Hyperspectral image clustering method and system based on spatial-spectral joint dynamic hypergraph

Abstract

The invention discloses a hyperspectral image clustering method and system based on a spatial-spectral joint dynamic hypergraph, and the method comprises the steps: determining a low-rank representation coefficient of a hyperspectral image, and obtaining a Laplace regular term of the hyperspectral image hypergraph and the weight of a hyperedge; according to the Laplacian regular term and the weight of the hyperedge, constructing a similarity-maintained low-rank subspace representation optimization model of the hypergraph structure; iteratively solving the low-rank subspace representation optimization model for keeping the similarity of the hypergraph structure to obtain a final low-rank representation coefficient, determining a Laplacian regular term of a new hypergraph and the weight of a hyperedge according to the low-rank representation coefficient solved in each round in the iteration solving process, and calculating the weight of the hyperedge by utilizing the Laplacian regular term of the new hypergraph. Performing the next round of solution; and determining a clustering result of the hyperspectral image according to the final low-rank representation coefficient. And the clustering precision is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of spectral image clustering, and in particular to a method and system for clustering hyperspectral images based on a spatial-spectral joint dynamic hypergraph. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Graph-based algorithms have been widely used in the fields of computer vision and machine learning in recent years. Graphs have been proven to successfully characterize the relationships between data samples and the popular structure of data. Compared with simple graphs that only consider the relationship between two data, hypergraphs construct hyperedges with data subsets with certain similarity attributes, which can effectively characterize the high-order relationships of data. With the continuous development of hypergraph learning, it has been widely used in feature extraction, band selection and dimensionality reduction of hyperspectral images.

[0004] The problem with existing hypergraph-based representation methods is that the pre-constructed hypergraph is generated by the original data through a fixed distance metric, rather than being obtained through dynamic learning and optimization. To address this problem, the literature [Zhang Z, Lu B, Liang Y, et al. Joint Hypergraph Learning and Sparse Regression for Feature Selection [J]. Pattern Recognition, 2017, 63: 291-309.] proposed a learning model for feature selection and data structure estimation by updating the weights of the hypergraph during the hypergraph learning process. The literature [Zhang Z, Lin H, Gao Y, BNRist, K. Dynamic Hypergraph Structure Learning. IJCAI, 2018, pp. 3162–3169.] proposed a dynamic hypergraph structure learning method, in which the indicator matrix of the hypergraph is learned by jointly learning the correlation between the data in the label space and the feature space. However, the data in the original feature space contains a lot of noise, and the performance of the algorithm is affected because it is related to the hypergraph. Summary of the invention

[0005] In order to solve the above problems, the present invention proposes a hyperspectral image clustering method and system based on spatial-spectral joint dynamic hypergraph.

[0006] To achieve the above object, the present invention adopts the following technical solution:

[0007] Firstly, a hyperspectral image clustering method based on spatial-spectral joint dynamic hypergraph is proposed, including:

[0008] Acquire hyperspectral images;

[0009] Determine the low-rank representation coefficient of the hyperspectral image, and obtain the Laplace regularization term and hyperedge weight of the hyperspectral image hypergraph;

[0010] According to the Laplace regularization term and the weight of the hyperedge, a low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure is constructed;

[0011] Iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient. In the iterative solution process, the Laplace regularization term and the weight of the hyperedge of the new hypergraph are determined according to the low-rank representation coefficient solved in each round, and the Laplace regularization term and the weight of the hyperedge of the new hypergraph are used to perform the next round of solution;

[0012] According to the final low-rank representation coefficient, the clustering result of the hyperspectral image is determined.

[0013] Further, a low-rank representation coefficient of the hyperspectral image is determined, and a representation feature in a low-rank subspace is determined according to the low-rank representation coefficient;

[0014] Determine the Laplacian matrix of the hypergraph according to the features represented in the low-rank subspace;

[0015] According to the Laplacian matrix of the hypergraph and the representation features in the low-rank subspace, the Laplacian regularization term of the hypergraph is determined.

[0016] Further, according to the representation features in the low-rank subspace, the indicator matrix of the hypergraph, the degree of the vertices, the weight of the hyperedge and the degree of the hyperedge are determined;

[0017] The Laplacian matrix of the hypergraph is determined based on the hypergraph indicator matrix, the degree of the vertex, the weight of the hyperedge and the degree of the hyperedge.

