Feature selection method and data reconstruction method for shoreline image feature selection

Abstract

The invention discloses a feature selection method and a data reconstruction method for shoreline image feature selection. The method comprises the following steps: S1, integrating original data into a sample data set matrix X; s2, initializing a reconstruction transformation matrix W, a transformation matrix Q, an eigenvalue regression coefficient matrix A, a coordinate basis matrix B, a coding matrix E, an auxiliary matrix F and an auxiliary matrix D as unit matrixes, initializing a weight vector p and a mean vector v of a data set as unit vectors, and initializing a weight matrix P = diag (p); and S3, updating the coding matrix E, the auxiliary matrix F and the like based on the data set matrix X, the mean vector v of the data set, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B and the weight matrix P. According to the invention, the accuracy of data reconstruction and the validity of feature selection can be improved.

Description

Technical Field

[0001] This invention relates to the field of data reconstruction technology, and in particular to a feature selection method and a data reconstruction method for shoreline image feature selection. Background Technology

[0002] With the rapid development of science and technology, the dimensionality of data is exploding. Directly using this high-dimensional data can lead to increased computational complexity and a significant decline in learning performance due to unimportant data features, and can also interfere with the algorithm's extraction of the data's essential structure. For example, in oceanography, advancements in marine observation technologies, such as remote sensing satellites, automated sensors, and underwater robots, have greatly increased the dimensionality and complexity of marine data. Coastline images contain various variables, including the intertidal zone, beach tide lines, wave break zones, wave crest lines, and vegetation lines. They are direct products and recorders of the interaction between ocean dynamics (tides, waves) and land (beach), serving as an indispensable "natural benchmark" for scientists to interpret coastal changes and conduct coastal management. However, directly using this high-dimensional data for analysis not only increases computational complexity but may also obscure the understanding of key ocean phenomena. Therefore, how to effectively reduce the dimensionality of these coastline images to extract key features has become an urgent problem to be solved in marine scientific research. The usual approach to processing high-dimensional data is to create a low-dimensional structure that reflects the essential structure of the data. Under this approach, there are two different research directions: feature selection and feature extraction (subspace learning).

[0003] Feature selection is the process of choosing a relevant subset of features from a raw feature set. Based on whether or not the data's label information is utilized, feature selection is divided into supervised and unsupervised learning methods. Supervised feature selection uses the label information inherent in the data to guide the model's optimization direction, selecting a subset of features that best represent the data. Supervised feature selection typically involves first training the model to optimize parameters, and then testing the model. Due to the introduction of data label information, supervised feature selection methods generally outperform unsupervised feature selection methods in testing. However, in practical applications, obtaining data label information is costly; therefore, unsupervised feature selection methods have a wider range of applications.

[0004] Many unsupervised feature selection methods have been proposed to find the optimal feature subset. The Laplacian Score (LS) measures feature importance by calculating the local correlation between different features. Multi-Cluster Feature Selection (MCFS) utilizes spectral analysis theory to preserve the multi-cluster structure of the data and consider the correlation between features to select the optimal feature subset. Both LS and MCFS consider the correlation between features when selecting feature subsets, thus achieving better results than traditional feature selection methods that ignore the correlation between features. Subsequently, feature selection algorithms focus on optimizing the feature selection process by utilizing the discriminative information (pseudo-labels) of the dataset. Unsupervised Discriminative Feature Selection (UDFS) obtains local discriminative information of the data by restricting the feature weight matrix. Nonnegative Discriminative Feature Selection (NDFS) obtains pseudo-labels, i.e., the discriminative information of the data, by performing spectral clustering on the data, which is used to optimize feature selection. The Simultaneous Orthogonal Basis Clustering Feature Selection (SOCFS) proposed by Han et al. integrates the two processes of vertical basis clustering and feature selection into a single term in the objective equation. The vertical basis clustering process and the feature selection process are carried out simultaneously. The pseudo-labels generated by vertical basis clustering are used to obtain the discriminative information of the data, thereby improving the effect of feature selection.

[0005] The feature selection methods proposed above do not consider the case where the data contains a large amount of noisy features. In cases of low data quality, if feature selection is performed directly on the original dataset, noisy features and outliers may interfere with the algorithm's search for the most effective feature subset, leading to poor algorithm performance. Subsequently, robust feature selection algorithms consider the impact of noisy features on the data, enhancing the algorithm's robustness to noise. Robust Unsupervised Feature Selection (RUFS) proposes a locally learned regularized robust nonnegative matrix factorization method to generate cluster pseudo-labels and enhance the algorithm's robustness to outliers and noise. Robust Spectral Learning for Unsupervised Feature Selection (RSFS) proposes a feature selection algorithm that combines a robust graph embedding process (pseudo-labels) and a robust spectral regression process, further enhancing the algorithm's robustness to noise and outliers. Recently, Yi et al. proposed Adaptive Weighted Sparse Principal Component Analysis (AW-SPCA), which combines feature selection and feature extraction, focusing on the reconstructed data obtained after reconstructing the original data, in order to enhance the algorithm's performance on heavily polluted data.

[0006] Feature selection chooses a subset of features from the original data, which can preserve data information relatively completely, reflect the nature of the data, and has good interpretability. However, if the original data is contaminated with noise, the effectiveness of feature selection algorithms will be greatly reduced. Feature extraction, on the other hand, maps the original data to a low-dimensional space, which can reflect the essential structural features of the data. Feature extraction is not simply selecting features from the original data to form a new feature subset, but rather obtaining the data through spatial transformation according to a certain strategy. Therefore, under a good transformation strategy, feature extraction methods can ensure the quality of dimensionality reduction while extracting the low-dimensional flow structure of the data, effectively eliminating the influence of noise and outliers. Classic feature extraction methods include Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA).

[0007] Feature selection and feature extraction methods each have their own advantages. In recent years, many new models have combined the two methods to improve model performance, which is a field worth studying. Summary of the Invention

[0008] In view of this, the purpose of this invention is to propose a feature selection method and a data reconstruction method for shoreline image feature selection. The method disclosed in this invention has better accuracy and robustness, especially with higher fitting on noisy datasets. Furthermore, it can perform dimensionality reduction on image data, video data, document data, or website data, thereby improving the effectiveness of dimensionality reduction.

