A hyperspectral band selection method and system based on hypergraph learning
By employing hypergraph learning methods to perform self-representation and sparse matrix processing on hyperspectral images, and combining matrix entropy theory, the high dimensionality and redundancy problems of hyperspectral images are solved, achieving efficient band selection and dimensionality reduction, and improving the accuracy and precision of the analysis.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HARBIN NORMAL UNIVERSITY
- Filing Date
- 2025-01-07
- Publication Date
- 2026-06-09
Smart Images
Figure CN119963994B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of image information processing technology, and more specifically, to a hyperspectral band selection method and system based on hypergraph learning. Background Technology
[0002] Hyperspectral images can capture hundreds of consecutive bands of an observed scene, providing rich spectral information and are widely used in remote sensing, environmental monitoring, and agriculture. However, this also brings challenges to data processing. First, high-dimensional data increases computational complexity and storage requirements. Second, redundant information often exists between adjacent bands, which may lead to information overlap and noise interference in subsequent analysis. Therefore, to reduce computational complexity, storage requirements, and improve the accuracy of subsequent analysis, dimensionality reduction of hyperspectral images is necessary. Band selection is a core fundamental problem in dimensionality reduction of hyperspectral images, aiming to select the most representative and useful bands for a specific task from hundreds of bands. Due to the lack of labeled samples or category information and the absence of prior guidance, unsupervised band selection methods that rely on the relationships or statistical properties between bands to select a subset of bands are more flexible. This method typically does not consider the association between bands and specific categories or targets, but focuses on selecting bands that can reflect the overall characteristics of the image or have certain statistical properties.
[0003] Due to the high dimensionality of hyperspectral image data, making reasonable use of the data's inherent structure can improve the performance of hyperspectral image band selection methods to a certain extent. To better address the aforementioned problems in hyperspectral image band selection, this invention first performs dimensionality reduction on the original data based on the self-representation of hyperspectral image data to mitigate the impact of limited labeled data. Then, based on hypergraph learning, the bands of the hyperspectral image are used as input samples for the proposed band selection method. Hypergraph Laplacian matrix regularization maintains the local spatial consistency between bands, enabling the capture of important data features in a lower-dimensional space. Finally, matrix entropy theory is used to remove redundancy, avoiding spurious correlations in the data and improving its representational power. Summary of the Invention
[0004] The technical problem to be solved by this invention is:
[0005] To address the issues of computational complexity of existing high-dimensional data and the potential for information overlap and noise interference in subsequent problem analysis due to redundant information between adjacent bands.
[0006] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:
[0007] This invention provides a hyperspectral band selection method based on hypergraph learning, comprising the following steps:
[0008] S100. Perform self-representation learning on hyperspectral data and use sparse matrices to maintain the sparsity of the weight matrix.
[0009] S200, Hypergraph learning, includes segmenting hyperspectral data, defining the hypergraph association matrix during the hypergraph construction process, and using the hypergraph Laplacian matrix to describe the node-to-node relationships in the hypergraph, and performing Laplacian regularization on the hyperspectral image after dimensionality reduction in step S100.
[0010] S300, Hyperparameter settings: Design a unified framework for joint self-representation model and hypergraph learning, optimize hyperparameters, and obtain the optimal hyperparameter combination for different datasets;
[0011] S400, Band selection of hyperspectral image, including updating the selection matrix based on the hypergraph correlation matrix obtained in step S200 and the optimal hyperparameter combination determined in step S300, and outputting the hyperspectral image bands based on the update result.
[0012] Furthermore, in step S100, the hyperspectral data containing d spectral bands is processed... Implement self-representation learning to acquire dimensionality-reduced hyperspectral data. Where P is the selection matrix; in this process, sparse matrices W1 and W2 are used to maintain the sparsity of the weight matrix.