[0018] Furthermore, a variable representing a low-rank representation coefficient is introduced into the low-rank subspace representation optimization model of the hypergraph structure similarity preservation, and an optimization model after the variable is introduced is obtained;

[0019] Obtain the augmented Lagrangian function corresponding to the optimization model after the variables are introduced;

[0020] The augmented Lagrangian function is iteratively solved by fixing other variables to obtain the final low-rank representation coefficients.

[0021] Furthermore, the specific process of iteratively solving the augmented Lagrangian function corresponding to the optimization model after the introduction of variables is as follows:

[0022] The newly introduced variables are calculated using the low-rank representation coefficients, noise matrix, hypergraph indicator matrix, hyperedge weights, Lagrange multipliers, and penalty parameters calculated in the previous round;

[0023] Using the newly introduced variables calculated in this round, and the noise matrix, hypergraph indicator matrix, hyperedge weights, Lagrange multipliers, Lagrange multipliers and penalty parameters calculated in the previous round, calculate new low-rank representation coefficients;

[0024] The new noise matrix is ​​calculated using the new low-rank representation coefficients and newly introduced variables obtained in this round of calculations, as well as the hypergraph indicator matrix, hyperedge weights, Lagrange multipliers, and penalty parameters calculated in the previous round.

[0025] According to the new low-rank representation coefficients and the new noise matrix obtained in this round of calculation, the indicator matrix and the degree of the hyperedge of the new hypergraph are calculated and determined;

[0026] According to the newly introduced variables, low-rank representation coefficients, indicator matrix of the hypergraph and degree of the hyperedge obtained in this round of calculation, the weight of the new hyperedge and the degree of the vertex are calculated and determined;

[0027] According to the new low-rank representation coefficient, the indicator matrix of the hypergraph and the weight of the hyperedge obtained in this round of calculation, a new Laplace regularization term is calculated;

[0028] The new Laplace regularization term, low-rank representation coefficient, Lagrange multiplier, penalty parameter, noise matrix, indicator matrix and hyperedge weight obtained through this round of calculation are used to perform the next round of calculation on the augmented Lagrangian function corresponding to the optimization model after the introduction of variables until the iteration termination condition is reached.

[0029] Furthermore, based on the final low-rank representation coefficient, the similarity map between the pixels of the hyperspectral image is calculated;

[0030] Spectral clustering is performed on the similarity graph to obtain the clustering results of the hyperspectral image.

[0031] Secondly, a hyperspectral image clustering system based on spatial-spectral joint dynamic hypergraph is proposed, including:

[0032] An image acquisition unit, used for acquiring a hyperspectral image;

[0033] A hypergraph construction unit, used to determine the low-rank representation coefficient of the hyperspectral image and obtain the Laplace regularization term and the weight of the hyperedge of the hyperspectral image hypergraph;

[0034] A model building unit, used to build a low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure according to the Laplace regularization term and the weight of the hyperedge;

[0035] A low-rank representation coefficient determination unit is used to iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient. In the iterative solution process, the Laplace regularization term and the weight of the hyperedge of the new hypergraph are determined according to the low-rank representation coefficient solved in each round, and the Laplace regularization term and the weight of the hyperedge of the new hypergraph are used to perform the next round of solution;

[0036] The clustering result acquisition unit is used to determine the clustering result of the hyperspectral image according to the final low-rank representation coefficient.

[0037] In a third aspect, a computer device is provided, the device comprising:

[0038] a processor adapted to execute a computer program;

[0039] A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, the method for clustering hyperspectral images based on a spatial-spectral joint dynamic hypergraph proposed in the first aspect is implemented.

[0040] In a fourth aspect, a computer-readable storage medium is proposed, wherein the computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor and executing a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph proposed in the first aspect.

[0041] In a fifth aspect, a computer program product is proposed, which includes a computer program. When the computer program is executed by a processor, it implements a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph proposed in the first aspect.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention proposes a hyperspectral image clustering method and system based on a spatial-spectral joint dynamic hypergraph. When iteratively solving a low-rank subspace representation optimization model that maintains the similarity of a hypergraph structure, the method determines a new hypergraph Laplace regularization term and a hyperedge weight according to the low-rank representation coefficient solved in each round, and uses the new hypergraph Laplace regularization term and the hyperedge weight to perform the next round of solution, thereby achieving an update of the hypergraph structure and fully mining the complex high-order manifold structure of the hyperspectral spectrum. Compared with traditional subspace clustering methods, the method has high clustering accuracy and high robustness to noise.

