A hyperspectral band selection method based on similarity matrix block diagonal partitioning

Abstract

The present invention relates to a hyperspectral band selection method, and more specifically to a hyperspectral band selection method based on block diagonal partitioning of a similarity matrix. The method is used to address the shortcomings of existing graph-based clustering algorithms, which all perform clustering on a fixed input data graph and require post-processing to extract clustering indicators. The hyperspectral band selection method based on block diagonal partitioning of a similarity matrix includes constructing an initial affinity matrix, building a block diagonal similarity matrix, and selecting representative bands. The method allows adaptive adjustment of the hyperspectral image itself during the clustering process, thereby generating a high-quality similarity graph. First, an accurate affinity matrix is learned by calculating the distance between bands in the hyperspectral image, and a block diagonal similarity matrix containing ordered partition points is constructed, while the bands are divided into multiple sub-block matrices. Finally, a representative band selection method based on linear combinations between bands is proposed.

Description

Technical Field

[0001] The present invention relates to a hyperspectral band selection method, and in particular to a hyperspectral band selection method based on similarity matrix block diagonal partitioning. Background Art

[0002] Hyperspectral remote sensing images are created using an imaging spectrometer. A single image can not only depict the spatial information of a ground object, but also its spectral information. Simply put, a hyperspectral image is a data cube capable of depicting both the spatial and spectral information of a target object, effectively integrating the spatial image information of the target's two-dimensional space with the spectral information of the target's radiation. Hyperspectral images also have the characteristic of collecting tens to hundreds of spectral response bands ranging from visible light to near-infrared wavelengths. This allows them to identify ground objects with subtle spectral differences and leverage this characteristic for subsequent processing of the objects. Consequently, hyperspectral remote sensing technology has been widely applied in numerous fields, such as marine remote sensing, vegetation research, geological exploration, and atmospheric environment research.

[0003] Due to the high correlation between bands, hyperspectral images often exhibit the "Hughes phenomenon," meaning that for a limited number of training samples, the classification accuracy of hyperspectral data decreases as the dimensionality increases. Therefore, dimensionality reduction should be used to reduce information redundancy without reducing the data information. In recent decades, the study of dimensionality reduction methods has become a hot topic in the field of hyperspectral remote sensing. Depending on whether the physical meaning of the original hyperspectral data has changed, dimensionality reduction methods can be divided into two categories: feature extraction and band selection. The essence of feature extraction methods is to extract basic information by transforming high-dimensional data into a space with fewer dimensions through projection. The purpose of band selection is to select unique and representative bands as the selected bands, rather than all bands for subsequent analysis, and effectively improve computational efficiency. Therefore, band selection is very suitable for hyperspectral data.

[0004] Among band selection methods, clustering-based approaches are a hot topic. To date, a large number of clustering methods have been proposed for hyperspectral image processing, including centroid-based clustering, density-based clustering, and graph-based clustering. Traditional centroid-based clustering algorithms include k-means, fuzzy c-means, and kernel-based fuzzy clustering. These methods are based on similarity metrics, but are sensitive to initialization and noise, making them prone to falling into local optima. Density-based clustering algorithms form clusters by directly searching for connected dense regions in the feature space, where clusters are defined as high-density regions separated by low-density regions in the feature space. Examples include the enhanced fast clustering algorithm based on density peaks, the fast search clustering algorithm, and the density peak finding algorithm. Graph-based clustering methods are currently very popular. They embed data into the feature space of the Laplacian matrix and apply k-means to this representation to obtain clusters. Methods such as spectral clustering, ratio cuts, normalized cuts, and sparse subspace clustering are examples.

[0005] Most of the current graph-based clustering algorithms have two weaknesses: one is that clustering is performed on a fixed input data graph; the other is that post-processing is required to extract clustering indicators. Summary of the Invention

[0006] The purpose of the present invention is to solve the shortcomings of existing graph-based clustering algorithms, which all perform clustering on a fixed input data graph and require post-processing to extract clustering indicators, and to provide a hyperspectral band selection method based on similarity matrix block diagonal partitioning.

