorithm uses... L The 1-norm method minimizes the reconstruction error to determine feature weights. However, based on... L The 1-norm method has limitations in its application to multiple classes of problems, so a different approach is adopted. L 2,1-norm, as a penalty term, provides a more refined feature selection strategy. By promoting matrix row sparsity and encouraging entire rows to be zero, it captures data structure information, similar to minimizing... L 1-norm and L 2-norm has different meanings, such as in unsupervised discriminative feature selection (UDFS) and adaptive weighted sparse principal component analysis (AW-SPCA). L 2,1 - Normalization enhances feature selection and robustness; Convex Sparse PCA (CSPCA) combines both the loss function and the regularization term. L 2,1 -norm, Zheng et al. employed positive semi-definite (PSD) projection optimization techniques to accelerate convergence and proposed several related algorithms. L 2,1 -norm is L 2,p -norm is a special case, and researchers have also incorporated it into feature selection, such as based on... L 2,p -norm sparse PCA (SPCAFS) enhances the sparsity of the projection matrix compared to PCA.

[0005] However, regularization terms based on a single specification, such as L 2,p -norm, typically assuming features are independent and ignoring the intrinsic structure between features, such as grouping and overlap properties, which are crucial for identifying key features. To address this issue, researchers have developed various sparse models that consider feature structure, such as the combination proposed by Zou. L 1-norm and L The 2-norm group-sparse elastic net model and its adaptive adjustment model aim to improve feature selection accuracy through grouping effects. However, while the elastic net model exhibits group sparsity in vector regularization, it has not been extended to a wider matrix form. The σ-norm model proposed by Ding et al. is based on... L 1-norm and L The 2-norm combination is flexible enough, but it is difficult to achieve robustness and sparsity in non-extreme cases, and the parameter σ needs to be manually adjusted, which increases the difficulty of model parameter selection.

[0006] In summary, existing regularization techniques face many challenges. For example, overemphasizing sparsity can suppress the weights of relevant features, ignore the relationships between important features, and the regularization terminology lacks adaptability and cannot adaptively balance between sparsity and group sparsity. Summary of the Invention

[0007] To address these shortcomings, this invention proposes a novel matrix-based regularization term—fuzzy elastic net—and integrates it into a PCA-based unsupervised feature selection model. This invention combines PCA with fuzzy elastic nets in a new model that enhances sparsity or promotes group sparsity through parameter adjustment. It also decomposes the projection matrix in PCA into encoding and decoding matrices, preserving orthogonality constraints and regularization effectiveness. The learned row-sparse decoding matrix retains the advantageous properties of PCA and can be used for feature selection. (Fuzzy elastic net fusion) L 2,2 -norm and L 2,p -norm in adaptive weighting schemes L 2,p -norm enhances sparsity to identify important features. L 2,2 - The normalization enhancement group emphasizes feature relevance, making optimization more stable and efficient. Adaptive weighting ensures that the model optimizes according to the characteristics of the dataset, improving generalization ability and the interpretability of feature selection.

[0008] According to one aspect of the present invention, a method for analyzing beach sediment data based on feature selection using a fuzzy elastic net is provided, the method comprising: S1. Transform raw beach sediment data into a data matrix. ; S2, Set the dimensions after dimensionality reduction hyperparameters , and And, convergence threshold , L P norm value, Maximum number of iterations ; S3, Project the matrix Decoupled into a decoding matrix and an encoding matrix ,satisfy ; data matrix Perform eigenvalue decomposition and take right singular matrix forward Initialization, The dimension after dimensionality reduction; initialize the centralized matrix. ,in, ; It is the identity matrix. It is a column vector with all elements being 1; S4, based on Update the left and right singular matrices , , It is a diagonal matrix composed of singular values; S5, based on Update the encoding matrix ; S6, based on ,renew ; S7, based on , , , , and decoding matrix Update the diagonal matrix Its diagonal element is ; S8, Based on Data Matrix Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix ; S9, according to Calculate the objective function value; S10. Determine if the termination condition is met; if the termination condition is met, execute S11; if the termination condition is not met, return to S4. S11. Sort the eigenvectors in the updated reconstructed transformation matrix and select the top ones. Construct the optimal feature subset from the largest eigenvectors. ; It is a positive integer greater than or equal to 1.

[0009] In the above technical solution, the method aims to reduce the dimensionality and extract features from beach sediment data. By introducing the concept of fuzzy elastic nets, a balance between the sparsity and globality of features is achieved during the feature selection process, improving the flexibility and adaptability of feature selection. This ensures that the selected features can both represent the original data well and adapt to different data characteristics and analytical needs.

[0010] S1~S3: These steps mainly involve preprocessing and initializing the raw data, including converting the data into matrix form, setting relevant parameters, initializing the decoding matrix and the centering matrix, etc., to prepare for the subsequent iterative optimization process.