[0044] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings in the specification, which constitute a part of the present application, are used to provide further understanding of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute improper limitations on the present application.

[0046] Figure 1 The present invention is a flowchart of a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph disclosed in an embodiment.

[0047] Figure 2 The clustering effect diagram of the Salinas-A dataset clustered by the method proposed in this invention and the existing clustering method is shown in the figure. Figure 2 (a) is the true value of the Salinas-A dataset; Figure 2 (b) is the clustering effect diagram of the Salinas-A data set using the K-means method; Figure 2 (c) is the clustering effect diagram of the Salinas-A data set using the FCM clustering method; Figure 2 (d) is the clustering effect diagram of the Salinas-A dataset using the spectral clustering method of the fully connected graph; Figure 2 (e) is the clustering effect diagram of the Salinas-A dataset using the spectral clustering method with local connection graph; Figure 2 (f) is the clustering effect diagram of the Salinas-A dataset using the sparse subspace clustering method; Figure 2 (g) is the clustering effect diagram of the Salinas-A dataset using the low-rank subspace clustering method; Figure 2 (h) is the clustering effect diagram of the Salinas-A dataset using the graph-based low-rank subspace clustering method; Figure 2 (i) is the clustering effect diagram of the Salinas-A dataset using the hypergraph-based low-rank subspace clustering method; Figure 2 (j) is a clustering effect diagram of the Salinas-A dataset using a hyperspectral image clustering method based on spatial-spectral joint dynamic hypergraph provided by the present invention.

[0048] Figure 3 The clustering effect diagram of the JasperRidge data set clustered by the method proposed by the present invention and the existing clustering method; Figure 3 (a) is the true value of the JasperRidge dataset; Figure 3 (b) is the clustering effect diagram of the Jasper Ridge dataset using the K-means method; Figure 3 (c) is the clustering effect diagram of the Jasper Ridge dataset using the FCM clustering method; Figure 3 (d) is the clustering effect diagram of the Jasper Ridge dataset using the spectral clustering method of the fully connected graph; Figure 3(e) is the clustering effect diagram of the Jasper Ridge dataset using the spectral clustering method of the local connection graph; Figure 3 (f) is the clustering effect diagram of the JasperRidge dataset using the sparse subspace clustering method; Figure 3 (g) is the clustering effect diagram of the Jasper Ridge dataset using the low-rank subspace clustering method; Figure 3 (h) is the clustering effect diagram of the Jasper Ridge dataset using the graph-based low-rank subspace clustering method; Figure 3 (i) is the clustering effect diagram of the Jasper Ridge dataset using the hypergraph-based low-rank subspace clustering method; Figure 3 (j) is a clustering effect diagram of the Jasper Ridge dataset using a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph provided by the present invention. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0050] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0051] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0052] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0053] Example 1

[0054] This embodiment aims at the hyperspectral unsupervised classification problem in the fields of land cover analysis, precision agriculture and mineral survey, and combines spatial and spectral information to propose a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph. It is a refined clustering method that does not require manual labeling of classification samples and is robust to noise.

[0055] This embodiment discloses a hyperspectral image clustering method based on spatial-spectral joint dynamic hypergraph. Figure 1-Figure 3 As shown, including:

[0056] S1: Acquire hyperspectral images.

[0057] The hyperspectral image acquired in this embodiment may be a ground coverage hyperspectral image, an agricultural hyperspectral image, a mineral hyperspectral image, and the like.

[0058] S2: Determine the low-rank representation coefficient of the hyperspectral image and obtain the Laplace regularization term and hyperedge weights of the hyperspectral image hypergraph.

[0059] Among them, the Laplace regularization term and the weight of the hyperedge of the hyperspectral image hypergraph are obtained:

[0060] S21: determining a low-rank representation coefficient of the hyperspectral image, and determining a representation feature in a low-rank subspace according to the low-rank representation coefficient;

[0061] For a hyperspectral image X0∈R W×H×L , where W and H represent the width and height of the image, respectively, and L represents the number of bands of the hyperspectral image. The hyperspectral image X0 is arranged pixel by pixel to form a matrix X∈R N×L , where N = W × H represents the number of hyperspectral pixels, according to the matrix X∈R N×L And the low-rank representation minimization model is used to determine the low-rank representation coefficients of the hyperspectral image.

[0062] Among them, the low-rank representation minimization model is:

[0063]

[0064] Where Z is the low-rank representation coefficient matrix, N∈R L×N is the noise matrix, ||Z|| * is the nuclear norm of Z, ||N|| 2,1 It is a mixture of N 2,1 norm, λ>0 is the regularization parameter.