[0013] Furthermore, step S200 specifically includes,
[0014] S210. Given a hyperspectral image X = [x1, x2, ..., x...] containing d spectral bands... d ] T Divide along the spectral dimension, and let each subspace have c bands, to obtain k subspaces:
[0015]
[0016] Wherein, [·] is defined as rounding up;
[0017] S220. Treat each band of the hyperspectral image as a node of the hypergraph, and each subspace in step S210 as a hyperedge, constructing a hypergraph G = (V, E, W), where V represents a vertex, E represents an edge, and W represents a weighted matrix or edge weight matrix; define the hypergraph incidence matrix as:
[0018]
[0019] Where, x i For the i-th band of the hyperspectral image, i.e., the i-th node v of the hypergraph i ;ej This refers to the j-th subspace in step S210, which is the j-th hyperedge of the hypergraph;
[0020] S230. Based on the definition of the hypergraph incidence matrix in step S220, the node-to-node relationships in the hypergraph are described using the hypergraph Laplacian matrix:
[0021]
[0022] Among them, D v D e Let W = diag([w1, w2, ..., w...)) be a diagonal matrix with the vertex degree and edge degree of the hypergraph as its diagonal elements. k ]) is the hyperedge weight matrix;
[0023] Finally, the hyperspectral image PX after dimensionality reduction in step S100 is subjected to Laplacian regularization.
[0024] Furthermore, in step S300, a broad search space is defined, and an objective function is constructed:
[0025]
[0026] st1 T w = 1, w ≥ 0, diag(P) = 0, P ≥ 0
[0027] in,‖·‖ F This indicates the calculation of the Frobenius norm of a matrix; The operator represents the element-wise product operator; T represents the matrix transpose operation; ||·||2 represents the 2-norm of the elements; diag(·) represents the diagonal vector of the matrix;
[0028] The objective function takes a set of hyperparameters as input and returns the accuracy of the algorithm on the validation set. Using the hyperopt.fmin function, a tree-structured Parzen estimator is used as the optimization algorithm to perform a comprehensive search for hyperparameters including α, β, λ, and γ. After multiple iterations, the optimal combination of hyperparameters is determined.
[0029] Further, step S400 includes S410, updating the selection matrix P.
[0030] Set the input variables: hyperspectral image data X, select matrix P, and hypergraph Laplacian matrix L;
[0031] Input hyperparameters: The hyperparameters α, λ, γ and parameter ε set in step S300 are 10. -5 ;
[0032] Internal algorithm iteration count: t max=100;
[0033] S411. In the t-th iteration, the intermediate variable W1 is calculated using the following formula:
[0034]
[0035] S412. In the t-th iteration, the intermediate variable W2 is calculated using the following formula:
[0036]
[0037] S413. The variable P estimated in the t-th iteration is updated according to the following formula:
[0038]
[0039] in, Represent an identity matrix;
[0040] S414. The termination condition for updating the selection matrix P is that if the number of iterations t = t in the classification process... max Then terminate the iteration and output. Otherwise, the algorithm proceeds to step S411 and continues execution until termination.
[0041] Furthermore, it also includes S420, selecting the band of the hyperspectral image.
[0042] The relevant parameters and input settings for band selection in hyperspectral images are as follows:
[0043] Input sample: Hyperspectral image data X;
[0044] Input hyperparameters: hyperparameters α, β, λ, γ and parameter ε set in step S300;
[0045] Number of external algorithm iterations: T max =200;
[0046] Internal algorithm iteration count: t max =100;
[0047] Initialization: P (0) w (0) L and c;
[0048] Calculate the number of subspaces divided by the spectral domain according to formula (1); the variable P estimated in the Tth iteration. (T) The selection matrix P generated in step S410; the Lagrangian multipliers in the T-th iteration are calculated using the following formula:
[0049]
[0050] Where “1” represents a k-dimensional vector of all 1s;
[0051] In the Tth iteration, the intermediate variable w is calculated using the following formula:
[0052]
[0053] in,(·) + Defined as (·) + =max{·,0};
[0054] The intermediate variable L in the Tth iteration is calculated using the following formula:
[0055]
[0056] The band selection termination condition for hyperspectral images is that if the number of iterations in the classification process T = T max Then terminate the iteration and output. Otherwise, iterate again until the selection matrix is output. When the algorithm stops, it outputs the selection matrix P. (T) ;
[0057] Calculate the output selection matrix P (T) For each column's l2 norm, sort the results in descending order, output the bands corresponding to the first s values, forming a new subset X. sub ;
[0058] When the algorithm stops, the output X sub This is the selected subset of hyperspectral image bands containing s bands.
