A kernel-free fast spectral clustering method based on weighted spatial spectral fusion

Abstract

This invention discloses a kernel-free fast spectral clustering method based on weighted spatial-spectral fusion, comprising: 1. Preprocessing the original hyperspectral image using weighted spatial-spectral fusion and neighbor imputation methods to obtain a preprocessed hyperspectral image; 2. Constructing a kernel-free similarity matrix Z of the preprocessed hyperspectral image; 3. Constructing a kernel-free adjacency matrix W of the preprocessed hyperspectral image and obtaining the Laplacian matrix L; 4. Clustering the Laplacian matrix L using a spectral clustering algorithm and outputting the clustering results. The method of this invention is simple in its steps. It preprocesses the hyperspectral image using weighted spatial-spectral fusion and neighbor imputation methods to construct a kernel-free adjacency matrix, and then uses a spectral clustering algorithm for clustering. This avoids manual parameter tuning, achieves adaptive parameter tuning, and saves manpower and resources.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing image processing technology, specifically relating to a kernelless fast spectral clustering method based on weighted spatial-spectral fusion. Background Technology

[0002] Hyperspectral remote sensing technology fuses spatial and spectral information of ground features to form a unified spatial-spectral hyperspectral image. Cluster analysis of hyperspectral images has been widely applied in military and civilian fields such as resource exploration, environmental monitoring, military mapping, intelligent intelligence analysis, target detection, and camouflage identification. However, most current hyperspectral clustering methods mainly focus on spectral information and do not adequately consider the spatial information of the image; moreover, the Gaussian function introduced during clustering requires manual optimization, which is time-consuming and labor-intensive. Summary of the Invention

[0003] The technical problem to be solved by this invention is to address the shortcomings of the prior art by providing a kernelless fast spectral clustering method based on weighted spatial-spectral fusion. The method has simple steps and reasonable design. It uses weighted spatial-spectral fusion and neighbor-filling methods to preprocess hyperspectral images and construct a kernelless adjacency matrix. Then, a spectral clustering algorithm is used for clustering, avoiding manual parameter tuning and achieving adaptive parameter tuning, thus saving manpower and resources.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a kernelless fast spectral clustering method based on weighted spatial-spectral fusion, characterized in that the method includes the following steps:

[0005] Step 1: Preprocess the original hyperspectral image using weighted spatial spectral and neighbor-filling methods to obtain the preprocessed hyperspectral image;

[0006] Step 2: Construct the kernel-free similarity matrix Z of the preprocessed hyperspectral image;

[0007] Step 3: Construct the kernel-free adjacency matrix W of the preprocessed hyperspectral image and obtain the Laplacian matrix L;

[0008] Step 4: Use the spectral clustering algorithm to cluster the Laplacian matrix L and output the clustering results.

[0009] The aforementioned kernelless fast spectral clustering method based on weighted spatial-spectral fusion is characterized by the following step: In step one, weighted spatial-spectral fusion and neighbor-filling methods are used to preprocess the original hyperspectral image. The specific process is as follows:

[0010] Step 101: Set the pixel in row a, column b of the original hyperspectral image to I. a,b The original hyperspectral image has A rows and B columns. Determine pixel I. a,bIs the image metadata zero? If image node I a,b If the image metadata is zero, it means that pixel point I a,b For blank points, proceed to step 102 for pixel point I. a,b Perform weighted spatial spectrum and neighbor-filling processing; otherwise, pixel point I a,b Normally, no processing is performed; where a and b are both positive integers, 1≤a≤A, 1≤b≤B;

[0011] Step 102: First, when a is 2 to A-1 and b is 2 to B-1, let pixel point I... a,b The image metadata is obtained by processing the image metadata of non-blank points in its neighborhood space using the VMF method.