[0007] In order to solve the deficiencies of the above-mentioned prior art, the present invention provides the following technical solutions:

[0008] A hyperspectral band selection method based on similarity matrix block diagonal partitioning is special in that it includes the following steps:

[0009] Step 1: Construct an initial affinity matrix;

[0010] Step 1.1: Treat each band of the hyperspectral image to be processed as a data point and form a data matrix X = {x1, x2, x3...x N}; where x1 is the first data point, x N is the Nth data point, N is the number of data points of the hyperspectral image, and N is a positive integer greater than 1;

[0011] Step 1.2: Learn the initial affinity matrix by calculating the distance between data points, obtain the affinity value between each data point, and then obtain the initial affinity matrix A;

[0012] Step 2: construct a block diagonal similarity matrix;

[0013] Using the initial affinity matrix A to learn, and adding rank constraints in the learning process, we finally get the block diagonal similarity matrix S = [S1, S2..., S k ]; where S1 is the first sub-block matrix, S k is the kth sub-block matrix, k <N;

[0014] Step 3: Select representative bands;

[0015] Each sub-block matrix is extracted from the block diagonal similarity matrix S, and the coefficient matrix corresponding to each sub-block matrix is obtained through dictionary learning. The band corresponding to the maximum value of the sum of the columns of each coefficient matrix is selected as the representative band of each sub-block matrix, and all representative bands form a representative band set.

[0016] Furthermore, in step 1.2, learning the initial affinity matrix by calculating the distance between data points is specifically implemented by the following formula:

[0017]

[0018] Among them, x i is the i-th data point, x j is the j-th data point, i, j are positive integers greater than 0 and less than or equal to N; is x i with x j The Euclidean distance between ij is x i with x j The affinity value between them; γ is used to adjust the regularization term The weight parameter of .

[0019] Furthermore, in step 1.2, obtaining the affinity value between each data point is specifically achieved by the following formula:

[0020]

[0021] in, is the optimal affinity value, m is the number of neighbors, where j <h≤m,

[0022] Furthermore, step 2 is specifically implemented by formula 1:

[0023]

[0024] in, This is to make the block diagonal similarity matrix S better approximate the minimization problem set by the affinity matrix A. is the F norm; is the sum of the k smallest eigenvalues of the Laplace matrix. The purpose is to make the obtained similarity matrix S contain k sub-block matrices. λ is a balance parameter of the minimization problem.

[0025] Furthermore, step 3 is specifically implemented by formula 2:

[0026]

[0027] in, is a minimization problem set for dictionary learning, where s i2 is the sub-block matrix S i2 Column vector, S i2 is the i2th sub-block matrix, i2 is a positive integer greater than 0 and less than or equal to k, c i2 is the coefficient vector to be obtained, ||c i2 ||1 is a regularization term set to obtain a more sparse coefficient matrix; δ is the sparse regularization term parameter.

[0028] Furthermore, in step 2, the parameter λ is 0.1, and the number of iterations of Formula 1 is 50.

[0029] Furthermore, in step 3, the δ is 0.5, and the number of iterations of Formula 2 is set to 100.

[0030] Compared with the prior art, the present invention has the following beneficial effects:

[0031] (1) The present invention provides a hyperspectral band selection method based on block diagonal partitioning of a similarity matrix, including constructing an initial affinity matrix, building a block diagonal similarity matrix, and selecting representative bands. The present invention allows for adaptive adjustment of the hyperspectral image itself during the clustering process, thereby generating a high-quality similarity graph. First, an accurate affinity matrix is learned by calculating the distance between bands in the hyperspectral image, a block diagonal similarity matrix containing ordered partitioning points is constructed, and the bands are divided into multiple sub-block matrices. Finally, a representative band selection method based on linear combinations between bands is proposed. The representative band subset formed by the present invention has a high amount of information and a low correlation, and the present invention has certain advantages in terms of speed.

[0032] (2) The present invention provides a hyperspectral band selection method based on similarity matrix block diagonal partitioning, which calculates the Euclidean distance between data points and imposes a constraint on it to ultimately obtain a sparser initial affinity matrix.

[0033] (3) The present invention provides a hyperspectral band selection method based on block diagonal partitioning of a similarity matrix. By adding a rank constraint, the resulting block diagonal similarity matrix is closer to the initial affinity matrix and has a block diagonal structure to facilitate the subsequent band selection process.

[0034] (4) The present invention provides a hyperspectral band selection method based on diagonal partitioning of similarity matrix blocks. A dictionary learning algorithm is applied to each sub-block matrix to obtain its corresponding coefficient matrix, and the band corresponding to the maximum value of the sum of the coefficient matrix columns is selected. These bands have higher information content and smaller correlation than the unselected bands. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 The figure is a flow chart of an embodiment of a hyperspectral band selection method based on similarity matrix block diagonal partitioning according to the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below with reference to the accompanying drawings and exemplary embodiments.