[0059] A hyperspectral band selection system based on hypergraph learning is provided. The system has program modules corresponding to the steps described above, and executes the steps in the hyperspectral band selection method based on hypergraph learning described above when running.
[0060] A computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement steps of a hypergraph learning-based hyperspectral band selection method.
[0061] Compared with the prior art, the beneficial effects of the present invention are:
[0062] Compared with several widely used hyperspectral image band selection methods, the proposed method exhibits superior performance. This is because the proposed method fully considers several challenges faced in current band selection problems, including the high dimensionality of hyperspectral images and insufficient training samples. Furthermore, the invention further considers the data structure and matrix information entropy of hyperspectral images, resulting in even better performance. Therefore, the technical solution of this invention is characterized by high reliability and relatively high accuracy, making it suitable for widespread application. Attached Figure Description
[0063] Figure 1 This is a comparison chart showing the performance of FNGBS, ONR, DLUFS, RDGSR, S4P, and the classification method described in this invention on a real hyperspectral image dataset of Indian pine trees.
[0064] Figure 2 This is a comparison chart showing the performance of FNGBS, ONR, DLUFS, RDGSR, S4P, and the classification method described in this invention on a real hyperspectral image dataset from Botswana.
[0065] Figure 3 This is a comparison chart showing the performance of FNGBS, ONR, DLUFS, RDGSR, S4P, and the classification method described in this invention on the real hyperspectral image Kennedy Space Center dataset. Detailed Implementation
[0066] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
[0067] This invention utilizes internationally available hyperspectral datasets for classification experiments, including those from Indian Pines, Botswana, and Kennedy Space Center. These datasets are widely used in hyperspectral image band selection tasks to evaluate the effectiveness of hyperspectral image band selection methods. Experiments based on these datasets demonstrate that the method proposed in this invention outperforms traditional band selection methods.
[0068] Specific Implementation Scheme 1: This invention provides a hyperspectral band selection method based on hypergraph learning, including the following steps:
[0069] S100. Perform self-representation learning on hyperspectral data.
[0070] To mitigate the impact of scarce labeled data in hyperspectral images, hyperspectral data containing d spectral bands... Implement self-representation learning techniques; this process aims to obtain dimensionality-reduced hyperspectral data. Here, P is the selection matrix. A crucial feature selection matrix is involved in this process, which plays the role of filtering key information. In order to further refine the feature set and ensure that only the most core features are retained, it is desirable that the weight matrix obtained is as sparse as possible, that is, only a few features are given significant importance. In this process, sparse matrices W1 and W2 are used to maintain the sparsity of the weight matrix.
[0071] Based on the principle of matrix information entropy and subspace orthogonality, band combinations that not only have high information entropy but are also orthogonal to each other in the subspace are selected. Orthogonality means that the bands exhibit a state of mutual independence in a specific subspace dimension, which means that the information content they carry does not interfere with or overlap with each other. This characteristic significantly reduces information redundancy, thereby ensuring the efficiency and accuracy of the selected band combinations in information expression.