[0009] According to one aspect of the present invention, a feature selection method is provided, the method comprising:

[0010] S1. Integrate the original data into a sample dataset matrix X;

[0011] S2. Initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p).

[0012] S3. Based on the dataset matrix X, the dataset mean vector v, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P, update the encoding matrix E and the auxiliary matrix F;

[0013] S4. Update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and auxiliary matrix F;

[0014] S5. Determine if the termination condition is met; if the termination condition is met, proceed to S6; if the termination condition is not met, return to S3.

[0015] S6. Sort the eigenvectors in the updated transformation matrix Q, and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1.

[0016] S7. Use the optimal feature subset W′ to denoise and reconstruct the dataset matrix X to obtain the denoised data.

[0017] In the aforementioned technical solutions, dimensionality reduction of high-dimensional data is a key task in processing complex data in fields such as oceanography. Feature selection and feature extraction are two mainstream methods, but each has its limitations: feature selection is easily compromised in noisy environments, while feature extraction can improve robustness through spatial transformation but may sacrifice interpretability. This solution proposes a feature selection method that introduces reconstruction transformation, matrix update, and iterative optimization processes, aiming to combine the advantages of feature selection and extraction to improve accuracy and robustness under noisy data. The following analysis will focus on the correlation between the solution steps and the background technology, emphasizing how it addresses noise interference, achieves the fusion of feature selection and extraction, and fulfills the aforementioned advantages.

[0018] First, in stages S1 and S2, the scheme integrates the original data into a matrix X and initializes multiple parameters (such as the reconstruction transformation matrix W, transformation matrix Q, etc.), which reflects the intention to model the essential structure of the data. Background technology points out that high-dimensional data often contains noisy features, and direct feature selection may be affected. This scheme, by initializing the weight matrix P and the mean vector v, lays the foundation for subsequent robust optimization and introduces regularization or non-negative matrix factorization to enhance resistance to outliers.

[0019] Secondly, the iterative update processes of S3 and S4 are the core of the scheme. By alternately updating the encoding matrix E, the auxiliary matrix F, and other parameters, the synergistic optimization of feature selection and extraction is demonstrated. Background techniques emphasize that feature selection methods such as UDFS and NDFS utilize pseudo-labels to guide optimization, while this scheme achieves a process similar to spectral clustering or local learning through matrix updates (such as the transformation matrix Q and the eigenvalue regression coefficient matrix A) to extract discriminative information from the data. Simultaneously, the update of the weight matrix P borrows the adaptive weighting strategy from AW-SPCA, assigning higher weights to important features to maintain stability in noisy environments, which aligns with the goal of robust feature selection methods mentioned in the background.

[0020] Finally, stages S6 and S7 construct the optimal feature subset by selecting the first d eigenvectors of the transformation matrix Q, and then perform data denoising and reconstruction, embodying the idea of ​​feature extraction. Background technology indicates that feature extraction can eliminate noise through spatial transformation, while this scheme introduces a reconstruction step after feature selection, which not only preserves the interpretability of feature selection but also integrates the denoising capabilities of feature extraction. The overall iterative framework of the scheme (termination condition S5) ensures optimization convergence and may improve the fitting accuracy on complex data such as images and videos.

[0021] In summary, this scheme effectively integrates the elements of feature selection and extraction through matrix initialization, iterative updates, and feature subset reconstruction. Its improved robustness and accuracy under noisy data benefit from the utilization of data discriminative information and the introduction of adaptive weights. Compared with traditional methods such as LS and MCFS in the background, this scheme is closer to robust methods such as RUFS and AW-SPCA, but further enhances the dimensionality reduction effect through integrated transformation and reconstruction steps.

[0022] In some embodiments, the termination condition includes: the number of iterations reaches a set number or the difference ΔJ between the target values ​​J obtained from two adjacent iterations is less than a set threshold.

[0023] In the above technical solutions, the termination condition is a key control element for the convergence of the optimization algorithm. The termination condition set in this solution aims to balance computational efficiency and solution accuracy, ensuring that the feature selection process can stably approach an optimal or suboptimal solution under noise interference, thereby supporting the accuracy and robustness of the solution.

[0024] First, the termination condition is determined by monitoring the convergence of the objective function value J. The core of feature selection is finding a low-dimensional subset that reflects the inherent structure of the data. In iterative optimization, the objective function J is defined as a metric to measure feature importance or data reconstruction error. When ΔJ is sufficiently small, it indicates that the algorithm's allocation of feature weights or the pseudo-labeling information of the data has stabilized. At this point, the resulting transformation matrix Q and weight matrix P can more reliably capture the essential features of the data, rather than overfitting noise.

[0025] Secondly, setting a maximum number of iterations as a backup termination condition enhances the algorithm's practicality and robustness under complex real-world data. Background technology indicates that high-dimensional data (such as shoreline images) often contains a large amount of noise and outliers, causing the optimization process to oscillate or converge slowly. Setting a maximum number of iterations prevents the algorithm from getting stuck in an infinite loop or excessively consuming computational resources, ensuring the method's feasibility within a finite timeframe.

[0026] Finally, this termination condition, together with the matrix iterative update (S3-S4) in the scheme, forms a complete closed-loop optimization framework. This allows the algorithm to adaptively determine the optimization depth: stopping early to save computation when data quality is good and convergence is fast; and refining the results through more iterations when noise interference is high and convergence is slow. This dynamic adjustment capability helps the final optimal feature subset W′ to more effectively remove noise and retain key information during data reconstruction in step S7, thus directly contributing to the scheme's advantage of "higher fit on noisy datasets."

[0027] In summary, the composite termination condition employed in this scheme is not an isolated step, but rather an important component embedded in its overall robust optimization logic. By ensuring the sufficiency and necessity of the optimization process, it indirectly improves the quality and stability of the feature selection results. Compared to earlier methods mentioned in the background (such as LS and MCFS), this design demonstrates finer control over the algorithm's convergence behavior.

[0028] In some embodiments, S3, updating the encoding matrix E and auxiliary matrix F based on the dataset matrix X, the mean vector v of the dataset, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P, specifically includes:

[0029] S31, Regarding B T AQ T MP+γF T Perform singular value decomposition to obtain the left singular matrix U. E and the right singular matrix V E ;

[0030] S32, according to Update the encoding matrix E;

[0031] S33, according to Update the auxiliary encoding matrix F.