[0011] S4~S5: Update the left and right singular matrices and the encoding matrix through singular value decomposition. This is a key operation in the matrix decomposition and dimensionality reduction process, which helps to extract the main feature components of the data.

[0012] The key parts are in the following four aspects: (1) Objective function design (S9): Objective function It incorporates the core ideas of fuzzy elastic networks. The first term is the data reconstruction error term, which measures the decoding matrix. and encoding matrix For raw data The first term is the reconstructing capability; the second term is the regularization term, which consists of two parts, namely... Here It is a dynamically adjusted parameter, balanced through fuzzy logic. L 2-norm sum L p The weight of the norm in regularization. L The 2-norm helps preserve the decoding matrix. The overall stability, and L p norm (0 < If ≤ 1), then sparsity can be introduced, making the decoding matrix... Some elements in the fuzzy elastic net are close to zero, thus achieving feature selection. and The parameters enable the algorithm to adaptively balance the sparsity of feature selection and overall stability, avoiding the limitations of fixed weights in traditional elastic net methods.

[0013] (2) Update (S6): The update formula is one of the key parts of the fuzzy elastic net. It is based on the current decoding matrix. The state of each feature vector. L 2-norm sum L p The relationship between norms is dynamically adjusted. The value of . This allows the algorithm to automatically determine the optimal value based on the characteristics of the data and the current optimization state. L 2-norm sum L p The degree of dependence on the norm enhances the algorithm's adaptability and flexibility. When decoding the matrix... eigenvectors in L When the 2-norm is more important, It will increase accordingly, increasing the impact on L The importance of 2-norm regularization; conversely, when the eigenvectors are in L p When the norm has a greater advantage in sparsity, It will decrease and strengthen the protection against L p Dependence on norm regularization.

[0014] (3) Diagonal matrix Update (S7): Based on the updated Update the diagonal matrix along with other parameters. This diagonal matrix The diagonal elements contain the fuzzy elastic net regularization term for the decoding matrix. The adaptive weight information for each feature vector. This is used in subsequent updates to the decoding matrix. During the process, this weight information can guide the optimization direction and intensity of each feature vector, further demonstrating the fine control of the fuzzy elastic network over the feature selection process.

[0015] (4) Decoding matrix Update (S8): In updating the decoding matrix At that time, the regularization term of the fuzzy elastic net guides the decoding matrix by influencing the gradient direction and magnitude of the objective function. Iterative updates are performed in a direction that both reconstructs the data well and satisfies a balance between sparsity and overall integrity. This allows the decoding matrix to... In the process of continuous optimization, the feature vectors gradually highlight important features while suppressing unimportant features, ultimately achieving effective feature selection.

[0016] S10 - S11: Determine if the termination condition is met. If it is, sort the eigenvectors in the updated reconstructed transformation matrix and select the top eigenvectors. Construct the optimal feature subset from the largest eigenvectors. If the feature selection process is not completed, return to S4 for iterative optimization.

[0017] In the above method, the introduction of fuzzy elastic nets enables the feature selection process to adaptively adjust the balance between sparsity and wholeness based on data characteristics and the current optimization state, avoiding the subjectivity and limitations of manually setting fixed weights, and improving the accuracy and effectiveness of feature selection. This is achieved by adjusting the fuzzy parameters. and hyperparameters , , This allows for flexible control over the intensity and direction of feature selection to adapt to different types of beach sediment data and varying data analysis needs. For example, in scenarios requiring a greater emphasis on feature sparsity, the intensity can be appropriately increased. The value of ; however, in scenarios where maintaining the overall stability of the decoding matrix is ​​required, it can be increased. The value of . Fuzzy elastic nets have a certain robustness to data noise and outliers. This is because they comprehensively consider in the regularization term. L 2-norm sum L p Norm, LThe 2-norm can mitigate the impact of noise on the overall model, while L p Norms can, to some extent, suppress the interference of outliers on feature selection, making the selected features more reflective of the essential characteristics and intrinsic structure of the data.

[0018] In some embodiments, the termination condition includes: The set number of iterations has been reached; And / or, The target value obtained in two consecutive iterations The difference Less than the set threshold.

[0019] In the above technical solution, the termination conditions include the following two situations: The number of iterations reaches the set number: When the iteration reaches the preset maximum number of iterations. At this point, regardless of whether the objective function value converges, the algorithm is considered to have completed the iterative process and can stop iterating. This setting ensures that the algorithm completes within a limited time and computational resources, avoiding indefinite execution. It provides a maximum time limit for the algorithm, ensuring its efficiency and practicality, which is especially important in scenarios involving large-scale data or requiring rapid results.

[0020] The target value obtained in two consecutive iterations The difference Less than a set threshold: Update the decoding matrix in each iteration. and encoding matrix Then, calculate the current objective function value. The difference between the objective function value and the value of the previous iteration If the difference is less than a preset threshold... If the objective function value changes very little between two consecutive iterations, the algorithm is considered to have converged, and the iteration can be stopped. This termination condition is based on the convergence of the algorithm. When the objective function value changes very little between two consecutive iterations, it means that the algorithm is close to the optimal solution or a stable state. Continuing to iterate may not significantly improve the result, so it can be terminated early to save computational resources.