[0065] ||Z|| * As the nuclear norm of the low-rank representation coefficient matrix Z, it is specifically defined as follows:

[0066]

[0067] Where trace(·) represents the trace operation of the matrix, σ i represents the singular values ​​of the matrix Z, and N represents the number of pixels in the hyperspectral image.

[0068] ||N|| 2,1 is a mixture of noise matrix N 2,1 Norm, specifically defined as follows:

[0069]

[0070] Where ni,j Represents the element in the i-th row and j-th column of the matrix N, N represents the number of pixels in the hyperspectral image, and L represents the number of bands of the hyperspectral image.

[0071] Let the matrix X∈R N×L Substitute it into the low-rank representation minimization model and solve the low-rank representation coefficient matrix Z = [z1, z2, L, z N ]∈R N×N .

[0072] In this embodiment, the low-rank representation coefficient is used to calculate the representation feature matrix XZ∈R in the low-rank subspace L×N , N represents the number of pixels in the hyperspectral image.

[0073] S22: Determine the Laplacian matrix of the hypergraph based on the representation features in the low-rank subspace, the process includes: determining the indicator matrix, vertex degrees, hyperedge weights and hyperedge degrees of the hypergraph based on the representation features in the low-rank subspace; determine the Laplacian matrix of the hypergraph based on the hypergraph indicator matrix, vertex degrees, hyperedge weights and hyperedge degrees.

[0074] Specifically, this embodiment uses a feature matrix XZ in a low-rank subspace to construct a hypergraph of a hyperspectral image, where XZ represents a set of vertices of the hypergraph, E represents a set of hyperedges of the hypergraph, and W represents a set of weights of hyperedges of the hypergraph. A hypergraph G = (XZ, E, W) is constructed, and the hypergraph Laplacian matrix L is calculated through the hypergraph. s .

[0075] The process of constructing the hyperedge of the hypergraph is:

[0076] Calculate the spatial spectrum joint information representing the feature matrix XZ in the low-rank subspace, and i ,n i ) at the hyperspectral pixel Xz i Select adjacent pixels and get Xz i A set of adjacent pixels Calculate Xz i The space-spectrum joint information The calculation formula is: Among them, the space-spectrum joint similarity weight f ij The calculation formula is:

[0077]

[0078] Where w is the size of the window, (m j ,n j ) is the pixel x j location.

[0079] Calculate the similarity weight matrix S∈R of the low-rank subspace representation feature based on the spatial-spectral joint information N×N , the calculation formula is:

[0080]

[0081] In the formula, S ij is the hyperspectral pixel Xz i With pixel Xz j similarities between; is the obtained similarity weight matrix, σ>0 represents the scale parameter.

[0082] According to the obtained similarity weight matrix S, According to the corresponding similarity weight S i ∈R N Select the most relevant K+1 pixels in, Will As The super edge e i , then the corresponding hyperedge set is E = [e1,e2,L,e N ];

[0083] This embodiment determines the weight of a hyperedge of a hypergraph according to a hyperedge and a hyperedge weight determination formula. The hyperedge weight determination formula is:

[0084]

[0085] In the formula, w(e i ) is the hyperedge e i The corresponding weight, is the Gaussian kernel parameter, express The most relevant K nearest neighbors.

[0086] This embodiment also determines the indicator matrix of the hypergraph. The specific indicator matrix H is:

[0087]

[0088] in,

[0089]

[0090] The degree of each vertex and the degree of each hyperedge of the hypergraph are determined according to the indicator matrix of the hypergraph and the weight of the hyperedge. The calculation formula of the degree is:

[0091]

[0092] In the formula, Represents a vertex The degree, Represents a vertex In the super edge j Within, w(e j ) represents the hyperedge e j The weight of .

[0093] The calculation formula of the degree of a hyperedge is:

[0094]

[0095] In the formula, δ(e j ) represents the hyperedge e j degree;

[0096] Determine the Laplace matrix L of the hypergraph based on the indicator matrix of the hypergraph, the degree of the hypergraph vertices, the degree of the hyperedges, and the weight of the hyperedges s .

[0097]

[0098] In the formula, is the diagonal matrix of vertex degrees, D e =diag([δ(e1),δ(e2),K,δ(e N )]) is the diagonal matrix of the degree of the hyperedge, W = diag([w(e1),w(e2),K,w(e N )]) is the weight matrix of the hyperedge.