[0032] In the above technical solution, within the iterative optimization framework of the feature selection method, the core task of step S3 is to update the encoding matrix E and its auxiliary matrix F. This process is not a simple parameter adjustment, but rather a deep mining and refinement of the data's intrinsic structure by introducing singular value decomposition (SVD) and specific nonlinear transformations. This step embodies the core ideas described in the background technology of "using the discriminative information (pseudo-labels) of the dataset to guide the optimization of the feature selection process" and "enhancing the algorithm's robustness to noise," and is crucial to ensuring that the entire method maintains high accuracy and strong robustness in noisy environments.

[0033] First, in step S31, the constructed matrix B... T AQ T MP+γF T Performing Singular Value Decomposition (SVD) is the essence of this step. SVD is a classic feature extraction technique that reveals the principal component structure of the data. The input matrix here integrates the coordinate basis matrix B, the eigenvalue regression coefficient matrix A, the transformation matrix Q, and the weight matrix P under the current iteration. The update process is not performed in isolation but is tightly coupled with the spatial transformation of the data (feature extraction idea) and the importance weights of the features (feature selection idea). Obtaining its principal components (left and right singular matrices) through SVD lays the foundation for the next step of generating a statistically superior encoding matrix E that better reflects the essential structure of the data.

[0034] Secondly, step S32 utilizes the results of SVD to perform calculations. To update the encoding matrix E. Here, I... n,k This is an identity matrix used to select the top k principal components. Mathematically, this operation is equivalent to projecting the data onto a low-dimensional subspace spanned by the principal singular vectors. The resulting encoding matrix E can be viewed as a pseudo-label obtained after a series of transformations of the original data; it encapsulates the discriminative information of the data under the current parameters. This is consistent with the approach of methods such as NDFS and SOCFS mentioned in the background, which use spectral clustering or vertical basis clustering to generate pseudo-labels to guide feature selection. However, its implementation path, through matrix decomposition and projection, offers greater numerical stability and theoretical assurance.

[0035] Finally, step S33 is achieved through the formula. Updating the auxiliary matrix F is a typical nonlinear operation based on the Rectified Linear Unit (ReLU) concept. This operation sets all negative values ​​in the encoding matrix E to zero, while retaining non-negative values. This design has two implications: first, it introduces nonlinearity, enabling the model to capture more complex data patterns; second, and more importantly, by enforcing nonnegativity, it enhances the sparsity and discriminativeness of the representation, helping to suppress random fluctuations caused by noise and outliers.

[0036] In summary, step S3, through a series of mathematical operations including SVD, projection, and nonlinear transformation, effectively updates the data encoding and auxiliary information. It integrates the subspace learning concept from feature extraction into the feature selection optimization framework, guiding subsequent feature weight learning by generating high-quality codes (pseudo-labels). This step not only inherits strategies like UDFS and NDFS that utilize discriminative information, but also enhances the algorithm's robustness to noise and outliers through the stability of SVD and the sparsity-enhancing properties of ReLU, achieving the core advantage of this invention: higher fitting accuracy on contaminated data.

[0037] In some embodiments, S4, updating the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and auxiliary matrix F, specifically includes:

[0038] S41, according to Update the transformation matrix Q;

[0039] S42. Calculate the central vector matrix v according to the following formula:

[0040]

[0041] S43, To E T PMT QA T Perform singular value decomposition to obtain the left singular matrix U. B and the right singular matrix V B ;according to Update the coordinate basis matrix B;

[0042] S44, Q T MM T Perform singular value decomposition to obtain the left singular matrix U. W and the right singular matrix V W ;according to Update and reconstruct the transformation matrix W;

[0043] S45, Q T MPEB T Perform singular value decomposition to obtain the left singular matrix U. A and the right singular matrix V A ;according to Update the eigenvalue regression coefficient matrix A;

[0044] S46, Through Calculate the minimized reconstruction error matrix G; according to Calculate the weight matrix P.

[0045] In the above technical solution, step S4 is responsible for updating the core parameters. Based on the encoding matrices E and F obtained in step S3, which contain data discrimination information, this step systematically updates all key parameters, including the transformation matrix Q, mean vector v, coordinate basis matrix B, reconstructed transformation matrix W, eigenvalue regression coefficient matrix A, and the crucial weight matrix P, through a series of matrix operations. This process is not an isolated parameter adjustment, but a tightly coupled systematic re-estimation, embodying the core ideas of "combining feature selection and feature extraction" and "enhancing the algorithm's robustness to noise and outliers." It is the cornerstone of the algorithm for achieving high-precision and robust dimensionality reduction.

[0046] First, steps S41, S43, S44, and S45 all update the key transformation matrices (Q, B, W, A) by solving closed-form solutions or performing singular value decomposition (SVD). These operations are essentially manifestations of the feature extraction process. For example, the formula for updating the transformation matrix Q in S41 includes reconstruction and encoding regression terms, and its inverse operation aims to find an optimal transformation that simultaneously balances data reconstruction fidelity and latent encoding representation. SVD is repeatedly used in S43, S44, and S45 to update B, W, and A. This allows the algorithm to continuously refine the orthogonal coordinate basis and essential structure of the data, ensuring dimensionality reduction quality while extracting the low-dimensional manifold structure of the data, effectively eliminating the influence of noise and outliers.

[0047] Secondly, step S46, by minimizing the reconstruction error and adaptively updating the weight matrix P accordingly, is the key mechanism for achieving robust feature selection in this method. This step first calculates the reconstruction error matrix G, whose Frobenius norm is minimized by the objective function. The quality of data reconstruction under the current parameters was measured. Then, according to the formula... Calculate the weight p for each feature i This design assigns smaller weights to features with large reconstruction errors (such as noise or outliers), thus suppressing them in subsequent iterations and enhancing the model's resistance to noise by dynamically evaluating feature quality.

[0048] Finally, step S42 updates the mean vector v of the dataset, a data centering process. The complex calculations aim to accurately estimate the center of the data, taking into account information from both the original data space and the encoding space. An accurate center estimate is crucial for all subsequent distance- or correlation-based calculations, effectively improving the overall stability of the algorithm, especially when dealing with imbalanced datasets or datasets containing global outliers.