[0021] By setting the maximum number of iterations This ensures the algorithm completes within a finite number of iterations, avoiding infinite loops caused by slow or non-convergent convergence, thus improving efficiency and practicality. For processing large-scale beach sediment data, computational resources and time are often limited; this termination condition guarantees a relatively stable result within an acceptable timeframe. (Target value) The difference As one of the termination conditions, it can effectively ensure the convergence of the algorithm. When When the value falls below a set threshold, it indicates that the algorithm is close to the optimal solution. Stopping the iteration at this point avoids unnecessary computation and ensures the stability of the result. This convergence-based termination condition is closely related to the optimization process of fuzzy elastic networks, because the goal of fuzzy elastic networks is to optimize the objective function through iterative optimization. Minimization, when the convergence condition is met, means that the fuzzy elastic net has achieved a good balance between the sparsity and globality of feature selection, and obtained a relatively stable feature subset.

[0022] In the iterative optimization process of fuzzy elastic networks, the decoding matrix and encoding matrix The continuous updating will cause the objective function value to... The change in the objective function value. The termination condition provides a clear stopping criterion for this dynamic optimization process. The optimization process of the fuzzy elastic net will stop when the number of iterations reaches its maximum or the change in the objective function value is sufficiently small, at which point the decoded matrix obtained will be... The feature vectors in the model have been thoroughly optimized and selected, and can well meet the requirements of feature selection. This termination condition setting allows the fuzzy elastic network to dynamically adjust within a limited number of iterations. By combining other parameters, an adaptive balance between feature sparsity and wholeness is achieved, ultimately resulting in a stable and effective feature subset.

[0023] In some embodiments, based on a data matrix Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix Specifically, this includes: through renew ;when It can be used renew .

[0024] In the above technical solution, this update method aims to optimize computational efficiency and ensure numerical stability. When Greater than the number of data points In this case, the data matrix The dimension is ,in Much greater than n. Directly through renew There may be computational challenges because It is The computational complexity of the inverse matrix of a given matrix is ​​relatively high, especially when... In very large cases. Use This formula is used to update This allows the computationally complex parts to be transferred to a... On the matrix. Because It is The inverse of a given matrix is ​​relatively easy to calculate, thus improving computational efficiency.

[0025] This adaptive update method aligns with the goal of fuzzy elastic networks, which is to achieve a balance between efficiency and effectiveness in the feature selection process. Fuzzy elastic networks dynamically adjust the diagonal matrix... This makes the decoding matrix The updates can better adapt to the characteristics of the data and the current optimization status. When When the value is large, the fuzzy elastic net adjusts the hyperparameters. sum matrix This allows the update formula to effectively handle high-dimensional data, avoiding the direct calculation of the inverse of the high-dimensional matrix, thus improving the algorithm's feasibility and efficiency. This demonstrates the flexibility and adaptability of fuzzy elastic networks in handling data of different scales. This update method ensures efficient updating of the decoding matrix even with high-dimensional data. This avoids the high computational cost of directly calculating the inverse of a high-dimensional matrix. Combined with fuzzy elastic nets, it ensures that the entire feature selection process remains efficient and stable across different data scales, further enhancing the practicality and wide applicability of the fuzzy elastic net method.

[0026] In some embodiments, S11, the eigenvectors in the updated reconstructed transformation matrix are sorted, and the top ones are selected. Construct the optimal feature subset from the largest eigenvectors. ; A positive integer greater than or equal to 1, followed by: S12. Utilizing the optimal feature subset The test data is denoised and reconstructed to obtain the transformed data.

[0027] In the above technical solution, the optimal feature subset is utilized. Denoising and reconstructing the test data is a crucial step in the practical application of this method. By projecting the test data onto a selected optimal feature subspace, noise components can be removed while retaining the main feature structures, resulting in clearer and more accurate transformed data. This process is significant for improving the accuracy and reliability of subsequent data analysis. (Feature subset selected by the fuzzy elastic net) The quality and characteristics of [the material] directly affect the denoising and reconstruction results. Because [the material]... It is obtained within the framework of fuzzy elastic nets by balancing the sparsity and wholeness of features. Therefore, it can better preserve the main features and intrinsic structure of the data during denoising, avoiding the loss of important information due to noise removal. Simultaneously, during the reconstruction process, it utilizes... It can more accurately restore the essential characteristics of data and improve the quality of reconstructed data.