[0099] S23: Determine the Laplacian regularization term of the hypergraph according to the Laplacian matrix of the hypergraph and the representation features in the low-rank subspace.

[0100] According to the Laplacian matrix L of the hypergraph s and the low-rank subspace to represent features and determine the Laplace regularization term of the hypergraph Among them, Tr(g) represents the trace of the matrix, XZ represents the feature matrix in the low-rank subspace, is the dynamically updated hypergraph Laplacian matrix. The specific process is as follows:

[0101] Based on hypergraph regularization, the local complex structure information of low-dimensional spatial data is maintained, and the space-spectrum joint dynamic hypergraph Laplace regularization term is established:

[0102]

[0103] The matrix form of the above model is:

[0104]

[0105] in, is the Laplacian matrix of the hypergraph.

[0106] S3: Based on the Laplace regularization term and the weights of hyperedges, a low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure is constructed.

[0107] The optimization model of low-rank subspace representation that preserves the similarity of the hypergraph structure is:

[0108]

[0109] Among them, λ1, λ2, λ3 are penalty parameters.

[0110] S4: Iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient. During the iterative solution process, determine the Laplace regularization term of the new hypergraph and the weight of the hyperedge based on the low-rank representation coefficient solved in each round, and use the new Laplace regularization term of the hypergraph and the weight of the hyperedge to perform the next round of solution.

[0111] This embodiment uses the Lagrange multiplier method to iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient Z * , the specific process is:

[0112] In the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure, a variable J representing the low-rank representation coefficient is introduced to obtain the optimization model after the variable J is introduced, so that the variables can be separated during the iterative optimization of the low-rank subspace representation optimization model. The optimization model after the variable J is introduced is:

[0113]

[0114] Obtain the augmented Lagrangian function corresponding to the optimization model after the variable J is introduced;

[0115] The augmented Lagrangian function is iteratively solved by fixing other variables to obtain the final low-rank representation coefficients.

[0116] The augmented Lagrangian function corresponding to the optimization model after the introduction of variable J is:

[0117]

[0118] Among them, C1, C2 and η are Lagrange multipliers, and μ is a penalty parameter. The variables J, Z, N, H, W and Lagrange multipliers are iteratively solved by fixing other variables until they converge.

[0119] Among them, the augmented Lagrangian function corresponding to the optimization model after the introduction of variables obtains the variable J, the low-rank representation coefficient Z, the noise matrix N, the hypergraph indicator matrix H, the hyperedge weight W, and the Laplace regularization term in each round of solution. Lagrange multipliers C1, C2 and η and penalty parameter μ.

[0120] The specific process of iteratively solving the augmented Lagrangian function corresponding to the optimization model after the introduction of variables is:

[0121] Using the low-rank representation coefficient Z calculated in the previous round t , noise matrix N t , hypergraph indicator matrix H t , the weight of the hyperedge W t , Lagrange multipliers and penalty parameter μ t , calculate the newly introduced variable J t+1 .

[0122] Specifically, with fixed variables Z, N, H, and W, the solution of variable J can be obtained by solving the following model:

[0123]

[0124] The solution calculated by the singular value threshold method is:

[0125]

[0126] Among them, Θ is the SVT operator, and the low-rank representation coefficient Z obtained by the previous round of solution is t , Lagrange multipliers and penalty parameter μ t Substituting into the above formula, we can calculate the variable J t+1 .

[0127] Using the newly introduced variable J calculated in this round t+1 , and the noise matrix N calculated in the previous round t , hypergraph indicator matrix H t , the weight of the hyperedge W t , Lagrange multipliers Lagrange multipliers and penalty parameter μ t , calculate the new low-rank representation coefficient Z t+1 Among them, the Lagrange multiplier here includes the Lagrange multiplier and Lagrange multipliers

[0128] Specifically, fix the variables J, N, H, and W, and obtain the objective function for solving Z:

[0129]

[0130] This problem is a quadratic minimization problem with an explicit solution. Solve the objective function of Z and obtain the solution function of Z as follows:

[0131]

[0132] The new low-rank representation coefficient Z obtained by this round of calculation t+1 and the newly introduced variable J t+1 , and the hypergraph indicator matrix H calculated in the previous round t , the weight of the hyperedge W t , Lagrange multipliers and penalty parameter μ t , calculate and obtain the new noise matrix N t +1 .