[0037] The experimental conditions of the embodiment of the present invention are as follows:

[0038] The CPU is The experiments were conducted using MATLAB on an i7-12700H 2.70GHz CPU, 16G memory, Legion Y9000P, and Win11 operating system.

[0039] Reference Figure 1 A hyperspectral band selection method based on similarity matrix block diagonal partitioning is characterized by comprising the following steps:

[0040] Step 1: Construct an initial affinity matrix;

[0041] Step 1.1: Treat each band of the hyperspectral image to be processed as a data point and form a data matrix X = {x1, x2, x3...x N}; where x1 is the first data point, x N is the Nth data point, N is the number of data points of the hyperspectral image, and N is a positive integer greater than 1;

[0042] Step 1.2: Learn the initial affinity matrix according to the Euclidean distance formula to obtain the affinity value between each data point, and then obtain the initial affinity matrix A. This is achieved by the following formula:

[0043]

[0044] Among them, x i is the i-th data point, x jis the j-th data point, i, j are positive integers greater than 0 and less than or equal to N; is x i with x j The Euclidean distance between ij is x i with x j The affinity value between them; γ is used to adjust the regularization term The weight parameter of

[0045] The affinity value is calculated according to the following formula:

[0046]

[0047] in, is the optimal affinity value, m is the number of neighbors, where j <h≤m,

[0048] Step 2: construct a block diagonal similarity matrix;

[0049] The initial affinity matrix A is used for learning, so that the final similarity matrix is closer to the initial affinity matrix to a greater extent, and the rank constraint is added in the learning process, and the final block diagonal similarity matrix S = [S1, S2..., S k ]; where S1 is the first sub-block matrix, S k is the kth sub-block matrix, k <N;

[0050] This is achieved specifically through the following formula:

[0051]

[0052] in, This is to make the block diagonal similarity matrix S better approximate the minimization problem set by the affinity matrix A. is the F norm; is the sum of the k smallest eigenvalues of the Laplace matrix of the matrix S. The purpose is to make the obtained similarity matrix S contain k sub-block matrices. λ is used to adjust the constraint term Parameters;

[0053] In this embodiment, through running experiments, the performance is optimal when the parameter λ is 0.1. In addition, by continuously updating the similarity matrix so that it has a block diagonal frame, the specific number of iterations of Formula 1 is set to 50 times;

[0054] Step 3: Select representative bands;

[0055] Based on the fact that the bands in each sub-block matrix can be represented by a low-dimensional manifold through the remaining bands, each sub-block matrix is extracted from the block diagonal similarity matrix S, and the coefficient matrix corresponding to each sub-block matrix is obtained through dictionary learning. The band corresponding to the maximum value of the sum of the coefficient matrix columns is selected as the representative band of each sub-block matrix. All representative bands form a representative band set, which is specifically implemented by the following formula:

[0056]

[0057] in, is a minimization problem set for dictionary learning, where s i2 is the sub-block matrix S i2 Column vector, S i2 is the i2th sub-block matrix, i2 is a positive integer greater than 0 and less than or equal to k, c i2 is the coefficient vector to be obtained, ||c i2 ||1 is a regularization term set to obtain a more sparse coefficient matrix; δ is the sparse regularization term parameter;

[0058] In this embodiment, the parameter δ is set to 0.5. In addition, in order to obtain a sparser coefficient vector and reduce the reconstruction error, the number of iterations of Formula 2 is set to 100.

[0059] In order to prove the superiority of the present invention, the following comparative experiments were performed:

[0060] 1. Setting of comparison objects;

[0061] A sorting algorithm (MVPCA) and a clustering algorithm (FNGBS) were selected as comparison algorithms; the MVPCA specifically involves: first constructing the covariance matrix of the bands and performing eigenvalue decomposition on the similarity matrix to construct the load factor matrix, and then sorting all the bands according to the matrix; the FNGBS specifically involves: adopting a coarse-fine partitioning strategy to group all the bands, and then obtaining the band with the largest product based on the local density and information entropy of each group.