[0028] According to another aspect of the present invention, a data analysis system for feature selection based on fuzzy elastic networks is provided, characterized in that, based on the above-described method, the system comprises: The data transformation module is used to transform raw beach sediment data into a data matrix. ; The first initialization module is used to set the dimensions after dimensionality reduction. hyperparameters , and And, convergence threshold , L P norm value, Maximum number of iterations ; The second initialization module is used to initialize the projection matrix. Decoupled into a decoding matrix and an encoding matrix ,satisfy ; data matrix Perform eigenvalue decomposition and take right singular matrix forward Initialization, The dimension after dimensionality reduction; initialize the centralized matrix. ,in, ; It is the identity matrix. It is a column vector with all elements being 1; The first update module is used for... Update the left and right singular matrices , , It is a diagonal matrix composed of singular values; The second update module is used for... Update the encoding matrix ; The third update module is used for... ,renew ; The fourth update module is used for... , , , , and decoding matrix Update the diagonal matrix Its diagonal element is ; The fifth update module is used for data matrix-based updates. Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix ; The sixth update module is used to update according to Calculate the objective function value; The judgment module is used to determine whether the termination condition is met; if the termination condition is met, the feature vector selection module is triggered; if the termination condition is not met, the first update module is triggered. The eigenvector selection module sorts the eigenvectors in the updated reconstructed transformation matrix and selects the first eigenvectors. Construct the optimal feature subset from the largest eigenvectors. ; It is a positive integer greater than or equal to 1.

[0029] In order to better utilize the above methods, this application proposes a data analysis system for feature selection based on fuzzy elastic networks. Each module corresponds to a step of the above methods, and its specific principles have been described above and will not be repeated here.

[0030] According to another aspect of the present invention, a method and apparatus for analyzing beach sediment data based on feature selection using a fuzzy elastic net are provided, comprising: At least one processor and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described above.

[0031] In the above technical solution, to better operate and process the method, the method is stored in memory, and the processor executes the stored method. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here.

[0032] According to another aspect of the present invention, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the above-described method.

[0033] In the above technical solution, to better operate and use the method, the method is stored in a computer-readable storage medium and implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated upon here. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a flowchart illustrating an embodiment of a beach sediment data analysis method based on feature selection using a fuzzy elastic network according to the present invention. Figure 2 This is an example of a beach sediment data analysis method based on fuzzy elastic nets according to the present invention, showing the feature selection results on a beach sediment dataset; Figure (a) shows the result of selecting 1 feature; Figure (b) shows the result of selecting 2 features. Figure 3 This is a schematic diagram of the feature selection results on the ORL dataset of an embodiment of the beach sediment data analysis method based on fuzzy elastic nets (from 100 to 900 features, with 100 features added in each step). Figure 4 This is a schematic diagram of an embodiment of a beach sediment data analysis method based on feature selection using fuzzy elastic networks. Detailed Implementation

[0036] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be particularly noted that the following embodiments are for illustrative purposes only and do not limit the scope of the invention. Similarly, the following embodiments are only some, not all, embodiments of the present invention, and all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] Example 1 Please see Figure 1 A method for analyzing beach sediment data based on feature selection using fuzzy elastic nets, the method comprising: S1. Transform raw beach sediment data into a data matrix. ; For example, suppose we sampled and measured beach sediments, measuring five different characteristics for each sample (such as particle size, organic carbon content, calcium content, magnesium content, median grain size, etc.), collecting a total of 10 samples. The raw data are shown in the table below:

[0038] Convert the above raw data into a data matrix. Each row represents a sample, and each column represents a feature. Matrix The dimension is 10×5, as detailed below:

[0039] Each row represents a beach sediment sample, and each column represents a specific measurement feature. For example, the first row represents all measurement features of sample 1, and the first column represents the particle size (mm) of all samples. This data matrix... It can be directly used in subsequent data analysis and processing steps, such as feature extraction, dimensionality reduction, and noise reduction.

[0040] S2, Set the dimensions after dimensionality reduction hyperparameters , and And, convergence threshold , L P norm value, Maximum number of iterations ; For example, continuing with the beach sediment data we just discussed, we already have a data matrix. Next, we need to set some parameters to prepare for subsequent dimensionality reduction and feature selection operations.

[0041] Dimensionality after dimensionality reduction Assuming that preliminary analysis or based on actual needs indicates that there are two main feature dimensions in the beach sediment data that can effectively represent the core information of the data, we can set... .

[0042] hyperparameters This parameter is used to balance the reconstruction error term and the regularization term in the objective function. Based on some experiments and reference to similar studies, it is set as follows: This value can be adjusted based on subsequent experimental results. If the feature selection is found to be too sparse, it may be necessary to reduce it. Conversely, if the feature selection is not sparse enough, the sparsity can be appropriately increased. .

[0043] hyperparameters This parameter is related to sparsity control in fuzzy elastic nets. Here, we set... This value can also be fine-tuned based on the actual data analysis results. If a sparser feature selection result is desired, it can be increased appropriately.