[0012] Next, pixel point I a,b For the pixel I of the original hyperspectral image 1,1 Then let pixel point I a,b The image metadata is pixel point I 2,2 Metadata;

[0013] Pixel point I a,b For the pixel I of the original hyperspectral image 1,B Then let pixel point I a,b The image metadata is pixel point I 2,(B-1) Metadata;

[0014] Pixel point I a,b For the pixel I of the original hyperspectral image A,1 Then let pixel point I a,b The image metadata is pixel point I (A-1),2 Metadata;

[0015] Pixel point I a,b For the pixel I of the original hyperspectral image A,B Then let pixel point I a,b The image metadata is pixel point I (A-1),(B-1) Metadata;

[0016] When a = 1 and b is between 2 and B-1, i.e., pixel point I a,b Pixel I in the original hyperspectral image 1,2 ~Pixel point I 1,(B-1) At the edge, let pixel point I a,b The image metadata is pixel point I 2,b ;

[0017] When a = A and b is 2 to B-1, i.e., pixel point I a,b Pixel I in the original hyperspectral image A,2 ~Pixel point I A,(B-1) At the edge, let pixel point Ia,b The image metadata is pixel point I (A-1),b ;

[0018] When a is 2 to A-1 and b = 1, that is, pixel point I a,b Pixel I in the original hyperspectral image 2,1 ~Pixel point I (A-1),1 At the edge, let pixel point I a,b The image metadata is pixel point I a,2 ;

[0019] When a is 2 to A-1 and b = B, that is, pixel point I a,b Pixel I in the original hyperspectral image 2,B ~Pixel point I (A-1),B At the edge, let pixel point I a,b The image metadata is pixel point I a,(B-1) ;

[0020] Step 103: Obtain the preprocessed hyperspectral image by following the methods described in steps 101 to 102;

[0021] Step 104: Set the size of the preprocessed hyperspectral image to A×B, then the pixel data of the preprocessed hyperspectral image is X, and X=[x1,...,x i ,...,x n ]; where x i Let i represent the pixel data of the i-th pixel in the hyperspectral image; i and n are both positive integers, and 1≤i≤n, n=AB.

[0022] The aforementioned kernel-free fast spectral clustering method based on weighted spatial-spectral fusion is characterized by: constructing the kernel-free similarity matrix Z of the preprocessed hyperspectral image in step two, the specific process of which is as follows:

[0023] Step 201: Using a computer, select m pixels from the pixel data X of the preprocessed hyperspectral image as anchor points to form anchor point data U, where U = [u1,...,u...]. j ,...,u m ]; where j and m are both positive integers, and 1≤j≤m, u j This represents the image data of the j-th anchor point, where m is less than n;

[0024] Step 202: Use a computer to construct the similarity matrix Z between image data points and anchor points, and Among them, z ij This represents the similarity between the i-th pixel and the j-th anchor point.

[0025] The aforementioned kernelless fast spectral clustering method based on weighted spatial-spectral fusion is characterized in that: in step 202, the similarity z between the i-th pixel and the j-th anchor point is... ij The specific process for obtaining it is as follows:

[0026] Step 2021: Using a computer according to... and The weight coefficient d between the i-th pixel and the j-th anchor point is obtained. ij ;in, This represents the square of the Euclidean distance between the i-th pixel and the j-th anchor point. This represents the average value of the pixel data in the neighborhood of the i-th pixel. Let α represent the average value of the pixel data in the neighborhood of the i-th pixel and the square of the Euclidean distance between the j-th anchor point and the i-th pixel. Let α represent the balance parameter and the value of α ranges from 0 to 1.

[0027] Step 2022: Use a computer to establish an optimization model for the similarity between the i-th pixel and the j-th anchor point, resulting in the following formula:

[0028] Where min represents the minimum value, and st represents the constraint condition. γ z represents the regularization parameter, ||||2 represents the 2-norm; i Let d represent the vector of elements in the i-th row of the similarity matrix Z. i Let d represent the weight coefficient vector of the i-th row, and d i =[d i1 … d ij … d im ], T represents the transpose, I represents a vector of size m×1 with all elements being 1, and I=[1 … 1 … 1];

[0029] Step 2023: Use a computer to establish the Lagrange function according to equation (1), as follows:

[0030] Where η is the first Lagrange multiplier, β i Let be the second Lagrange multiplier vector, and β i Each multiplier element is greater than or equal to zero;

[0031] Step 2024: Solve the Lagrangian function (2) using a computer under the Carlow-Kuhn-Tucker conditions to obtain z. i The optimal solution (z) i ) * Among them, (z i ) * The optimal solution for the similarity between the i-th pixel and the j-th anchor point is: and

[0032] The aforementioned kernel-free fast spectral clustering method based on weighted spatial-spectral fusion is characterized by: in step three, constructing the kernel-free adjacency matrix W of the preprocessed hyperspectral image and obtaining the Laplacian matrix L, the specific process is as follows:

[0033] Step 301: Use a computer to calculate W=ZΛ -1 Z T This yields a kernel-free adjacency matrix W; where Λ is an m×m diagonal matrix with all off-diagonal elements being 0. -1 Represents the inverse of matrix Λ, and the jj-th diagonal element Λ of matrix Λ. jj for The size of the kernelless adjacency matrix W is n×n;

[0034] Step 302: Using a computer, obtain the Laplace matrix L according to L = DW; where D is the degree matrix, and D has a size of n×n. The degree matrix D is a diagonal matrix, and all off-diagonal elements are 0. The i′i′th diagonal element D in the degree matrix D is... i′i′ for i′ represents the number of rows in the kernel-free adjacency matrix W, j′ represents the number of columns in the kernel-free adjacency matrix W, and w i′j′ Let i' represent the value of the element in the i'th row and j'th column of the kernelless adjacency matrix W, where i' and j' are positive integers, 1≤i'≤n, and 1≤j'≤n.

[0035] Step 303: Use a computer to obtain the eigenvectors corresponding to the first k eigenvalues ​​of the Laplacian matrix L as the eigenma matrix; wherein the first k eigenvalues ​​are smaller than the other eigenvalues.

[0036] Step 304: Using a computer, each row of the feature matrix is ​​treated as a sample. The computer then uses the k-means clustering algorithm to cluster each sample and outputs the clustering results.

[0037] The aforementioned kernelless fast spectral clustering method based on weighted spatial-spectral fusion is characterized by: the average value of pixel data in the neighborhood space of the i-th pixel in step 2021. The specific process for obtaining it is as follows:

[0038] Step A: When the i-th pixel is a corner point of the preprocessed hyperspectral image, the number of pixels in the neighborhood space centered on the i-th pixel is 3. Therefore, the average value of the data from these 3 neighborhood pixels is taken as...

[0039] When the i-th pixel is an edge of the preprocessed hyperspectral image but not a corner point, the number of pixels in the neighborhood space centered on the i-th pixel is 5. Therefore, the average value of the data from these 5 neighborhood pixels is taken as...

[0040] When the i-th pixel is neither an edge nor a corner of the preprocessed hyperspectral image, the number of pixels in the neighborhood space centered on the i-th pixel is 8. Therefore, the average value of the data from these 8 neighborhood pixels is taken as...

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] 1. The method of this invention has simple steps and reasonable design, which solves the problem that the Gaussian function introduced in clustering needs to be manually tuned, which is time-consuming and labor-intensive.

[0043] 2. This invention preprocesses hyperspectral images using weighted spatial spectral and neighbor-filling methods to reconstruct data at blank pixels, enhance the correlation between pixel data, and reduce the interference of noise and anomalous data in hyperspectral images.

[0044] 3. This invention constructs a kernelless adjacency matrix W using a kernelless similarity matrix Z, avoiding the use of a Gaussian kernel function and avoiding the impact of unsuitable adjustment of the hot kernel parameter in the Gaussian kernel function on the clustering performance of the spectral clustering algorithm. This avoids manual parameter tuning, achieves adaptive parameter tuning, and saves manpower and resources.

[0045] 4. This invention constructs a similarity matrix by using image data points and anchor points, which greatly reduces the amount of data and accelerates the clustering speed.

[0046] 5. When constructing the kernelless similarity matrix Z, this invention considers the spatial information of the image when obtaining the similarity between the pixel point and the anchor point, thereby helping to improve the clustering effect.