[0049] In summary, step S4 is a multi-objective, collaboratively optimized parameter update stage. It mines the essential structure of the data by fusing feature extraction techniques (SVD, matrix factorization) while embedding a robust feature selection mechanism (adaptive weight update) to dynamically identify and suppress the interference of noisy features. This deep integration of feature selection and feature extraction not only responds to the research trend mentioned in the background section of the invention—"combining the two methods to improve model performance"—but also ensures, through systematic parameter coupling optimization, the core advantages of this invention: higher fitting accuracy and stronger robustness on noisy data.

[0050] In some embodiments, the coordinate basis matrix B satisfies B T Orthogonal constraint condition B = I;

[0051] The encoding matrix E satisfies E T The constraints are E = I and E ≥ 0.

[0052] The auxiliary variable matrix F satisfies the constraint E = F.

[0053] In the above technical solution, the constraints imposed on the coordinate basis matrix B, the encoding matrix E, and the auxiliary matrix F are the core design for achieving the algorithm's objective. These constraints collectively construct a stable, efficient, and highly interpretable optimization space, fulfilling the core requirements described in the background technology of "finding a low-dimensional structure that reflects the essential structure of the data" and "enhancing the robustness of the algorithm."

[0054] First, the coordinate basis matrix B satisfies B TThe B = I (orthogonality) constraint forces the column vectors of matrix B to form a set of orthonormal bases. Its advantages are: orthonormal bases ensure that features across dimensions are uncorrelated after dimensionality reduction, thus avoiding information redundancy and ensuring the efficiency of extracted features. Orthogonal transformations preserve norm, significantly improving the numerical stability of the algorithm in iterative optimization and preventing ill-conditioned matrix problems. This method can find an orthogonal subspace that best represents the variance distribution of the original data, thereby better capturing the essential manifold structure of the data.

[0055] Secondly, the E that the encoding matrix E satisfies T The dual constraints of E = I (orthogonality) and E ≥ 0 (non-negativity) are key to achieving high-quality pseudo-labels. T The E=I constraint ensures that the encoded vectors are orthogonal to each other, representing different "clusters" or "components" in the data, facilitating the separation of discriminative information and preserving the multi-cluster structure of the data. The E≥0 constraint introduces sparsity and partial basis representation. Non-negative encoding is easier to interpret, as its elements often correspond to the "presence" or "contribution" of specific features, rather than abstract values ​​of positive and negative cancellation. This "additive" combination helps the model capture the local composition of the data and has been shown to be more robust to noise.

[0056] Finally, within the optimization framework of the method, an auxiliary variable matrix F is introduced and the constraint E = F is imposed. Its core objective is to address the complex constrained optimization problem (E) where the encoding matrix E is non-convex, non-smooth, and orthogonal. T The problem (E = I, E ≥ 0) is decomposed into a series of more manageable and computationally stable subproblems. Ensuring the non-negativity of the final encoding E guarantees the feasibility and convergence of the entire iterative algorithm. Given E... T Solving for a non-negative matrix E≥0 under the condition E=I is a computationally difficult non-convex optimization problem. Many standard matrix factorization algorithms (such as SVD) do not inherently guarantee the non-negativity of the result when generating orthogonal bases. Therefore, the solution adopts a variable splitting strategy, that is, introducing an auxiliary variable F equal to E, thereby decomposing the original problem: (1) Update E. In this step (S31, S32), the algorithm can temporarily "ignore" the non-negativity constraint and focus on optimizing the objective function under orthogonality constraints through singular value decomposition (SVD) to obtain an orthogonal intermediate encoding matrix that best reflects the current discriminative structure of the data but may contain negative values. SVD provides a numerically stable and theoretically complete solution for this. (2) Update F. In this step (S33), the algorithm focuses on handling non-negativity. Formula This is a classic Rectified Linear Unit (ReLU) operation that sets all negative elements in the intermediate encoding matrix E to zero, thus producing a purely non-negative auxiliary matrix F. Mathematically, this operation is equivalent to projecting onto a non-negative orthogonal matrix. Secondly, the constraint E = F serves as a bridge connecting these two subproblems, ensuring that the split variables are eventually unified. In an ideal convergence state, the algorithm finds a solution that makes E obtained through SVD identical to F obtained through ReLU, i.e., E = F and F ≥ 0. At this point, the encoding matrix E obtained through SVD is naturally a non-negative matrix. Therefore, the constraint E = F essentially sets a goal for the entire optimization process: to find an encoding matrix that simultaneously satisfies orthogonality and non-negativity. This constraint guides E and F to approach and correct each other during iterations until they reach a consensus. This design allows the encoding matrix E to simultaneously possess the discriminative power of an orthogonal basis and the sparsity and robustness of a non-negative representation.

[0057] In summary, the constraint design for B, E, and F forms an interconnected and synergistic organic whole. Orthogonal constraints aim to find a concise, non-redundant, and highly discriminative data representation space; non-negativity constraints enhance the model's interpretability and robustness to noise; and equality constraints serve as the computational bridge for this complex optimization process. These constraints collectively ensure that this feature selection method can stably extract essential, discriminative low-dimensional structures from potentially contaminated high-dimensional data, demonstrating the core advantages of this invention in terms of accuracy and robustness.

[0058] In some embodiments, S7 involves denoising and reconstructing the dataset matrix X using the optimal feature subset W′ to obtain denoised data, and then further includes:

[0059] The reconstructed data after dimensionality reduction is evaluated, and the quality of dimensionality reduction and denoising is analyzed. Among them, K-means clustering is performed on multiple reconstructed data, and the accuracy is represented by the ACC index.

[0060] In the above technical solution, the evaluation step introduced in step S7—namely, performing K-means clustering on the dimensionality-reconstructed data and using the ACC (Accuracy) metric for quantitative analysis—directly links the evaluation of the unsupervised dimensionality reduction effect to the performance of downstream machine learning tasks, providing objective and quantifiable empirical evidence for "better accuracy and robust performance."

[0061] First, since this method is unsupervised (does not rely on true labels), its dimensionality reduction effect needs to be indirectly measured by the performance of unsupervised learning tasks. Clustering, as one of the most classic and widely used unsupervised learning tasks, directly reflects whether the data retains its inherent cluster structure after dimensionality reduction. A high-quality dimensionality reduction and denoising process should make the essential cluster structure of the data clearer and more separable, thereby improving the performance of the clustering algorithm.