[0133] Specifically, the variables J, Z, H, and W are fixed, and the objective function for solving N is obtained as follows:

[0134]

[0135] According to the objective function of solving N, the solution function of the noise matrix is ​​obtained as:

[0136]

[0137] in, P i and N i is the i-th column of matrices P and N.

[0138] The new low-rank representation coefficient Z obtained by this round of calculation t+1 and the noise matrix N t+1 , calculate and determine the indicator matrix H of the new hypergraph t+1 and the degree of the hyperedge

[0139] According to the newly introduced variable J obtained in this round of calculation t+1 , low-rank representation coefficient Z t+1 , the indicator matrix H of the hypergraph t+1 and the degree of the hyperedge Calculate and determine the weight W of the new hyperedge t+1 and the degree of the vertex

[0140] Specifically, by fixing the variables J, Z, N, and H, the objective function for solving the weight W of the hyperedge is as follows:

[0141]

[0142] Where t is the number of iterations, make

[0143] According to the KKT condition, the objective function of solving the weight W of the hyperedge is solved, and the closed-form solution function of the weight of the hyperedge is obtained as:

[0144] The new low-rank representation coefficient Z obtained by this round of calculation t+1 , the indicator matrix H of the hypergraph t+1 and the weight W of the hyperedge t +1 , calculate the new Laplace regularization term

[0145] The new Laplace regularization term obtained through this round of calculation is Low rank representation coefficient Z t+1 , Lagrange multiplier, penalty parameter, noise matrix N t+1 , indicator matrix H t+1 and the weight W of the hyperedge t+1 , the augmented Lagrangian function corresponding to the optimization model after the introduction of variable J is calculated in the next round until the iteration termination condition is reached.

[0146] The iteration termination condition is: ||Z t -J t || ∞ <ε or ||X-XZ t -N t ‖ ∞ <ε or t> MaxIter,

[0147] Get the final low-rank representation coefficient Z * , where MaxIter is the set number of times and ε is the set threshold.

[0148] S5: Calculate the similarity graph according to the final low-rank representation coefficient as the input of spectral clustering to obtain the clustering result of the hyperspectral image.

[0149] This embodiment calculates a similarity map between pixels of the hyperspectral image based on the final low-rank representation coefficient;

[0150] Spectral clustering is performed on the similarity graph to obtain the clustering results of the hyperspectral image.

[0151] Using the Salinas-A dataset and the Jasper Ridge dataset, a hyperspectral image clustering method based on space-spectrum joint dynamic hypergraph (SSDH-LRSC) disclosed in this embodiment is compared with the existing K-means method, FCM clustering method, globally connected graph spectral clustering method (globally connected graph, GSC), locally connected graph spectral clustering method (locally connected graph, LSC), sparse subspace clustering method (SSC), low-rank subspace clustering method (LRSC), graph-based low-rank subspace clustering method (graphbasedLRSC, GLRSC) and hypergraph-based low-rank subspace clustering method (hypergraphbasedLRSC, HGLRSC) to verify the clustering effect of the method disclosed in this embodiment. In order to compare the fairness, the average of the 10 experimental results is finally used as the final experimental result.

[0152] The Salinas-A dataset is a subset of the Salinas images collected by the AVIRIS sensor in the Salinas Valley, California. It removes 20 water-absorbing bands (108-112, 154-167, 224), contains a total of 204 bands, and the image size is 86×83. The JasperRidge dataset contains 512×614 pixels, each of which records 224 bands continuously imaged in the spectral range from 380 to 2500 nanometers. After removing 26 noise bands (1-3, 108-112, 154-166 and 220-224), 198 valid bands remain in the data. The resolution of the scene data is 9.46 nanometers. In order to reduce the complexity of the calculation in this embodiment, the spatial dimension size is truncated to 100×100 pixels. The typical ground objects (Groundtruth) of this scene include 4 types of objects.

[0153] This embodiment uses the classic Overall Accuracy (OA), Average Accuracy (AA), Kappa coefficient, Producer's Accuracy (PA) and User's Accuracy (UA) to measure clustering performance. In addition, the NMI clustering evaluation index is also used.

[0154] Figure 2The visual effect diagrams of various algorithms on the Salinas-A dataset are shown, and Table 1 gives the corresponding quantitative analysis results. Among all the compared algorithms, SSC and LRSC only use representation learning to obtain new representation features for clustering, GSC and LSC only use graph theory for clustering, however, GLRSC and HGLRSC combine graph theory and representation learning for hyperspectral image clustering. It can be found from Table 1 that the clustering accuracy of GSC, LSC, SSC and LRSC is lower than that of GLRSC and HGLRSC. This also further verifies that learning local geometric structure information can effectively improve clustering accuracy. In addition, K-means and FCM methods are methods that obtain the lowest clustering accuracy. Compared with the above methods, the SSDH-LRSC method proposed in this embodiment effectively improves the clustering accuracy by dynamically updating the hypergraph.