[0047] 6. This invention solves the problem that classical spectral clustering algorithms cannot be used for large-scale hyperspectral data. Compared with other clustering algorithms, it improves clustering accuracy, speeds up clustering, and has good robustness.

[0048] In summary, the method of this invention is simple in steps and reasonable in design. It uses weighted spatial spectrum and neighbor-filling methods to preprocess hyperspectral images and construct a kernel-free adjacency matrix. Then, it uses a spectral clustering algorithm for clustering, avoiding manual parameter tuning and achieving adaptive parameter tuning, thus saving manpower and resources.

[0049] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0051] like Figure 1As shown, the present invention provides a kernelless fast spectral clustering method based on weighted spatial spectral fusion, comprising the following steps:

[0052] Step 1: Preprocess the original hyperspectral image using weighted spatial spectral and neighbor-filling methods to obtain the preprocessed hyperspectral image;

[0053] Step 2: Construct the kernel-free similarity matrix Z of the preprocessed hyperspectral image;

[0054] Step 3: Construct the kernel-free adjacency matrix W of the preprocessed hyperspectral image and obtain the Laplacian matrix L;

[0055] Step 4: Use the spectral clustering algorithm to cluster the Laplacian matrix L and output the clustering results.

[0056] In this embodiment, step one involves preprocessing the original hyperspectral image using a weighted spatial spectrum and neighbor-filling method. The specific process is as follows:

[0057] Step 101: Set the pixel in row a, column b of the original hyperspectral image to I. a,b The original hyperspectral image has A rows and B columns. Determine pixel I. a,b Is the image metadata zero? If image node I a,b If the image metadata is zero, it means that pixel point I a,b For blank points, proceed to step 102 for pixel point I. a,b Perform weighted spatial spectrum and neighbor-filling processing; otherwise, pixel point I a,b Normally, no processing is performed; where a and b are both positive integers, 1≤a≤A, 1≤b≤B;

[0058] Step 102: First, when a is 2 to A-1 and b is 2 to B-1, let pixel point I... a,b The image metadata is obtained by processing the image metadata of non-blank points in its neighborhood space using the VMF method.

[0059] Next, pixel point I a,b For the pixel I of the original hyperspectral image 1,1 Then let pixel point I a,b The image metadata is pixel point I 2,2 Metadata;

[0060] Pixel point I a,b For the pixel I of the original hyperspectral image 1,B Then let pixel point I a,b The image metadata is pixel point I 2,(B-1) Metadata;

[0061] Pixel point I a,bFor the pixel I of the original hyperspectral image A,1 Then let pixel point I a,b The image metadata is pixel point I (A-1),2 Metadata;

[0062] Pixel point I a,b For the pixel I of the original hyperspectral image A,B Then let pixel point I a,b The image metadata is pixel point I (A-1),(B-1) Metadata;

[0063] When a = 1 and b is between 2 and B-1, i.e., pixel point I a,b Pixel I in the original hyperspectral image 1,2 ~Pixel point I 1,(B-1) At the edge, let pixel point I a,b The image metadata is pixel point I 2,b ;

[0064] When a = A and b is 2 to B-1, i.e., pixel point I a,b Pixel I in the original hyperspectral image A,2 ~Pixel point I A,(B-1) At the edge, let pixel point I a,b The image metadata is pixel point I (A-1),b ;

[0065] When a is 2 to A-1 and b = 1, that is, pixel point I a,b Pixel I in the original hyperspectral image 2,1 ~Pixel point I (A-1),1 At the edge, let pixel point I a,b The image metadata is pixel point I a,2 ;

[0066] When a is 2 to A-1 and b = B, that is, pixel point I a,b Pixel I in the original hyperspectral image 2,B ~Pixel point I (A-1),B At the edge, let pixel point I a,b The image metadata is pixel point I a,(B-1) ;

[0067] Step 103: Obtain the preprocessed hyperspectral image by following the methods described in steps 101 to 102;

[0068] Step 104: Set the size of the preprocessed hyperspectral image to A×B, then the pixel data of the preprocessed hyperspectral image is X, and X=[x1,...,x i ,...,x n ]; where x iLet i represent the pixel data of the i-th pixel in the hyperspectral image; i and n are both positive integers, and 1≤i≤n, n=AB.