[0062] Secondly, the supervised metric ACC (Accuracy) is used to evaluate unsupervised clustering results. The procedure involves obtaining cluster labels (pseudo-labels) and comparing them with the true labels of the data (if known). The ACC is calculated by determining the proportion of correctly assigned samples across all samples. This requires the evaluator to have information about the true categories of the data. The advantage of this approach is that it provides a clear and objective numerical measure of the clustering quality of the dimensionality-reduced data and its close match to real-world classifications, avoiding subjective judgment. A high ACC can also prevent a significant decline in the performance of the learning task; a higher ACC means that the dimensionality-reduced data is more conducive to subsequent pattern recognition and knowledge discovery, such as more accurately identifying different coastal zone types in shoreline images.

[0063] Finally, this evaluation step, together with the preceding steps, forms a complete processing-verification chain. The optimal feature subset W′ is obtained through iterative optimization in S1-S6, with the goal of extracting the essential structure and removing noise. Data reconstruction and denoising in S7 are the direct outputs of this goal. The final clustering evaluation verifies whether this output truly and effectively mitigates the problem. If a high ACC is achieved in this step, it strongly demonstrates that the method has successfully extracted key features with discriminative information, effectively eliminated the interference of noise and outliers, improved data purity, and realized the advantages of combining feature selection and feature extraction, thereby improving the performance of the learning task.

[0064] According to another aspect of the present invention, a data reconstruction method for shoreline image feature selection is provided, the method comprising: selecting features of the shoreline image using the above method for data reconstruction.

[0065] In the above technical solution, the robust dimensionality reduction method that integrates feature selection and feature extraction is applied to shoreline image data processing. This method, through adaptive weight learning and structured matrix factorization, can effectively extract key features from high-dimensional shoreline images containing environmental noise and achieve high-quality data reconstruction, providing a reliable data foundation for coastline change analysis. The performance advantages of this method in shoreline image processing are mainly reflected in the following three aspects:

[0066] First, this method exhibits significant robustness to complex noise in shoreline images. Shoreline images typically contain interfering factors such as wave foam, cloud shadows, and water reflections. Through a dynamic update mechanism of the adaptive weight matrix P, the algorithm can identify and suppress the contribution of these non-essential features. Simultaneously, the non-negativity and orthogonality constraints of the encoding matrix E ensure that the learned feature representations have clear physical meaning, avoiding interference from transient noise on the feature selection results.

[0067] Secondly, this method effectively preserves the structural characteristics of coastal landforms. The shoreline system is a complex spatial system composed of multiple elements such as the intertidal zone, beach surface, and vegetation line. Through orthogonal constraints of the coordinate basis matrix B and an iterative optimization process, the algorithm can capture the inherent spatial relationships between these elements and maintain their topological structure during dimensionality reduction. This allows the reconstructed data to better reflect the interaction mechanism between coastal dynamics and landform morphology.

[0068] Finally, this method significantly improves the performance of downstream analysis tasks. Quantitative evaluation using K-means clustering and the ACC index shows that the shoreline data processed by this method exhibits better inter-class separation in the feature space. This verifies the effectiveness of this method in preserving the discriminative features of different shoreline types (such as bedrock shorelines and sandy shorelines), providing more reliable data support for subsequent automatic shoreline classification and change detection.

[0069] A shoreline image feature selection and reconstruction method combines the interpretability of feature selection with the robustness of feature extraction to effectively reduce the dimensionality of high-dimensional shoreline image data. This method can suppress environmental noise interference while preserving the essential structural features of the coastline, providing a reliable technical means for coastline monitoring and research.

[0070] According to another aspect of the present invention, a feature selection system is provided, the system being based on the above-described method, comprising:

[0071] The data integration module is used to integrate the raw data into a sample dataset matrix X;

[0072] The initialization module is used to initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F, and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p).

[0073] The module for calculating the encoding matrix E and the auxiliary matrix F is used to update the encoding matrix E and the auxiliary matrix F based on the dataset matrix X, the mean vector v of the dataset, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P.

[0074] The update module is used to update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and the auxiliary matrix F.

[0075] The judgment module is used to determine whether the termination condition is met; if the termination condition is met, S6 is executed; if the termination condition is not met, S3 is returned.

[0076] The eigenvector selection module is used to sort the eigenvectors in the updated transformation matrix Q and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1.

[0077] The data reconstruction module is used to construct reconstructed data based on the updated reconstruction transformation matrix Q, the mean vector v of the dataset, and the dataset matrix X.

[0078] In order to better utilize the above method, this application proposes a feature selection system, in which each module corresponds to each step of the above method. The specific principle of the system has been described above and will not be repeated here.

[0079] According to another aspect of the present invention, a feature selection device is provided, comprising:

[0080] At least one processor and a memory communicatively connected to said at least one processor;

[0081] 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.

[0082] 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.

[0083] According to a final aspect of the present invention, a computer-readable storage medium is provided storing a computer program, characterized in that the computer program, when executed by a processor, implements the above-described method.

[0084] 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.

[0085] According to another aspect of the present invention, a data reconstruction system is provided, the system being based on the above-described method, comprising:

[0086] The data integration module is used to integrate the raw data into a sample dataset matrix X;

[0087] The initialization module is used to initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F, and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p).

[0088] The module for calculating the encoding matrix E and the auxiliary matrix F is used to update the encoding matrix E and the auxiliary matrix F based on the dataset matrix X, the mean vector v of the dataset, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P.

[0089] The update module is used to update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and the auxiliary matrix F.

[0090] The judgment module is used to determine whether the termination condition is met; if the termination condition is met, S6 is executed; if the termination condition is not met, S3 is returned.

[0091] The eigenvector selection module is used to sort the eigenvectors in the updated transformation matrix Q and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1.

[0092] The data reconstruction module is used to construct reconstructed data based on the updated reconstruction transformation matrix Q, the mean vector v of the dataset, and the dataset matrix X.

[0093] In order to better utilize the above methods, this application proposes a data reconstruction system, in which each module corresponds to each step of the above methods. The specific principles have been described above and will not be repeated here. Attached Figure Description

[0094] 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.