[0072] S200, Hypergraph Learning, specifically includes,
[0073] S210. Considering that the correlation between adjacent bands is higher than that between non-adjacent bands, the hyperspectral image X = [x1, x2, ..., x...] containing d spectral bands is first... d ] T Dividing along the spectral dimension, let the number of bands in each subspace be c, thus obtaining k subspaces:
[0074]
[0075] Wherein, [·] is defined as rounding up;
[0076] S220. In the hypergraph construction process, each band of the hyperspectral image is regarded as a node of the hypergraph, and each subspace in step S210 is regarded as a hyperedge. A hypergraph G = (V, E, W) can be constructed, where V represents a vertex, E represents an edge, and W represents a weighted matrix or edge weight matrix. Specifically, the hypergraph association matrix (node-hyperedge relationship matrix) is defined as:
[0077]
[0078] Where, x i The i-th band of the hyperspectral image is also the i-th node v in the hypergraph. i ;e j This is the j-th subspace in step S210, and also the j-th hyperedge of the hypergraph;
[0079] S230. Based on the definition of the hypergraph incidence matrix in step S220, the node-to-node relationships in the hypergraph are described using the hypergraph Laplacian matrix, as follows:
[0080]
[0081] Among them, D v D e Let W = diag([w1, w2, ..., w2) be a diagonal matrix with the vertex degree and edge degree of the hypergraph as its diagonal elements. k ]) is the hyperedge weight matrix;
[0082] In order to effectively utilize the local relationships between data, the hyperspectral image PX after dimensionality reduction in step S100 is subjected to Laplacian regularization.
[0083] S300, hyperparameter settings, specifically including...
[0084] In this invention, a unified framework combining a self-representation model and hypergraph learning is designed for the band selection task, and the hyperparameters are optimized with the help of the hyperopt library. The key hyperparameters to be optimized include α, β, λ, and γ.
[0085] Define a broad search space for hyperopt, with a regularization strength of 10. -6 Up to 10 6 The parameters were adjusted between the parameters; then, an objective function was constructed as shown in formula (4). This objective function takes a set of hyperparameters as input and returns the accuracy (Acc) of the algorithm on the validation set. The hyperopt.fmin function was used, and the tree structure Parzen estimator (TPE) was used as the optimization algorithm to perform a comprehensive search for hyperparameters. After multiple iterations, different optimal combinations of hyperparameters were determined for different datasets. After using the optimal hyperparameters, the accuracy of the algorithm gradually improved. This significant improvement fully verified the effectiveness of hyperparameter optimization.
[0086]
[0087] st1 T w = 1, w ≥ 0, diag(P) = 0, P ≥ 0
[0088] in,‖·‖ F This indicates the calculation of the Frobenius norm of a matrix; This represents the element-wise product operator; the superscript T indicates the matrix transpose operation; ||·|2 indicates the 2-norm of the elements. diag(·) indicates the diagonal vector of the matrix;
[0089] S400. Band selection for hyperspectral images: Based on the hypergraph correlation matrix H obtained in step S200 and the optimal hyperparameter combination determined in step S300, band selection is performed, specifically including:
[0090] S410, the update of the selection matrix P, including,
[0091] Set the input variables: hyperspectral image data X, select matrix P, and hypergraph Laplacian matrix L;
[0092] Input hyperparameters: The hyperparameters α, λ, γ and parameter ε set in step S300 are 10. -5 ;
[0093] Internal algorithm iteration count: t max =100;
[0094] S411. In the t-th iteration, the intermediate variable W1 is calculated using the following formula:
[0095]
[0096] Where, diag(·) is defined as a diagonal matrix with "·" as the diagonal vector;
[0097] S412. In the t-th iteration, the intermediate variable W2 is calculated using the following formula:
[0098]
[0099] S413. The variable P estimated in the t-th iteration is updated according to the following formula:
[0100]
[0101] in, Represent an identity matrix;
[0102] S414. The termination condition for updating the selection matrix P is that if the number of iterations t = t in the classification process... max Then terminate the iteration and output. Otherwise, the algorithm proceeds to step S411 and continues execution until termination;
[0103] S420, band selection for hyperspectral images, specifically including,
[0104] The relevant parameters and input settings for band selection in hyperspectral images are as follows:
[0105] Input sample: Hyperspectral image data X;
[0106] Input hyperparameters: hyperparameters α, β, λ, γ and parameter ε set in step S300;
[0107] Number of external algorithm iterations: T max =200;
[0108] Internal algorithm iteration count: t max =100;
[0109] Initialization: P( 0 ), w( 0 ), L and c;
[0110] Calculate the number of subspaces (hyperedges) divided by the spectral domain, as shown in formula (1); the variable P estimated in the Tth iteration. (T) The selection matrix P generated in step S410; the Lagrangian multipliers in the T-th iteration are calculated using the following formula:
[0111]
[0112] Where “1” is a k-dimensional vector of all 1s;
[0113] In the Tth iteration, the intermediate variable w is calculated using the following formula:
[0114]
[0115] in,(·) + Defined as (·) + =max{·,0};
[0116] In the Tth iteration, the intermediate variable L is calculated using the following formula:
[0117]
[0118] The band selection termination condition for hyperspectral images is that if the number of iterations in the classification process T = T max Then terminate the iteration and output. Otherwise, the algorithm is re-executed; the algorithm outputs a selection matrix. When the algorithm stops, it outputs the selection matrix P. (T) ;
[0119] Calculate the output selection matrix P (T) For each column's l2 norm, sort the results in descending order, output the bands corresponding to the first s values, forming a new subset X. sub ;
[0120] When the algorithm stops, the output X of the algorithm is... sub It is the selected subset of hyperspectral image bands containing s bands.