[0069] In this embodiment, the kernel-free similarity matrix Z of the preprocessed hyperspectral image is constructed in step two, and the specific process is as follows:

[0070] Step 201: Using a computer, select m pixels from the pixel data X of the preprocessed hyperspectral image as anchor points to form anchor point data U, where U = [u1,...,u...]. j ,...,u m ]; where j and m are both positive integers, and 1≤j≤m, u j This represents the image data of the j-th anchor point, where m is less than n;

[0071] Step 202: Use a computer to construct the similarity matrix Z between image data points and anchor points, and Among them, z ij This represents the similarity between the i-th pixel and the j-th anchor point.

[0072] In this embodiment, the similarity z between the i-th pixel and the j-th anchor point in step 202 is... ij The specific process for obtaining it is as follows:

[0073] Step 2021: Using a computer according to... and The weight coefficient d between the i-th pixel and the j-th anchor point is obtained. ij ;in, This represents the square of the Euclidean distance between the i-th pixel and the j-th anchor point. This represents the average value of the pixel data in the neighborhood of the i-th pixel. Let α represent the average value of the pixel data in the neighborhood of the i-th pixel and the square of the Euclidean distance between the j-th anchor point and the i-th pixel. Let α represent the balance parameter and the value of α ranges from 0 to 1.

[0074] Step 2022: Use a computer to establish an optimization model for the similarity between the i-th pixel and the j-th anchor point, resulting in the following formula:

[0075] Where min represents the minimum value, st represents the constraint condition, γ represents the regularization parameter, and ||||2 represents the 2-norm; z i Let d represent the vector of elements in the i-th row of the similarity matrix Z. i Let d represent the weight coefficient vector of the i-th row, and d i =[d i1 … d ij … d im], T represents the transpose, I represents a vector of size m×1 with all elements being 1, and I=[1 … 1 … 1];

[0076] Step 2023: Use a computer to establish the Lagrange function according to equation (1), as follows:

[0077] Where η is the first Lagrange multiplier, β i Let be the second Lagrange multiplier vector, and β i Each multiplier element is greater than or equal to zero;

[0078] Step 2024: Solve the Lagrangian function (2) using a computer under the Carlow-Kuhn-Tucker conditions to obtain z. i The optimal solution (z) i ) * Among them, (z i ) * The optimal solution for the similarity between the i-th pixel and the j-th anchor point is: and

[0079] In this embodiment, step three involves constructing the kernel-free adjacency matrix W of the preprocessed hyperspectral image and obtaining the Laplacian matrix L. The specific process is as follows:

[0080] Step 301: Use a computer to calculate W=ZΛ -1 Z T This yields a kernel-free adjacency matrix W; where Λ is an m×m diagonal matrix with all off-diagonal elements being 0. -1 Represents the inverse of matrix Λ, and the jj-th diagonal element Λ of matrix Λ. jj for The size of the kernelless adjacency matrix W is n×n;

[0081] Step 302: Using a computer, obtain the Laplace matrix L according to L = DW; where D is the degree matrix, and D has a size of n×n. The degree matrix D is a diagonal matrix, and all off-diagonal elements are 0. The i′i′th diagonal element D in the degree matrix D is... i′i′ for i′ represents the number of rows in the kernel-free adjacency matrix W, j′ represents the number of columns in the kernel-free adjacency matrix W, and w i′j′ Let i' represent the value of the element in the i'th row and j'th column of the kernelless adjacency matrix W, where i' and j' are positive integers, 1≤i'≤n, and 1≤j'≤n.

[0082] Step 303: Use a computer to obtain the eigenvectors corresponding to the first k eigenvalues ​​of the Laplacian matrix L as the eigenma matrix; wherein the first k eigenvalues ​​are smaller than the other eigenvalues.