[0095] Figure 1 This is a flowchart illustrating an embodiment of a feature selection method according to the present invention;

[0096] Figure 2 These are multiple 128×128 pixel data images from an embodiment of a feature selection method of the present invention;

[0097] Figure 3 This is a schematic diagram illustrating the results of a feature selection method according to an embodiment of the present invention and other feature selection algorithms on the EUVP dataset under the ACC metric.

[0098] Figure 4 This is a schematic diagram of an embodiment of a feature selection system according to the present invention. Detailed Implementation

[0099] 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.

[0100] This invention provides a feature selection method and a data reconstruction method for shoreline image feature selection, which can improve the accuracy of data reconstruction and the effectiveness of feature selection.

[0101] Example 1

[0102] Please see Figure 1 A feature selection method, the method comprising:

[0103] S1. Integrate the original data into a sample dataset matrix X;

[0104] For example, taking oceanographic plankton concentration data as an example, suppose we conducted 5 samplings in 3 different sea areas (A, B, C). Each sampling measured 5 variables: ocean temperature, salinity, current velocity, sea surface height, and plankton concentration. These raw data are then integrated into a sample dataset matrix X, as shown in the following example:

[0105] (1) Data sampling and variable description

[0106] Sea Area A: ① Temperature (°C): 22.5, 23.0, 22.8, 22.2, 23.1; ② Salinity (psu): 34.2, 34.5, 34.3, 34.0, 34.6; ③ Current velocity (m / s): 0.8, 0.9, 0.7, 0.8, 0.95; ④ Sea surface height (m): 1.2, 1.3, 1.1, 1.25, 1.35; ⑤ Plankton concentration (cells / mL): 500, 550, 520, 480, 530.

[0107] Sea Area B: ① Temperature: 24.0, 24.5, 23.8, 24.2, 23.9; ② Salinity: 35.0, 35.2, 34.8, 35.1, 34.9; ③ Current velocity: 1.2, 1.3, 1.1, 1.25, 1.4; ④ Sea surface height: 1.5, 1.6, 1.45, 1.55, 1.65; ⑤ Plankton concentration: 450, 420, 470, 460, 440.

[0108] Sea Area C: ① Temperature: 20.5, 21.0, 21.2, 20.8, 20.6; ② Salinity: 33.5, 33.7, 33.9, 33.6, 33.8; ③ Current velocity: 0.5, 0.55, 0.6, 0.55, 0.65; ④ Sea surface height: 1.0, 1.1, 0.95, 1.05, 1.15; ⑤ Plankton concentration: 600, 580, 620, 590, 570.

[0109] (2) Construction of sample dataset matrix X

[0110] The above data is integrated into a sample dataset matrix X, where the rows represent different sampled samples (15 samples in total) and the columns represent different variables (5 variables in total). Matrix X is as follows:

[0111]

[0112] S2. Initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p).

[0113] In this embodiment, the coordinate basis matrix B must satisfy B. T The orthogonality constraint condition B = I; the encoding matrix E needs to satisfy E T The condition E = I, E ≥ 0; to ensure the non-negativity of the encoding matrix E, an auxiliary variable matrix F is introduced, such that E = F, as a constraint.

[0114] For example, the initial reconstruction transformation matrix W is the identity matrix, the transformation matrix Q that projects the original high-dimensional matrix into the low-dimensional space is the identity matrix, the eigenvalue regression coefficient matrix A is the identity matrix, the k mutually perpendicular and independent coordinate basis matrices B of dimension m in the clustering process are the identity matrix, the encoding matrix E of each sample based on the encoding auxiliary matrix F is the identity matrix, the auxiliary matrix D introduced for the relaxation optimization problem is the identity matrix, the vector p formed by the weights assigned to the reconstruction error of the i-th sample is the unit vector, the mean vector v of the dataset matrix X is the unit vector, and the corresponding elements on the diagonal of the diagonal matrix P are the corresponding elements of the weight vector p.

[0115] Suppose we have 15 samples (n=15) and 5 features (m=5), then the initialization of each matrix and vector is as follows:

[0116] Reconstruct the transformation matrix W: W∈R m×m It is a 5×5 identity matrix, representing that in the initial state each feature itself constitutes a basis vector, without any transformation.

[0117]

[0118] Transformation matrix Q: Q∈R m×m It is a 5×5 identity matrix, representing that no linear transformation has been performed between features in the initial state.

[0119]

[0120] Eigenvalue regression coefficient matrix A: A∈R m×m It is a 5×5 identity matrix, indicating that the regression coefficient of each feature is 1 in the initial state, that is, each feature has complete explanatory power for itself.

[0121]

[0122] Coordinate basis matrix B: B∈R m×k It is a 5×5 identity matrix, indicating that the coordinate basis vectors are orthonormal basis vectors in the initial state.

[0123]

[0124] Encoding matrix E: E∈R n×k It is a 15×5 identity matrix, representing the encoding of each sample in the feature space as a standard basis vector in the initial state.

[0125]

[0126] Auxiliary matrices F and D: Both D and are initialized to 15×5 identity matrices to aid the optimization process.

[0127]

[0128] Weight vector p: p is a unit vector of length 5, indicating that the weights of each feature are equal in the initial state.

[0129]

[0130] The mean vector v of the dataset: v is a unit vector of length 5, representing the initial mean as the unit value of each feature.

[0131]

[0132] Weight matrix P: P is a 5×5 diagonal matrix, and the diagonal elements are the elements of the weight vector p, indicating that in the initial state, the weights of each feature are the same and independent of each other.

[0133]

[0134] After initialization, all matrices and vectors are in an unbiased initial state, providing a unified starting point for subsequent iterative optimization processes.

[0135] S3. Based on the dataset matrix X, the dataset mean vector v, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P, update the encoding matrix E and the auxiliary matrix F;

[0136] In this embodiment, S3, updating the encoding matrix E and auxiliary matrix F based on the dataset matrix X, the dataset mean vector v, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P, specifically includes:

[0137] S31, Regarding B T AQ T MP+γF T Perform singular value decomposition to obtain the left singular matrix U. E and the right singular matrix V E ; For B T AQ T MP+γF T Perform singular value decomposition to obtain the left singular matrix U. E and the right singular matrix V E Where P represents the weight matrix, F represents the encoding auxiliary matrix, Q represents the transformation matrix that projects the original high-dimensional matrix onto the low-dimensional space, A represents the eigenvalue regression coefficient matrix, M represents the decentralized matrix, and B represents the coordinate basis matrix.