[0121] Specific implementation scheme 2: The present invention provides a hyperspectral band selection system based on hypergraph learning. The system has a program module corresponding to the above steps, and executes the steps in the hyperspectral band selection method based on hypergraph learning described above when running.
[0122] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.
[0123] Specific Implementation Scheme 3: The present invention provides a computer-readable storage medium storing a computer program configured to implement, when called by a processor, the steps of a hypergraph-based hyperspectral band selection method.
[0124] The other combinations and connections in this implementation scheme are the same as in Specific Implementation Scheme 1.
[0125] To verify the effectiveness of the classification method proposed in this invention, experiments were conducted using internationally available hyperspectral image datasets, including those of Indian Pines, Botswana, and Kennedy Space Center (KSC), employing FNGBS, ONR, DLUFS, RDGSR, S4P, and the classification method described in this invention. The hyperspectral images of Indian Pines comprise 200 bands, each consisting of 145×145 pixels, with a spatial resolution of 20m per pixel, and contain 16 material categories. The hyperspectral images of Botswana comprise 145 bands, each consisting of 1476×256 pixels, with a spatial resolution of 30m per pixel, and contain 14 material categories. The hyperspectral images of Kennedy Space Center comprise 176 bands, each consisting of 421×444 pixels, with a spatial resolution of 18m per pixel, and contain 13 material categories.
[0126] In the experiments, overall accuracy (OA) and the Kappa coefficient were used to measure the performance of each classification method. During the experiments, we progressively increased the number of training samples, presenting the performance of the proposed method on the datasets Indian Pines, Botswana, and Kennedy Space Center (KSC) as the number of training samples increased from 10 to 50. The results are shown below. Figure 1 , Figure 2 and Figure 3 As shown in the figure, the overall performance of the band selection method proposed in this invention is superior to other comparative methods, and this experiment fully demonstrates the effectiveness of the proposed method.
[0127] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.