[0083] Step 304: Using a computer, each row of the feature matrix is ​​treated as a sample. The computer then uses the k-means clustering algorithm to cluster each sample and outputs the clustering results.

[0084] In this embodiment, the average value of the pixel data in the neighborhood space of the i-th pixel point in step 2021 is... The specific process for obtaining it is as follows:

[0085] Step A: When the i-th pixel is a corner point of the preprocessed hyperspectral image, the number of pixels in the neighborhood space centered on the i-th pixel is 3. Therefore, the average value of the data from these 3 neighborhood pixels is taken as...

[0086] When the i-th pixel is an edge of the preprocessed hyperspectral image but not a corner point, the number of pixels in the neighborhood space centered on the i-th pixel is 5. Therefore, the average value of the data from these 5 neighborhood pixels is taken as...

[0087] When the i-th pixel is neither an edge nor a corner of the preprocessed hyperspectral image, the number of pixels in the neighborhood space centered on the i-th pixel is 8. Therefore, the average value of the data from these 8 neighborhood pixels is taken as...

[0088] In this embodiment, the adjacent space in step 102 refers to the space with pixel point I. a,b The eight pixels surrounding the center are called pixel I. a,b The adjacent space.

[0089] In this embodiment, the VMF method is the weighted mean filtering method.

[0090] In this embodiment, the constraints This indicates that the sum of the elements in the i-th row of the similarity matrix Z is 1, and each element is greater than or equal to 0.

[0091] In this embodiment, the hyperspectral images are from the Pavia Centre dataset, as shown in Table 1:

[0092] Table 1. Relevant parameters of the hyperspectral dataset

[0093]

[0094] In this embodiment, the method of the present invention, the K-means algorithm, fuzzy C-means clustering (FCM), and the swarm intelligence-based WSN hierarchical routing algorithm (FCM_SI) were used to conduct clustering experiments on the hyperspectral dataset Pavia Centre. The quantitative results of the experiments are shown in Table 2.

[0095] Table 2. Quantitative evaluation of clustering performance of different algorithms on the Pavia Centre dataset.

[0096]

[0097] Commonly used quantitative evaluation metrics for assessing the clustering effect of hyperspectral images include: User's Accuracy (UA), Average Accuracy (AA), Overall Accuracy (OA), and the Kappa coefficient. UA represents the clustering accuracy of each category (labeled data) in an image. AA is the sum of all User Accuracy (UA) values ​​divided by the number of categories, representing the average accuracy of UA and demonstrating the statistical clustering effect of the labeled data. OA represents the clustering accuracy of all data (labeled data and background) in an image, reflecting the statistical clustering effect of all data. The values ​​of UA, AA, and OA are all between 0 and 1, with higher values ​​indicating higher accuracy. The Kappa coefficient measures the consistency between the original labels and the predicted labels; the Kappa value is between 0 and 1, with a larger Kappa indicating better consistency.

[0098] As shown in Table 2, the average accuracy (AA) of the method proposed in this invention is 54.56%, which is higher than that of K-means, FCM, and FCM_S1 algorithms, indicating an improvement over traditional clustering methods. The overall accuracy (OA) of the method proposed in this invention reaches 75%, and the Kappa coefficient reaches 0.66. The clustering time of the method proposed in this invention is 62.6 s, demonstrating a faster clustering speed. The method proposed in this invention exhibits a significant advantage in clustering efficiency on large-scale hyperspectral image data, fully demonstrating the effectiveness of the kernel-free strategy and weighted spatial spectrum processing.

[0099] In summary, the method of this invention is simple in steps and reasonable in design. It uses weighted spatial spectrum and neighbor-filling methods to preprocess hyperspectral images and construct a kernel-free adjacency matrix. Then, it uses a spectral clustering algorithm for clustering, avoiding manual parameter tuning and achieving adaptive parameter tuning, thus saving manpower and resources.