[0062] 2. Experimental dataset setting;

[0063] The experimental datasets used are the Pavia University dataset, the Botswana dataset, and the Salinas dataset. The Pavia University dataset is a subset of hyperspectral data from an image of the city of Pavia, Italy, taken in 2003 by the German airborne Reflective Optics Spectrographic Imaging System (ROSIS-03). The hyperspectral image cube has 115 bands and is 610×340 pixels in size. This dataset removes some bands with low signal-to-noise ratios, resulting in 103 spectral bands in nine categories. The Botswana dataset was acquired by the NASA EO-1 satellite over the Okavango Delta in Botswana between 2001 and 2004. It contains 242 bands, and 145 bands are typically used after removing 97 bands affected by noise. The image size is 1476×256, so it contains 377,856 pixels. Salinas dataset: It was captured by the 224-band AVIRIS sensor over Salinas Valley, California. This dataset has a total of 224 bands, and generally uses images of the 204 bands remaining after removing bands 108-112, 154-167, and the 224th band that cannot be reflected by water. The image size is 512×217 pixels, containing a total of 111,104 pixels.

[0064] 3. Classifier settings;

[0065] In order to test the performance of the band selection method, two classifiers were introduced: KNN (K-Nearest Neighbor) classifier and SVM (Support Vector Machine) classifier to classify the experimental data set. The same parameter settings were set in the experiment to ensure the accuracy of the experiment. The parameter of KNN was set to 5, and the penalty factor of SVM was set to 1×10 4 , with a gamma coefficient of 0.5. For both classifiers, 10% of the samples were used for training, with the remaining samples used as testing. Each algorithm was tested five times, with the average of the results taken as the final result. The overall accuracy (OA) for different numbers of bands in the range [5, 50] and the average overall accuracy (AOA) for bands in the range [5, 50] were used as metrics to test the performance of all band selection algorithms.

[0066] 4. Experimental results;

[0067] 4.1. The Pavia University dataset was used as the experimental data set. The SVM classifier and the KNN classifier were used to test the present invention, MVPCA, and FNGBS.

[0068] Table 1 shows the OA (%) of the SVM classifier for the three algorithms on the Pavia University dataset:

[0069] Table 1

[0070]

[0071]

[0072] Table 2 shows the OA (%) of the KNN classifier for the three algorithms on the Pavia University dataset:

[0073] Table 2

[0074] Number of bands The present invention MVPCA FNGBS 5 83.17 61.15 82.68 7 85.92 65.12 84.03 10 85.05 68.79 85.56 12 85.57 78.11 84.48 15 85.66 81.98 85.17 20 85.23 83.21 85.8 25 86.55 87.24 86.16 30 85.82 86.47 86.85 40 85.63 87.79 85.78 50 87.11 87.49 86.28

[0075] As can be seen from Tables 1 and 2, the present invention has a superior performance advantage on the Pavia University dataset, especially when the number of selected bands is small, where the OA of the present invention is higher than other algorithms. Even under extreme conditions, the accuracy gap can reach 20%.

[0076] 4.2. The experimental data set uses the Botswana data set, and the SVM classifier and KNN classifier are used to test the present invention, MVPCA and FNGBS;

[0077] Table 3 shows the OA (%) of the SVM classifier against the three algorithms on the Botswana dataset:

[0078] Table 3

[0079] Number of bands The present invention MVPCA FNGBS 5 85.7 66.47 79.362 7 87.66 69.15 83.44 10 87.62 72.78 86.7 12 88.76 70.48 86.01 15 88.41 84.4 87.76 20 89.13 88.17 87.35 25 89.61 88.41 89.51 30 91.19 88.31 89.33 40 90.78 88.07 91.15 50 91.94 89.784 91.98

[0080] Table 4 shows the OA (%) of the KNN classifier against the three algorithms on the Botswana dataset:

[0081] Table 4

[0082]

[0083]

[0084] It can be seen from Tables 3 and 4 that the present invention still shows a good advantage on the Botswana dataset. When the number of selected bands is relatively small, it has superior performance compared with both the SVM classifier and the KNN classifier. As the number of selected bands increases, the classification accuracy of the three algorithms gradually approaches.

[0085] 4.3. The experimental data set uses the Salinas data set, and the SVM classifier and KNN classifier are used to test the present invention, MVPCA and FNGBS;

[0086] Table 5 shows the OA (%) of the SVM classifier for the three algorithms on the Salinas dataset:

[0087] Table 5

[0088] Number of bands The present invention MVPCA FNGBS 5 88.87 75.886 87.32 7 90.15 79.415 89.35 10 91.14 81.99 91.17 12 90.8 83.29 91.14 15 91.28 84.53 91.57 20 91.39 87.61 91.45 25 92.01 88.32 91.73 30 92.12 90.08 92.15 40 92.31 91.23 92.3 50 92.92 91.29 92.7