[0138] S32, according to Update the encoding matrix E; where I n,k Let V represent an n x k matrix of all 1s. This can be achieved using the right singular matrix V. E All-1 matrix I n,k and the left singular matrix U E The transpose of the expression is used to update the encoding matrix E.

[0139] S33, according to Update the auxiliary encoding matrix F. This step updates F by taking the non-negative part of the encoding matrix E, which helps improve the stability of the subsequent optimization process.

[0140] S4. Update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and auxiliary matrix F;

[0141] In this embodiment, S4, updating the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and auxiliary matrix F, specifically includes:

[0142] S41, according to Update the transformation matrix Q;

[0143] S42. Calculate the central vector matrix v according to the following formula:

[0144]

[0145] in, The operator represents the Kronecker product; 1 represents a column vector of all 1s, I represents the identity matrix, P represents the weight matrix, vec() represents vectorization of the matrix by column, v represents the center vector matrix, and X represents the sample vector.

[0146] S43, To E T PM T QA T Perform singular value decomposition to obtain the left singular matrix U. B and the right singular matrix V B Where P represents the weight matrix, E represents the encoding matrix, Q represents the transformation matrix projecting the original high-dimensional matrix onto the low-dimensional space, A represents the eigenvalue regression coefficient matrix, and M represents the decentralized matrix; according to Update the coordinate basis matrix B; where, I m,k This represents an m-row, k-column matrix of all 1s.

[0147] S44, Q T MM T Perform singular value decomposition to obtain the left singular matrix U. W and the right singular matrix V W Where Q represents the transformation matrix projecting the original high-dimensional matrix onto a low-dimensional space, and M represents the matrix after decentralization; according to Update and reconstruct the transformation matrix W;

[0148] S45, Q T MPEB T Perform singular value decomposition to obtain the left singular matrix U. A and the right singular matrix V AWhere P represents the weight matrix, E represents the encoding matrix, Q represents the transformation matrix projecting the original high-dimensional matrix onto the low-dimensional space, B represents the coordinate basis matrix, and M represents the decentralized matrix; according to Update the eigenvalue regression coefficient matrix A;

[0149] S46, Through Calculate the minimized reconstruction error matrix G; G = [g1, g2, ... g n ] T g n This represents the reconstruction error of the nth sample; according to Calculate the weight matrix P. Where P = [p1, p2, ..., p... n ] T p n Let (·) represent the weight corresponding to the nth reconstruction error. + Let max(·,0) represent the number of activated samples, i = 1, 2, ..., n. c is usually taken as 50% to 80% of the number of samples and should be rounded down.

[0150] S5. Determine if the termination condition is met; if the termination condition is met, proceed to S6; if the termination condition is not met, return to S3.

[0151] In this embodiment, the termination conditions include: the number of iterations reaches a set number; and / or, the difference ΔJ between the target values ​​J obtained from two adjacent iterations is less than a set threshold.

[0152] S6. Sort the eigenvectors in the updated transformation matrix Q, and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1.

[0153] S7. Use the optimal feature subset W′ to denoise and reconstruct the dataset matrix X to obtain the denoised data.

[0154] In this embodiment, S7, the dataset matrix X is denoised and reconstructed using the optimal feature subset W′ to obtain the denoised data. The specific formula is as follows:

[0155] WQ T (X-v1 T )+v1 T

[0156] Where Q represents the updated reconstruction transformation matrix, v represents the mean vector of the dataset, and X represents the dataset matrix. Step S7 removes some irrelevant information, achieving the purpose of feature selection and denoising.

[0157] In this embodiment, the coordinate basis matrix B of the present invention must satisfy B TThe orthogonality constraint condition B = I; the encoding matrix E needs to satisfy E T The condition E = I, E ≥ 0; to ensure the non-negativity of the encoding matrix E, an auxiliary variable matrix F is introduced, such that E = F, as a constraint.

[0158] In this embodiment, step S7 involves using the optimal feature subset W′ to denoise and reconstruct the dataset matrix X to obtain denoised data. The process then includes:

[0159] The reconstructed data after dimensionality reduction is evaluated, and the quality of dimensionality reduction and denoising is analyzed. Specifically, K-means clustering is performed on multiple reconstructed datasets, utilizing... Characterization accuracy; where, l i Let c represent the i-th data. i Let represent the reconstructed data obtained from the i-th data reconstruction, N represent the total number of data, and map(·) represent the function that maps each cluster index to the best class label. δ(·) represents the δ function, that is, when two input parameters l i and c i If the values ​​are the same, the value is 1; otherwise, it is 0. The higher the ACC value, the higher the clustering accuracy.

[0160] 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:

[0161]

[0162] Where n is the number of samples, C is the confusion matrix, and the elements C ij C represents the number of samples that simultaneously belong to both the i-th cluster of cluster A and the j-th cluster of cluster B. A (C B The NMI value represents the total number of clusters in the A(B) clustering result. The larger the NMI value, the more similar the clustering results A and B are.

[0163] Example 2

[0164] A vertical basis clustering data reconstruction method for shoreline image feature selection is provided, which uses features selected by the method described in one embodiment for data reconstruction. The implementation scheme is illustrated using a shoreline image dataset as an example. Figure 2 As shown, the sample image is segmented into multiple 128×128 pixel data images, and each sample image is then integrated into a vector x. i ∈R 1 ×16384This involves arranging all pixels of a sample image into a row to form a sample vector, with a one-to-one correspondence between the sample image and the sample vector. The sample vector is then used to extract beach tidal line features and reconstruct the shoreline image using the method disclosed in Example 1; the specific steps are not detailed here.

[0165] To verify the effectiveness and correctness of the method disclosed in this invention, its performance is compared with that of classic unsupervised feature selection algorithms such as UDFS, MCFS, LS and SOCFS.

[0166] Clustering results on the original dataset: To demonstrate the data processing capabilities of the algorithm disclosed in this invention, representative images were selected from a coastal image dataset and manually labeled. Clustering experiments were then conducted on the dataset. Figure 3 It can be seen that the algorithm proposed in this invention outperforms other feature selection algorithms on the coastal image dataset under the ACC metric, verifying the effectiveness of the proposed algorithm. Compared to SOCFS, the algorithm disclosed in this invention introduces feature extraction and data reconstruction terms, enhancing the algorithm's discriminative power for data-related features and reducing the loss of useful features caused by a single discrimination criterion. Robust feature selection algorithms AW-SPCA and UDFS show relatively stable performance across different datasets, while LS and MCFS fully consider the correlation between features, and their performance is generally positively correlated with the number of features selected.