[0100] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A kernel-free fast spectral clustering method based on weighted spatial-spectral fusion, characterized in that, The method includes the following steps: Step 1: Preprocess the original hyperspectral image using weighted spatial spectral and neighbor-filling methods to obtain the preprocessed hyperspectral image; Step 2: Construct the kernel-free similarity matrix Z of the preprocessed hyperspectral image; Step 3: Construct the kernel-free adjacency matrix W of the preprocessed hyperspectral image and obtain the Laplacian matrix L; Step 4: Use the spectral clustering algorithm to cluster the Laplacian matrix L and output the clustering results; In step two, the kernel-free similarity matrix Z of the preprocessed hyperspectral image is constructed. The specific process is as follows: Step 201: Using a computer, select m pixels from the pixel data X of the preprocessed hyperspectral image as anchor points to form anchor point data U, where U = [u1,...,u...]. j ,...,u m ]; where j and m are both positive integers, and 1≤j≤m, u j This represents the image data of the j-th anchor point, where m is less than n; Step 202: Use a computer to construct the similarity matrix Z between image data points and anchor points, and Among them, z ij This represents the similarity between the i-th pixel and the j-th anchor point; In step three, the kernel-free adjacency matrix W of the preprocessed hyperspectral image is constructed, and the Laplacian matrix L is obtained. The specific process is as follows: Step 301: Use a computer to calculate W=ZΛ -1 Z T This yields a kernel-free adjacency matrix W; where Λ is an m×m diagonal matrix with all off-diagonal elements being 0. -1 Represents the inverse of matrix Λ, and the jj-th diagonal element Λ of matrix Λ. jj for The size of the kernelless adjacency matrix W is n×n; Step 302: Using a computer, obtain the Laplace matrix L according to L = DW; where D is the degree matrix, and D has a size of n×n. The degree matrix D is a diagonal matrix, and all off-diagonal elements are 0. The i′i′th diagonal element D in the degree matrix D is... i′i′ for i′ represents the number of rows in the kernel-free adjacency matrix W, j′ represents the number of columns in the kernel-free adjacency matrix W, and w i′j′ Let i' represent the value of the element in the i'th row and j'th column of the kernelless adjacency matrix W, where i' and j' are positive integers, 1≤i'≤n, and 1≤j'≤n. Step 303: Use a computer to obtain the eigenvectors corresponding to the first k eigenvalues ​​of the Laplacian matrix L as the eigenma matrix; wherein the first k eigenvalues ​​are smaller than the other eigenvalues. Step 304: Using a computer, each row of the feature matrix is ​​treated as a sample. The computer then uses the k-means clustering algorithm to cluster each sample and outputs the clustering results.

2. The kernelless fast spectral clustering method based on weighted spatial-spectral fusion according to claim 1, characterized in that: In step one, the original hyperspectral image is preprocessed using weighted spatial spectral density and neighbor-filling methods. The specific process is as follows: Step 101: Set the pixel in row a, column b of the original hyperspectral image as I. a,b The original hyperspectral image has A rows and B columns. Determine pixel I. a,b Is the image metadata zero? If image node I a,b If the image metadata is zero, it means that pixel point I a,b For blank points, proceed to step 102 for pixel point I. a,b Perform weighted spatial spectrum and neighbor-filling processing; otherwise, pixel point I a,b Normally, no processing is performed; where a and b are both positive integers, 1≤a≤A, 1≤b≤B; Step 102: First, when a is 2 to A-1 and b is 2 to B-1, let pixel point I... a,b The image metadata is obtained by processing the image metadata of non-blank points in its neighborhood space using the VMF method. Next, pixel point I a,b For the pixel I of the original hyperspectral image 1,1 Then let pixel point I a,b The image metadata is pixel point I 2,2 Metadata; Pixel point I a,b For the pixel I of the original hyperspectral image 1,B Then let pixel point I a,b The image metadata is pixel point I 2,(B-1) Metadata; Pixel point I a,b For the pixel I of the original hyperspectral image A,1 Then let pixel point I a,b The image metadata is pixel point I (A-1),2 Metadata; Pixel point I a,b For the pixel I of the original hyperspectral image A,B Then let pixel point I a,b The image metadata is pixel point I (A-1),(B-1) Metadata; When a = 1 and b is between 2 and B-1, i.e., pixel point I a,b Pixel I in the original hyperspectral image 1,2 ~Pixel point I 1,(B-1) At the edge, let pixel point I a,b The image metadata is pixel point I 2,b ; When a = A and b is 2 to B-1, i.e., pixel point I a,b Pixel I in the original hyperspectral image A,2 ~Pixel point I A,(B-1) At the edge, let pixel point I a,b The image metadata is pixel point I (A-1),b ; When a is 2 to A-1 and b = 1, that is, pixel point I a,b Pixel I in the original hyperspectral image 2,1 ~Pixel point I (A-1),1 At the edge, let pixel point I a,b The image metadata is pixel point I a,2 ; When a is 2 to A-1 and b = B, that is, pixel point I a,b Pixel I in the original hyperspectral image 2,B ~Pixel point I (A-1),B At the edge, let pixel point I a,b The image metadata is pixel point I a,(B-1) ; Step 103: Obtain the preprocessed hyperspectral image by following the methods described in steps 101 to 102; Step 104: Set the size of the preprocessed hyperspectral image to A×B, then the pixel data of the preprocessed hyperspectral image is X, and X=[x1,...,x i ,...,x n ]; where x i Let i represent the pixel data of the i-th pixel in the hyperspectral image; i and n are both positive integers, and 1≤i≤n, n=AB.