[0044] hyperparameters This parameter controls the degree of fuzziness and affects the fuzzy elastic network. Dynamic adjustment. Settings In practical applications, different methods can be tried. The value is used to observe the impact on feature selection, and then a more suitable range of values ​​is determined.

[0045] Convergence threshold : It is a very small value used to prevent non-convergence and to determine convergence. (Setting) That is, when the difference between the objective function values ​​of two adjacent iterations is less than When the algorithm has converged, it is considered to have converged and the iteration can be stopped.

[0046] L P norm Value: Setting = 0.5, which satisfies conditions. The choice of value affects how the sparsity of features is measured in the regularization term; a smaller value results in a lower value. The value will make the features sparser, but the computational difficulty may also increase accordingly.

[0047] Maximum number of iterations Based on practical experience and computing resources, set That is, regardless of whether the algorithm converges, it will stop after a maximum of 500 iterations.

[0048] The parameters described above provide basic control conditions for subsequent dimensionality reduction and feature selection operations, enabling the algorithm to iteratively optimize according to predetermined rules. Properly setting these parameters is crucial for ensuring the algorithm's performance and the accuracy of the results. In practical applications, methods such as cross-validation and grid search can be used to further optimize the values ​​of these parameters to adapt to specific beach sediment datasets and analysis objectives.

[0049] S3, Project the matrix Decoupled into a decoding matrix and an encoding matrix ,satisfy ; data matrix Perform eigenvalue decomposition and take right singular matrix forward Initialization, The dimension after dimensionality reduction; initialize the centralized matrix. ,in, ; It is the identity matrix. It is a column vector with all elements being 1; For example, continue using the previous beach sediment data matrix. Its dimensions are 10×5. We have already defined the dimensions after dimensionality reduction. .

[0050] (1) Project the matrix Decoupled into decoding matrix and encoding matrix Projection matrix Projection matrix Typically, this is an orthogonal matrix used to project the original data into a lower-dimensional space. In this example, The dimension will be 5×2 (because the original data has 5 features, and the dimension after dimensionality reduction is 2). Decoupling is... and encoding matrix :Will Decoupled into a decoding matrix and an encoding matrix ,satisfy .here, The dimension is 5×2. The dimension is 2×2.

[0051] (2) Initialize the decoding matrix

[0052] Eigenvalue decomposition: for a data matrix Perform Singular Value Decomposition (SVD). SVD will... Decomposed into ,in, It is a left singular matrix. It is a diagonal matrix composed of singular values. It is a right singular matrix.

[0053] Take the right singular matrix The former One eigenvector: In this example, take The first two eigenvectors are used as the decoding matrix. Initialization. Assume... The first two feature vectors are:

[0054] These feature vectors represent the two most important feature directions in the data.

[0055] (3) Initialize the centralized matrix

[0056] Centralized matrix Centralized matrix The definition of ,in yes n × n The identity matrix, yes n A vector of all 1s of size ×1.

[0057] identity matrix In this example, n =10, therefore It is a 10×10 identity matrix with 1s on the diagonal and 0s on the rest.

[0058] Complete Vector 1: is a 10×1 column vector of all 1s.

[0059] calculate For example, when n When =10, The calculation is as follows:

[0060] Here It is a 10×10 matrix of all ones, multiplied by After that, the value of each element is 0.1. Therefore, It is a matrix with diagonal elements of 0.9 and off-diagonal elements of -0.1.

[0061] initialization :calculate This step will transform the data matrix. The matrix is ​​centered, resulting in a 5×5 matrix. This is used in subsequent iterative optimization processes.

[0062] Initialize the decoding matrix by SVD decomposition , making the initial The orientation of the data is closer to its main features, which helps accelerate the convergence of subsequent iterative optimization processes. Initializing the centralization matrix ensures that the data is decentralized in subsequent processing, which helps improve the stability and convergence speed of the algorithm.

[0063] S4, based on Update the left and right singular matrices , , It is a diagonal matrix composed of singular values; For example, continue using the previous beach sediment data matrix. Its dimensions are 10×5. The decoding matrix has already been initialized in S3. It is a 5×2 matrix, and the centered matrix is ​​initialized. In S4, based on the formula Update the left and right singular matrices and , It is a diagonal matrix composed of singular values.

[0064] calculate : It is a 5×5 matrix representing the data matrix. The covariance matrix.

[0065] Multiply by the decoding matrix :Will Multiply by the decoding matrix (With dimensions of 5×2), we obtain a 5×2 matrix, denoted as... .Right now:

[0066] right Perform singular value decomposition (SVD) on the matrix Performing singular value decomposition, we obtain:

[0067] matrix : is a 5×2 matrix, and its column vectors are The left singular vector.

[0068] matrix : is a 2×2 diagonal matrix, whose diagonal elements are The singular values ​​are sorted in descending order.

[0069] matrix : is a 2×2 matrix, and its row vectors are The right singular vector.