[0155] Figure 3 Table 2 and Table 3 give the visual and quantitative analysis results of the Jasper Ridge dataset. It can be seen from Table 2 that the clustering effects achieved by the partition-based methods and the spectrum-based methods - K-means, FCM, GSC, LSC, SSC and LRSC - are worse than those achieved by the graph-based and hypergraph-based clustering methods. Specifically, GLRSC and HGLRSC achieve higher clustering accuracy than LRSC. The SSDH-LRSC algorithm proposed in this embodiment outperforms all other compared algorithms.

[0156] Table 1 Clustering results of different classification methods on the Salinas-A dataset

[0157]

[0158]

[0159] Table 2 Clustering results of different classification methods on the Jasper Ridge dataset

[0160]

[0161] The present embodiment discloses a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph, which effectively utilizes the spatial structure information and spectral feature information of hyperspectral data, dynamically learns and updates the hypergraph using low-dimensional subspace features, and fully exploits the complex high-order manifold structure of the hyperspectral image. Compared with the traditional subspace clustering method, the method has high clustering accuracy and high robustness to noise. It can be widely used in unsupervised classification in the fields of land resources, mineral surveys, and precision agriculture.

[0162] Example 2

[0163] In this embodiment, a hyperspectral image clustering system based on spatial-spectral joint dynamic hypergraph is disclosed, comprising:

[0164] An image acquisition unit, used for acquiring a hyperspectral image;

[0165] A hypergraph construction unit, used to determine the low-rank representation coefficient of the hyperspectral image and obtain the Laplace regularization term and the weight of the hyperedge of the hyperspectral image hypergraph;

[0166] A model building unit, used to build a low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure according to the Laplace regularization term and the weight of the hyperedge;

[0167] A low-rank representation coefficient determination unit is used to iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient. In the iterative solution process, the Laplace regularization term and the weight of the hyperedge of the new hypergraph are determined according to the low-rank representation coefficient solved in each round, and the Laplace regularization term and the weight of the hyperedge of the new hypergraph are used to perform the next round of solution;

[0168] The clustering result acquisition unit is used to determine the clustering result of the hyperspectral image according to the final low-rank representation coefficient.

[0169] The present invention also discloses a computer device, which includes:

[0170] a processor adapted to execute a computer program;

[0171] A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph disclosed in Example 1 is implemented.

[0172] The present invention also discloses a computer-readable storage medium storing a computer program, wherein the computer program is suitable for being loaded by a processor and executing a hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph disclosed in Example 1.

[0173] The present invention also discloses a computer program product, which includes a computer program. When the computer program is executed by a processor, the method for clustering hyperspectral images based on a spatial-spectral joint dynamic hypergraph disclosed in Example 1 is implemented.

[0174] The method disclosed in Example 1 can be directly embodied as a hardware processor, or can be executed by a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0175] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with this embodiment can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0176] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A hyperspectral image clustering method based on spatial-spectral joint dynamic hypergraph, characterized in that: include: Acquire hyperspectral images; Determine the low-rank representation coefficient of the hyperspectral image, and obtain the Laplace regularization term and hyperedge weight of the hyperspectral image hypergraph; According to the Laplace regularization term and the weight of the hyperedge, a low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure is constructed; Iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient. In the iterative solution process, the Laplace regularization term and the weight of the hyperedge of the new hypergraph are determined according to the low-rank representation coefficient solved in each round, and the Laplace regularization term and the weight of the hyperedge of the new hypergraph are used to perform the next round of solution; According to the final low-rank representation coefficient, the clustering result of the hyperspectral image is determined.

2. The method for clustering hyperspectral images based on spatial-spectral joint dynamic hypergraph as claimed in claim 1, characterized in that: Determine a low-rank representation coefficient of the hyperspectral image, and determine a representation feature in a low-rank subspace according to the low-rank representation coefficient; Determine the Laplacian matrix of the hypergraph according to the features represented in the low-rank subspace; According to the Laplacian matrix of the hypergraph and the representation features in the low-rank subspace, the Laplacian regularization term of the hypergraph is determined.