3. The kernel-free fast spectral clustering method based on weighted spatial-spectral fusion according to claim 1, characterized in that: In step 202, the similarity z between the i-th pixel and the j-th anchor point is... ij The specific process for obtaining it is as follows: Step 2021: Using a computer according to... and The weight coefficient d between the i-th pixel and the j-th anchor point is obtained. ij ;in, This represents the square of the Euclidean distance between the i-th pixel and the j-th anchor point. This represents the average value of the pixel data in the neighborhood of the i-th pixel. Let α represent the average value of the pixel data in the neighborhood of the i-th pixel and the square of the Euclidean distance between the j-th anchor point and the i-th pixel. Let α represent the balance parameter and the value of α ranges from 0 to 1. Step 2022: Use a computer to establish an optimization model for the similarity between the i-th pixel and the j-th anchor point, resulting in the following formula: Where min represents the minimum value, st represents the constraint condition, γ represents the regularization parameter, and |||2 represents the 2-norm; z i Let d represent the vector of elements in the i-th row of the similarity matrix Z. i Let d represent the weight coefficient vector of the i-th row, and d i =[d i1 …d ij …d im ], T represents the transpose, I represents a vector of size m×1 with all elements being 1, and I=[1…1…1]; Step 2023: Use a computer to establish the Lagrange function according to equation (1), as follows: Where η is the first Lagrange multiplier, β i Let be the second Lagrange multiplier vector, and β i Each multiplier element is greater than or equal to zero; Step 2024: Solve the Lagrangian function (2) using a computer under the Carlow-Kuhn-Tucker conditions to obtain z. i The optimal solution (z) i ) * Among them, (z i ) * The optimal solution for the similarity between the i-th pixel and the j-th anchor point is: and 4. A kernelless fast spectral clustering method based on weighted spatial spectral fusion according to claim 3, characterized in that: The average value of pixel data in the neighborhood space of the i-th pixel in step 2021 The specific process for obtaining it is as follows: Step A: When the i-th pixel is a corner point of the preprocessed hyperspectral image, the number of pixels in the neighborhood space centered on the i-th pixel is 3. Therefore, the average value of the data from these 3 neighborhood pixels is taken as... When the i-th pixel is an edge of the preprocessed hyperspectral image but not a corner point, the number of pixels in the neighborhood space centered on the i-th pixel is 5. Therefore, the average value of the data from these 5 neighborhood pixels is taken as... When the i-th pixel is neither an edge nor a corner of the preprocessed hyperspectral image, the number of pixels in the neighborhood space centered on the i-th pixel is 8. Therefore, the average value of the data from these 8 neighborhood pixels is taken as...

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