Claims
1. A hyperspectral band selection method based on hypergraph learning, characterized in that, Includes the following steps: S100. Perform self-representation learning on hyperspectral data and use sparse matrices to maintain the sparsity of the weight matrix. S200, Hypergraph learning, includes segmenting hyperspectral data, defining the hypergraph association matrix during the hypergraph construction process, and using the hypergraph Laplacian matrix to describe the node-to-node relationships in the hypergraph, and performing Laplacian regularization on the hyperspectral image after dimensionality reduction in step S100. include, S210, containing Hyperspectral images in spectral bands Divide along the spectral dimension, and let the number of bands in each subspace be... ,get Subspace: in, Defined as rounding up; S220. Treat each band of the hyperspectral image as a node of the hypergraph, and treat each subspace in step S210 as a hyperedge to construct the hypergraph. Where V represents a vertex, E represents an edge, and W represents a weighted matrix or edge weight matrix; the hypergraph incidence matrix is defined as: in, The first hyperspectral image The band, i.e., the first band of the supergraph Nodes ; For the first step in S210 The subspace, i.e., the first subspace of the hypergraph Strip of edge; S230. Based on the definition of the hypergraph incidence matrix in step S220, the node-to-node relationships in the hypergraph are described using the hypergraph Laplacian matrix: in, , These are diagonal matrices with the vertex degree and edge degree of the hypergraph as their diagonal elements. This is the hyperedge weight matrix; Finally, the hyperspectral image after dimensionality reduction in step S100 is processed. Perform Laplacian regularization; S300, Hyperparameter settings: Design a unified framework for joint self-representation model and hypergraph learning, optimize hyperparameters, and obtain the optimal hyperparameter combination for different datasets; include, Define a broad search space and construct the objective function: in, This indicates the calculation of the Frobenius norm of a matrix; This represents the element-wise product operator; T represents the matrix transpose operation. This indicates the 2-norm of an element; This indicates finding the diagonal vector of a matrix; To select the matrix; and Represents a sparse matrix; The objective function takes a set of hyperparameters as input and returns the accuracy of the algorithm on the validation set. Using the `hyperopt.fmin` function, a tree-structured Parzen estimator is employed as the optimization algorithm to optimize the hyperparameters, including... A comprehensive search is performed; after multiple iterations, the optimal combination of hyperparameters is determined. S400, Band selection of hyperspectral image, including updating the selection matrix based on the hypergraph correlation matrix obtained in step S200 and the optimal hyperparameter combination determined in step S300, and outputting the hyperspectral image bands based on the update result.
2. The hyperspectral band selection method based on hypergraph learning according to claim 1, characterized in that: In step S100, for the containing Hyperspectral data in spectral bands Implement self-representation learning to acquire dimensionality-reduced hyperspectral data. ,in, To select the matrix; sparse matrices are used in this process. and This achieves the goal of maintaining the sparsity of the weight matrix.
3. The hyperspectral band selection method based on hypergraph learning according to claim 2, characterized in that: Step S400 includes S410, selecting the matrix. Update Input variable: Hyperspectral image data Select matrix Hypergraph Laplace matrix ; Input hyperparameters: Hyperparameters set in step S300 and parameters ; Internal algorithm iteration count: ; S411, in the Intermediate variables in the second iteration Calculate using the following formula: S412, in the Intermediate variables in the second iteration Calculate using the following formula: S413, in the The variables estimated in the next iteration Update as follows: in," " represents an identity matrix; S414, Selection Matrix The update termination condition is that if the number of iterations in the classification process is... Then terminate the iteration and output. Otherwise, the algorithm proceeds to step S411 and continues execution until termination.
4. The hyperspectral band selection method based on hypergraph learning according to claim 3, characterized in that: It also includes S420, selecting the band for the hyperspectral image. The relevant parameters and input settings for band selection in hyperspectral images are as follows: Input sample: Hyperspectral image data ; Input hyperparameters: Hyperparameters set in step S300 and parameters ; Number of external algorithm iterations: ; Internal algorithm iteration count: ; initialization: , , and ; Calculate the number of subspaces divided according to the spectral domain using formula (1); in the first... The variables estimated in the next iteration The selection matrix generated in step S410 ; in the The Lagrangian multipliers in the next iteration are calculated using the following formula: in," "for one" A 1-dimensional vector; In the Intermediate variables in the second iteration Calculate using the following formula: in, Defined as ; In the Intermediate variables in the second iteration Calculate using the following formula: The band selection termination condition for hyperspectral images is that if the number of iterations in the classification process... Then terminate the iteration and output. Otherwise, iterate again until the selection matrix is output. When the algorithm stops, it outputs a selection matrix. ; Calculate the selection matrix of the output The l2 norm of each column is used to sort the results in descending order, and the first column is output. The bands corresponding to each value form a new subset. ; When the algorithm stops, the output is For the selected content A subset of hyperspectral image bands in each band.
5. A hyperspectral band selection system based on hypergraph learning, characterized in that: The system has a program module corresponding to the steps of any one of claims 1-4 above, and executes the steps in the hyperspectral band selection method based on hypergraph learning described above when running.
6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the hyperspectral band selection method based on hypergraph learning as described in any one of claims 1-4.