3. The method for clustering hyperspectral images based on spatial-spectral joint dynamic hypergraph as claimed in claim 2, characterized in that: According to the representation features in the low-rank subspace, the indicator matrix, vertex degree, hyperedge weight and hyperedge degree of the hypergraph are determined; The Laplacian matrix of the hypergraph is determined based on the hypergraph indicator matrix, the degree of the vertex, the weight of the hyperedge and the degree of the hyperedge.

4. The method for clustering hyperspectral images based on spatial-spectral joint dynamic hypergraph as claimed in claim 1, characterized in that: Introducing variables representing low-rank representation coefficients into a low-rank subspace representation optimization model that preserves the similarity of a hypergraph structure, and obtaining an optimization model after the variables are introduced; Obtain the augmented Lagrangian function corresponding to the optimization model after the variables are introduced; The augmented Lagrangian function is iteratively solved by fixing other variables to obtain the final low-rank representation coefficients.

5. The method for clustering hyperspectral images based on spatial-spectral joint dynamic hypergraph as claimed in claim 4, characterized in that: The specific process of iteratively solving the augmented Lagrangian function corresponding to the optimization model after the introduction of variables is: The newly introduced variables are calculated using the low-rank representation coefficients, noise matrix, hypergraph indicator matrix, hyperedge weights, Lagrange multipliers, and penalty parameters calculated in the previous round; Using the newly introduced variables calculated in this round, and the noise matrix, hypergraph indicator matrix, hyperedge weights, Lagrange multipliers, Lagrange multipliers and penalty parameters calculated in the previous round, calculate new low-rank representation coefficients; The new noise matrix is ​​calculated using the new low-rank representation coefficients and newly introduced variables obtained in this round of calculations, as well as the hypergraph indicator matrix, hyperedge weights, Lagrange multipliers, and penalty parameters calculated in the previous round. According to the new low-rank representation coefficients and the new noise matrix obtained in this round of calculation, the indicator matrix and the degree of the hyperedge of the new hypergraph are calculated and determined; According to the newly introduced variables, low-rank representation coefficients, indicator matrix of the hypergraph and degree of hyperedges obtained in this round of calculation, the weights of new hyperedges and degrees of vertices are calculated and determined; According to the new low-rank representation coefficient, the indicator matrix of the hypergraph and the weight of the hyperedge obtained in this round of calculation, a new Laplace regularization term is calculated; The new Laplace regularization term, low-rank representation coefficient, Lagrange multiplier, penalty parameter, noise matrix, indicator matrix and hyperedge weight obtained through this round of calculation are used to perform the next round of calculation on the augmented Lagrangian function corresponding to the optimization model after the introduction of variables until the iteration termination condition is reached.

6. The method for clustering hyperspectral images based on spatial-spectral joint dynamic hypergraph according to claim 1, characterized in that: According to the final low-rank representation coefficient, the similarity map between the pixels of the hyperspectral image is calculated; the similarity map is spectrally clustered to obtain the clustering result of the hyperspectral image.

7. A hyperspectral image clustering system based on spatial-spectral joint dynamic hypergraph, characterized in that: include: An image acquisition unit, used for acquiring a hyperspectral image; A hypergraph construction unit, used to determine the low-rank representation coefficient of the hyperspectral image and obtain the Laplace regularization term and the weight of the hyperedge of the hyperspectral image hypergraph; A model building unit, used to build a low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure according to the Laplace regularization term and the weight of the hyperedge; A low-rank representation coefficient determination unit is used to iteratively solve the low-rank subspace representation optimization model that preserves the similarity of the hypergraph structure to obtain the final low-rank representation coefficient. In the iterative solution process, the Laplace regularization term and the weight of the hyperedge of the new hypergraph are determined according to the low-rank representation coefficient solved in each round, and the Laplace regularization term and the weight of the hyperedge of the new hypergraph are used to perform the next round of solution; The clustering result acquisition unit is used to determine the clustering result of the hyperspectral image according to the final low-rank representation coefficient.

8. An electronic device, characterized in that: The device comprises: a processor adapted to execute a computer program; A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, the method for clustering hyperspectral images based on a spatial-spectral joint dynamic hypergraph according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor and executing the hyperspectral image clustering method based on a spatial-spectral joint dynamic hypergraph according to any one of claims 1 to 6.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method for clustering hyperspectral images based on a spatial-spectral joint dynamic hypergraph as claimed in any one of claims 1 to 6 is implemented.

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