[0167] Example 3

[0168] Please see Figure 4 A feature selection system, the system being based on a method described in one embodiment, comprising: a data integration module for integrating raw data into a sample dataset matrix X;

[0169] The initialization module is used to initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F, and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p).

[0170] The module for calculating the encoding matrix E and the auxiliary matrix F is used to update the encoding matrix E and the auxiliary matrix F based on the dataset matrix X, the mean vector v of the dataset, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P.

[0171] The update module is used to update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and the auxiliary matrix F.

[0172] The judgment module is used to determine whether the termination condition is met; if the termination condition is met, S6 is executed; if the termination condition is not met, S3 is returned.

[0173] The eigenvector selection module is used to sort the eigenvectors in the updated transformation matrix Q and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1.

[0174] The data reconstruction module is used to construct reconstructed data based on the updated reconstruction transformation matrix Q, the mean vector v of the dataset, and the dataset matrix X.

[0175] In order to better utilize the above methods, this application proposes a data reconstruction system, in which each module corresponds to each step of the above methods. The specific principles have been described above and will not be repeated here.

[0176] Example 4

[0177] A feature selection device includes: at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the method described in one or two embodiments.

[0178] In this embodiment, to better run and process the methods described in one or two of the embodiments, the above methods are stored in a memory, and the stored methods are executed using a processor. It should be noted that the principles and effects of each step have been described above and will not be elaborated upon here.

[0179] Example 5

[0180] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method described in one or two embodiments.

[0181] In this embodiment, to better operate and use the method described in one of the embodiments, the above method is stored in a computer-readable storage medium, and the above method is 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.

[0182] 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 feature selection method, characterized in that, The method includes: S1. Integrate the original data into a sample dataset matrix X; S2. Initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p). S3. Based on the dataset matrix X, the dataset mean vector v, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P, update the encoding matrix E and the auxiliary matrix F; S4. Update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and auxiliary matrix F; S5. Determine if the termination condition is met; if the termination condition is met, proceed to S6; if the termination condition is not met, return to S3. S6. Sort the eigenvectors in the updated transformation matrix Q, and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1. S7. Use the optimal feature subset W′ to denoise and reconstruct the dataset matrix X to obtain the denoised data.

2. The feature selection method as described in claim 1, characterized in that, The termination conditions include: the number of iterations reaches a set number or the difference ΔJ between the target values ​​J obtained from two adjacent iterations is less than a set threshold.

3. The feature selection method as described in claim 1, characterized in that, S3. Based on the dataset matrix X, the dataset's mean vector v, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P, update the encoding matrix E and the auxiliary matrix F, specifically including: S31, Regarding B T AQ T MP+γF T Perform singular value decomposition to obtain the left singular matrix U. E and the right singular matrix V E ; S32, according to Update the encoding matrix E; S33, according to Update the auxiliary encoding matrix F.

4. A feature selection method as described in claim 1 or 3, characterized in that, S4. Update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and auxiliary matrix F, specifically including: S41, according to Update the transformation matrix Q; S42. Calculate the central vector matrix v according to the following formula: S43, To E T PM T QA T Perform singular value decomposition to obtain the left singular matrix U. B and the right singular matrix V B ;according to Update the coordinate basis matrix B; S44, Q T MM T Perform singular value decomposition to obtain the left singular matrix U. W and the right singular matrix V W ;according to Update and reconstruct the transformation matrix W; S45, Q T MPEB T Perform singular value decomposition to obtain the left singular matrix U. A and the right singular matrix V A ;according to Update the eigenvalue regression coefficient matrix A; S46, Through Calculate the minimized reconstruction error matrix G; according to Calculate the weight matrix P.

5. A feature selection method as described in any one of claims 1 to 4, characterized in that, The coordinate basis matrix B satisfies B T Orthogonal constraint condition B = I; The encoding matrix E satisfies E T The constraints are E = I and E ≥ 0. The auxiliary variable matrix F satisfies the constraint E = F.

6. A feature selection method as described in any one of claims 1, characterized in that, S7. Denoise and reconstruct the dataset matrix X using the optimal feature subset W′ to obtain the denoised data. This process also includes: The reconstructed data after dimensionality reduction is evaluated, and the quality of dimensionality reduction and denoising is analyzed. Among them, K-means clustering is performed on multiple reconstructed data, and the accuracy is represented by the ACC index.

7. A data reconstruction method for shoreline image feature selection, characterized in that, The method includes: selecting features of the shoreline image for data reconstruction using the method of any one of claims 1-6.

8. A feature selection system, characterized in that, The system, based on the method according to any one of claims 1-6, includes: The data integration module is used to integrate the raw data into a sample dataset matrix X; The initialization module is used to initialize the reconstruction transformation matrix W, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, encoding matrix E, auxiliary matrix F, and auxiliary matrix D as identity matrices, initialize the weight vector p and the mean vector v of the dataset as unit vectors, and initialize the weight matrix P = diag(p). The module for calculating the encoding matrix E and the auxiliary matrix F is used to update the encoding matrix E and the auxiliary matrix F based on the dataset matrix X, the mean vector v of the dataset, the transformation matrix Q, the eigenvalue regression coefficient matrix A, the coordinate basis matrix B, and the weight matrix P. The update module is used to update the mean vector v, transformation matrix Q, eigenvalue regression coefficient matrix A, coordinate basis matrix B, and weight matrix P of the dataset based on the encoding matrix E and the auxiliary matrix F. The judgment module is used to determine whether the termination condition is met; if the termination condition is met, S6 is executed; if the termination condition is not met, S3 is returned. The eigenvector selection module is used to sort the eigenvectors in the updated transformation matrix Q and select the top d largest eigenvectors to construct the optimal feature subset W′; d is a positive integer greater than or equal to 1. The data reconstruction module is used to construct reconstructed data based on the updated reconstruction transformation matrix Q, the mean vector v of the dataset, and the dataset matrix X.

9. A feature selection device, 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 6.

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 6.

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