[0089] Table 6 shows the OA (%) of the KNN classifier for the three algorithms on the Salinas dataset:

[0090] Table 6

[0091] Number of bands The present invention MVPCA FNGBS 5 87.64 73.44 85.83 7 88.14 76.28 86.7 10 88.5 79.22 88.32 12 88.35 79.46 88.13 15 88.74 80.1 88.2 20 88.85 85.17 88.33 25 88.67 85.22 88.4 30 88.91 85.88 88.7 40 88.57 87.2 89.01 50 89.03 87.77 89.06

[0092] It can be seen from Tables 5 and 6 that the present invention shows a great advantage on the Salinas dataset. Although there are some fluctuations in OA when the KNN classifier is used when the number of bands is large, the present invention is generally better than the other two algorithms.

[0093] 4.4. The number of bands is [5,50], and the AOA of the present invention, MVPCA and FNGBS on the experimental dataset is obtained by SVM classifier and KNN classifier;

[0094] Table 7 shows the AOA (%) of the SVM classifier for the present invention, MVPCA and FNGBS on the experimental data set:

[0095] Table 7

[0096]

[0097]

[0098] Table 8 shows the AOA (%) of the KNN classifier for the present invention, MVPCA and FNGBS on the experimental data set:

[0099] Table 8

[0100]

[0101] It can be seen from Tables 7 and 8 that, regardless of whether it is the KNN classifier or the SVM classifier, the AOA of the present invention on each experimental data set is better than the other two algorithms, which fully demonstrates the performance advantage and robustness of the present invention and further proves the superiority of block diagonal matrix clustering.

[0102] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them. For ordinary professional and technical personnel in this field, the specific technical solutions recorded in the above embodiments can be modified, or some of the technical features therein can be replaced by equivalents. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions protected by the present invention.

Claims

1. A hyperspectral band selection method based on similarity matrix block diagonal partitioning, characterized in that: The steps include: Step 1: Construct an initial affinity matrix; Step 1.1: Treat each band of the hyperspectral image to be processed as a data point and form a data matrix X = {x1, x2, x3...x N }; where x1 is the first data point, x N is the Nth data point, N is the number of data points of the hyperspectral image, and N is a positive integer greater than 1; Step 1.2: Learn the initial affinity matrix by calculating the distance between data points, obtain the affinity value between each data point, and then obtain the initial affinity matrix A. This is achieved by the following formula: Among them, x i is the i-th data point, x j is the j-th data point, i, j are positive integers greater than 0 and less than or equal to N; is x i with x j The Euclidean distance between ij is x i with x j The affinity value between them; γ is used to adjust the regularization term The weight parameter of The affinity value is calculated according to the following formula: in, is the optimal affinity value, m is the number of neighbors, where j <h≤m, Step 2: construct a block diagonal similarity matrix; Learn using the initial affinity matrix A and add a rank constraint during the learning process to finally obtain the block diagonal similarity matrix S = [S1, S2..., S k ; where S1 is the first sub-block matrix, S k is the k-th sub-block matrix, k < N, which is specifically implemented through Equation (1): in, This is to make the block diagonal similarity matrix S better approximate the minimization problem set by the affinity matrix A. is the F norm; is the sum of the k smallest eigenvalues of the Laplace matrix. The purpose is to make the obtained similarity matrix S contain k sub-block matrices. λ is a balancing parameter of the minimization problem. Step 3: Select representative bands; Extract each sub-block matrix from the block diagonal similarity matrix S, obtain the coefficient matrix corresponding to each sub-block matrix through dictionary learning, select the band corresponding to the maximum value of the sum of the coefficient matrix columns as the representative band of each sub-block matrix, and all representative bands form a representative band set, which is specifically implemented by Formula 2: in, is a minimization problem set for dictionary learning, where s i2 is the sub-block matrix S i2 Column vector, S i2 is the i2th sub-block matrix, i2 is a positive integer greater than 0 and less than or equal to k, c i2 is the coefficient vector to be obtained, ||c i2 ||1 is a regularization term set to obtain a more sparse coefficient matrix; δ is the sparse regularization term parameter.

2. The hyperspectral band selection method based on similarity matrix block diagonal partitioning according to claim 1, characterized in that: In step 2, the parameter λ is 0.1, and the number of iterations of formula 1 is 50.

3. The hyperspectral band selection method based on similarity matrix block diagonal partitioning according to claim 2, characterized in that: In step 3, the parameter δ is 0.5, and the number of iterations of Formula 1 is 100.

Images