[0070] Extracting the matrix through singular value decomposition The main feature components are used for subsequent updates to the encoding matrix. and decoding matrix Provides the foundation. In step S4, although the original data has 5 features, we only extracted 2 main feature directions (from...). and This helps reduce the dimensionality of the data while retaining its core information.

[0071] S5, based on Update the encoding matrix ; For example, in S4, the matrix has already been obtained through singular value decomposition (SVD). and In S5, based on the formula Update the encoding matrix .matrix : is a 5×2 matrix, and its column vectors are The left singular vector. Matrix : is a 2×2 matrix, and its row vectors are The right singular vector. Encoding matrix. : Through calculation The resulting encoding matrix has a dimension of 5×2. Each row represents the representation of a feature of the original data in the reduced-dimensional space. This matrix allows us to visualize the original data... Mapped to a low-dimensional space. Encoding matrix. This will be used to update the decoding matrix in subsequent steps. And ultimately used for feature selection and data reconstruction.

[0072] S6, based on ,renew ; In S3, the decoding matrix has already been initialized. It is a 5×2 matrix, and the correlation matrix is ​​updated in S4 and S5. Parameters The update formula reflects the dynamic adjustment characteristics of the fuzzy elastic network. This is achieved by combining the decoding matrix... of L 2-norm sum L p Norm, Able to adaptively adjust the regularization term L 2-norm sum L p The norm weights are used to balance sparsity and globality during feature selection. Updated This will be used as a diagonal matrix in subsequent steps. The update further guides the decoding matrix. The direction of optimization.

[0073] S7, based on , , , , and decoding matrix Update the diagonal matrix Its diagonal element is ; matrix diagonal elements This reflects the effect of each feature vector on the current decoding matrix. The relative importance and sparsity of the matrix. These values ​​will be used in subsequent steps to decode the matrix. The update is performed by updating the diagonal matrix. Fuzzy elastic networks can dynamically adjust the weight of each feature, thereby better balancing the sparsity and wholeness of features in subsequent optimization processes.

[0074] S8, Based on Data Matrix Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix ; In this embodiment, the decoding matrix is ​​updated. The formula is:

[0075] When data dimensions d Much larger than the number of data points n When needed, the following formula can be used to update. :

[0076] By combining data matrices Centralized matrix diagonal matrix Encoding matrix The updated decoding matrix It is better adapted to the characteristics of the data and the current optimization status. Updated This will be used for feature selection and data reconstruction in subsequent steps to further optimize the objective function. .

[0077] S9, according to Calculate the objective function value; objective function This includes a data reconstruction error term and a regularization term. The data reconstruction error term measures the decoding matrix. and encoding matrix For raw data The reconstruction capability is enhanced, and the regularization term balances the sparsity and globality of feature selection through the characteristics of fuzzy elastic networks. Objective function The value is used to determine the convergence and optimization direction of the algorithm. During subsequent iterations, the algorithm will continuously adjust... and To minimize .

[0078] S10. Determine if the termination condition is met; if the termination condition is met, proceed to S11; if the termination condition is not met, return to S4; in this embodiment, the termination condition includes: the number of iterations reaches a set number; and / or, the target value obtained in two adjacent iterations... The difference Less than the set threshold.

[0079] S11. Sort the eigenvectors in the updated reconstructed transformation matrix and select the top ones. Construct the optimal feature subset from the largest eigenvectors. ; It is a positive integer greater than or equal to 1. This is achieved by calculating the eigenvector of each feature vector. L Using the 2-norm and sorting it in descending order, we can determine which eigenvectors are more important for representing the data. Larger eigenvectors... L The 2-norm indicates that the eigenvector has a stronger representational power in the data. Before selection... Construct the optimal feature subset from the largest eigenvectors. This ensures that the selected feature subset retains the main features and information of the original data to the greatest extent possible.

[0080] In this embodiment, S11, the eigenvectors in the updated reconstructed transformation matrix are sorted, and the top ones are selected. Construct the optimal feature subset from the largest eigenvectors. ; A positive integer greater than or equal to 1, followed by: S12. Utilizing the optimal feature subset The test data is denoised and reconstructed to obtain the transformed data.

[0081] For example, based on the formula:

[0082] Test data matrix Denoising and reconstruction are performed, among which It is the data matrix to be tested. It is the optimal feature subset. This is the corresponding encoding matrix. It is achieved by projecting the test data onto a subset of optimal features. Reconstructing the data within a defined low-dimensional space removes noise while preserving key structural features. This improves the accuracy and reliability of subsequent data analysis. The final transformed data... It is data that has been denoised and reconstructed, which can better reflect the essential characteristics of the data and is suitable for further analysis and modeling.

[0083] Example 2 This embodiment, based on the method described in one of the embodiments, uses a feature selection method based on fuzzy elastic networks to analyze beach sediment data. After dimensionality reduction to 1D and 2D, it employs the k-means clustering algorithm for cluster analysis. Please refer to [link to relevant documentation]. Figure 2 Experimental results show that the ACC and NMI indices reach 100% in both dimensionality reduction cases, which fully demonstrates that the fuzzy elastic net algorithm can effectively select the most representative features from the original data, reduce the dimensionality of the data, and retain the key information of the data, proving the high accuracy and effectiveness of the proposed method in feature selection.

[0084] Example 3 This embodiment, based on the method described in one of the embodiments, uses the ORL face image dataset as an example to illustrate the implemented scheme. The sample image is segmented into multiple 32×32 pixel face images. The above sample images are then used to reconstruct the face images using the method disclosed in one of the embodiments; the specific steps are not detailed here. The parameters... The value was gradually adjusted from 0.1 to 0.9, and the number of features was gradually increased from 100 to 900, with 100 features added at each step. The purpose was to observe the performance of the fuzzy elastic net in balancing group sparsity and sparsity (see [link to relevant documentation]). Figure 3 (The gray area represents the selected features, and the white area represents the unselected features).

[0085] The results of Examples 2 and 3 fully verify the effectiveness of the algorithm of the present invention. The algorithm of the present invention is expected to show better performance when processing more complex datasets in practical applications (including genomics, computer vision, medicine, speech recognition, and pharmaceuticals).

[0086] Example 4 Please see Figure 4 A data analysis system for feature selection based on fuzzy elastic networks, characterized in that, based on the method described in one of the embodiments, the system includes: The data transformation module is used to transform raw beach sediment data into a data matrix. ; The first initialization module is used to set the dimensions after dimensionality reduction. hyperparameters , and And, convergence threshold , L P norm value, Maximum number of iterations ; The second initialization module is used to initialize the projection matrix. Decoupled into a decoding matrix and an encoding matrix ,satisfy ; data matrix Perform eigenvalue decomposition and take right singular matrix forward Initialization, The dimension after dimensionality reduction; initialize the centralized matrix. ,in, ; It is the identity matrix. It is a column vector with all elements being 1; The first update module is used for... Update the left and right singular matrices , , It is a diagonal matrix composed of singular values; The second update module is used for... Update the encoding matrix ; The third update module is used for... ,renew ; The fourth update module is used for... , , , , and decoding matrix Update the diagonal matrix Its diagonal element is ; The fifth update module is used for data matrix-based updates. Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix ; The sixth update module is used to update according to Calculate the objective function value; The judgment module is used to determine whether the termination condition is met; if the termination condition is met, the feature vector selection module is triggered; if the termination condition is not met, the first update module is triggered. The eigenvector selection module sorts the eigenvectors in the updated reconstructed transformation matrix and selects the first eigenvectors. Construct the optimal feature subset from the largest eigenvectors. ; It is a positive integer greater than or equal to 1.

[0087] In order to better utilize the above methods, this application proposes a data analysis system for feature selection based on fuzzy elastic networks. Each module corresponds to a step of the above methods, and its specific principles have been described above and will not be repeated here.

[0088] In this embodiment, the termination condition includes: The set number of iterations has been reached; Or the target value obtained from two adjacent iterations The difference Less than the set threshold.

[0089] In this embodiment, the fifth update module is specifically used for: through renew ;when It can be used renew .

[0090] In this embodiment, the system further includes: a data reconstruction module; This data reconstruction module is used to utilize the optimal feature subset. The test data is denoised and reconstructed to obtain the transformed data.

[0091] In this embodiment, the system further includes a result evaluation module, which evaluates the data reconstruction results using accuracy (ACC) and standard mutual information entropy (NMI).

[0092] In the results evaluation module, this invention uses ACC and NMI to evaluate the dimensionality-reduced data; For the data dimensionality reduction evaluation process, the clustering results of the data were further compared using a k-means classifier, with the accuracy of cluster recognition being a key factor. . Indicates the first i The real number labels of each instance, and It is the corresponding clustering index. This represents a function that maps each cluster index to the best class label. express A function, that is, when two input parameters are given... and If the values ​​are the same, the value is 1; otherwise, it is 0. The higher the ACC value, the higher the clustering accuracy.

[0093] Furthermore, the standard mutual information entropy (NMI) is used as a control. For two different clustering results A and B, the standard mutual information is defined as follows:

[0094] in, It is the sample size. It is a confusion matrix, with elements... This indicates that it belongs to the A-class cluster result of the first... i The results of clustering classes A and B are as follows: j Number of samples in the class This represents the total number of clusters in the clustering results of A (B). The larger the NMI value, the more similar the clustering results A and B are.

[0095] Example 5 A data analysis device for feature selection based on fuzzy elastic networks, comprising: At least one processor and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the method described in one of the embodiments.

[0096] In the above technical solution, in order to better operate and process the method described in one of the embodiments, the method is stored in a memory, and the stored method is executed by a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated further here.

[0097] Example 6 A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in one of the embodiments.

[0098] In the above technical solution, to better operate and use the method described in one of the embodiments, the method is stored in a computer-readable storage medium and implemented using a processor. It should be noted that the principle and effect of each step have been described above and will not be elaborated further here.

[0099] The above description is only a part of the embodiments of the present invention and does not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made based on the content of the present invention specification and drawings, or direct or indirect application in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for analyzing beach sediment data based on feature selection using fuzzy elastic nets, characterized in that, The method includes: S1. Transform raw beach sediment data into a data matrix. , n The number of data points d For data dimensions; S2, Set the dimensions after dimensionality reduction hyperparameters , and And, convergence threshold , L P norm value, Maximum number of iterations ; S3, Project the matrix Decoupled into a decoding matrix and an encoding matrix ,satisfy ; data matrix Perform eigenvalue decomposition and take right singular matrix forward Initialization, The dimension after dimensionality reduction; initialize the centralized matrix. ,in, ; It is the identity matrix. It is a column vector with all elements being 1; S4, based on Update the left and right singular matrices , , It is a diagonal matrix composed of singular values; S5, based on Update the encoding matrix ; S6, based on ,renew , Representation matrix W The i OK; S7, based on , , , , and decoding matrix Update the diagonal matrix Its diagonal element is ; S8, Based on Data Matrix Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix ; S9, according to Calculate the objective function value; S10. Determine if the termination condition is met; if the termination condition is met, execute S11; if the termination condition is not met, return to S4. S11. Sort the eigenvectors in the updated reconstructed transformation matrix and select the top ones. Construct the optimal feature subset from the largest eigenvectors. ; It is a positive integer greater than or equal to 1.

2. The method for analyzing beach sediment data based on feature selection using a fuzzy elastic net as described in claim 1, characterized in that, The termination conditions include: The set number of iterations has been reached; And / or, The target value obtained in two consecutive iterations The difference Less than the set threshold.

3. The method for analyzing beach sediment data based on feature selection using a fuzzy elastic net, as described in claim 1, is characterized in that... Based on data matrix Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix Specifically, this includes: through renew ;when ,use renew .

4. The method for analyzing beach sediment data based on feature selection using a fuzzy elastic net as described in claim 1, characterized in that, S11. Sort the eigenvectors in the updated reconstructed transformation matrix and select the top ones. Construct the optimal feature subset from the largest eigenvectors. ; A positive integer greater than or equal to 1, followed by: S12. Utilizing the optimal feature subset The test data is denoised and reconstructed to obtain the transformed data.

5. A beach sediment data analysis system based on feature selection using fuzzy elastic nets, characterized in that, Based on the method according to any one of claims 1-4, the system comprises: The data transformation module is used to transform raw beach sediment data into a data matrix. ; The first initialization module is used to set the dimensions after dimensionality reduction. hyperparameters , and And, convergence threshold , L P norm value, Maximum number of iterations ; The second initialization module is used to initialize the projection matrix. Decoupled into a decoding matrix and an encoding matrix ,satisfy ; data matrix Perform eigenvalue decomposition and take right singular matrix forward Initialization, The dimension after dimensionality reduction; initialize the centralized matrix. ,in, ; It is the identity matrix. It is a column vector with all elements being 1; The first update module is used for... Update the left and right singular matrices , , It is a diagonal matrix composed of singular values; The second update module is used for... Update the encoding matrix ; The third update module is used for... ,renew ; The fourth update module is used for... , , , , and decoding matrix Update the diagonal matrix Its diagonal element is ; The fifth update module is used for data matrix-based updates. Centralized matrix diagonal matrix Encoding matrix Update the decoding matrix ; The sixth update module is used to update according to Calculate the objective function value; The judgment module is used to determine whether the termination condition is met; if the termination condition is met, the feature vector selection module is triggered; if the termination condition is not met, the first update module is triggered. The eigenvector selection module sorts the eigenvectors in the updated reconstructed transformation matrix and selects the first eigenvectors. Construct the optimal feature subset from the largest eigenvectors. ; It is a positive integer greater than or equal to 1.

6. The beach sediment data analysis system based on feature selection using a fuzzy elastic net as described in claim 5, characterized in that, The termination conditions include: The set number of iterations has been reached; Or the target value obtained from two adjacent iterations The difference Less than the set threshold.

7. The beach sediment data analysis system based on feature selection using a fuzzy elastic net as described in claim 5, characterized in that, The fifth update module is specifically used for: through renew ;when It can be used renew .

8. The beach sediment data analysis system based on feature selection using a fuzzy elastic net as described in claim 5, characterized in that, The system also includes: a data reconstruction module; This data reconstruction module is used to utilize the optimal feature subset. The test data is denoised and reconstructed to obtain the transformed data.

9. A beach sediment data analysis device based on feature selection using a fuzzy elastic net, characterized in that, include: At least one processor and a memory communicatively connected to said at least one processor; The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method as described in any one of claims 1 to 4.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 4.

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