Unsupervised hyperspectral image classification method based on hybrid spectral-spatial information

Abstract

The application provides a kind of unsupervised hyperspectral image classification method based on mixed space spectrum information, comprising the following steps: S1, obtains binary segmentation graph by entropy rate superpixel segmentation algorithm, applies binary segmentation graph on original hyperspectral image to obtain segmented superpixel block, converts input hyperspectral image into multiple homogeneous regions based on superpixel segmentation, removes redundant information and guides data purification;S2, optimize the redundant information in principal component domain by two-dimensional singular spectrum analysis method, enhance spatial spectral feature;S3, realize the unsupervised classification of large-scale hyperspectral image by anchor point graph clustering unsupervised classification method.The application is closer to actual engineering application compared with existing supervised classification method, can process larger image scale compared with existing unsupervised classification method, has the advantages of not needing prior information reference, high classification precision, fast classification speed and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hyperspectral remote sensing image, and particularly relates to an unsupervised hyperspectral image classification method based on mixed spatial-spectral information. BACKGROUND

[0002] Hyperspectral image classification has been successfully applied to many fields such as military surveillance, forest early warning and precision agriculture. With the rapid development of portable hyperspectral image acquisition devices, many technical breakthroughs have been made in unmanned aerial vehicle platforms and laboratory hyperspectral image analysis. However, the collected image data lack sufficient labeled data for training classification models, which limits the application of this technology in practical scenarios.

[0003] Most of the current hyperspectral image classification methods are based on supervised classification framework and have achieved good classification results (overall accuracy OA can reach 95%-99%) on public standard datasets. In the process of practical application, the collected data often require analysis before being labeled with true values, and the pixel distribution of the actual collected image data is more complex than that of the standard dataset, and there are many unnecessary subclasses, shadows and noise. This all poses greater challenges to unsupervised hyperspectral image classification algorithms that cannot rely on any prior knowledge and labeled information.

[0004] In the field of hyperspectral image classification, unsupervised methods are mainly achieved through data clustering. However, the high dimensionality and large amount of information of hyperspectral image data inevitably contain a lot of redundant information data. Therefore, it may not be possible to accurately classify all types of ground objects. In addition, the actual collected hyperspectral image needs to generate analysis results in a very short time, and most unsupervised classification algorithms have high computational complexity. Therefore, it is necessary to invent a classification method that does not require reference to prior data labels, has shorter time consumption, and only processes the main information in the hyperspectral image data. SUMMARY

[0005] The purpose of the present application is to overcome the defects of the prior art and provide an unsupervised hyperspectral image classification method based on mixed spatial-spectral information.

[0006] To achieve the above purpose, the present application adopts the following specific technical solutions:

[0007] An unsupervised hyperspectral image classification method based on mixed spatial-spectral information, comprising the following steps:

[0008] S1, the principal component image is obtained by an entropy rate superpixel segmentation method to obtain a binary segmentation image; the binary segmentation image is applied to the original hyperspectral image to obtain a segmented superpixel block, and a plurality of homogeneous regions are generated based on the segmented superpixel block to remove redundant information and guide data purification;

[0009] S2, using the principal component analysis method of superpixel to reduce dimension of the segmented superpixel block to obtain principal component components, using two-dimensional singular spectrum analysis method to enhance the spatial spectral characteristics of the obtained principal component components and remove noise;

[0010] S3, based on the principal component components with enhanced spatial spectral characteristics, using anchor point graph clustering unsupervised classification framework method to realize unsupervised classification of large-scale hyperspectral images.

[0011] Preferably, step S1 includes the following sub-steps:

[0012] S11, constructing a graph structure by entropy rate superpixel segmentation algorithm , the vertex V is the pixel of the image to be segmented, the edge E is the similarity weight set between the pair of pixels, by selecting the subset of the edge , the graph structure is divided into connected sub-graphs to obtain a sub-graph structure containing a preset connected component , the objective function of the entropy rate superpixel segmentation is as follows:

[0013]

[0014] Wherein represents the trace of the matrix, H(A) is the entropy rate term obtained based on random walk in the constructed sub-graph structure , which is used as a standard to obtain compact and uniform clustering; B(A) is a balance term, which is defined as a monotone increasing and submodular function with similar size on cluster distribution, used to reduce the number of unbalanced superpixels, is the weight of the balance term, argmax represents taking the maximum value, s.t represents under the constraint condition;

[0015] S12, assuming that the original hyperspectral image data has a size of , wherein M, N and B respectively represent the width, height and dimension of the hyperspectral image, before the entropy rate superpixel segmentation, the average value of all dimension images is obtained to extract the main information with a size of , based on , the binary segmentation graph Y is obtained by entropy rate superpixel segmentation, wherein 1 represents the edge of the superpixel and 0 represents the non-edge pixel, by applying Y on , the input image can be segmented into superpixels, as follows:

[0016]

[0017] Wherein is the i-th superpixel, n is the number of superpixels, and the superpixel block ​The average spectral information of all the pixels within the superpixel is used to replace the information of the pixels within the original superpixel block, s j represents the jth superpixel, i and j are not overlapped, and the intersection is empty.

[0018] S13, the two-dimensional singular spectrum analysis method includes transforming into :

[0019]

[0020] The elements in the matrix are smooth and homogeneous regions.

[0021] Preferably, step S2 includes the following sub-steps:

[0022] S21, after performing principal component analysis in the principal component domain, the number of spectral bands is reduced from B to , where , is set to 15, B is more than one hundred, and a new image is obtained by combining the reduced dimension superpixel blocks together as follows:

[0023]

[0024] S22, for each spectral band within , a two-dimensional singular spectrum analysis method is applied to enhance the spatial spectral characteristics and remove noise, and the feature-enhanced hyperspectral image is used for hyperspectral image classification:

[0025]

[0026] S23, for an image with a single spectral band size of h x w, set the size of the embedding window to u x v (where 1≤u≤h and 1≤v≤w), move from the top left corner to the bottom right corner of the image to construct a trajectory matrix G, the pixels in the window are unfolded and connected as column vectors of the matrix trajectory , as shown below:

[0027]

[0028] The eigenvalues and corresponding eigenvectors of are represented as and

[0029]

[0030] where and These are the empirical orthogonal function and the principal component components of G. The 2vctic heterospectral analysis method extracts different components from the input image, including trends. The data is processed by removing oscillations and noise to obtain smoothed and denoised data. Finally, a two-step diagonal averaging process is used to... Convert it again to a new image of size h×w.

[0031] Preferably, step S3 includes the following sub-steps:

[0032] S31, Image The input is classified using the anchor graph structure spectrum clustering method; the anchor graph structure spectrum clustering method will classify the input hyperspectral image. Represented as an undirected graph, where each pixel is considered a vertex of the anchor graph structure, and the similarity between pairs of vertices is considered an edge of the anchor graph structure, the anchor graph structure spectral clustering method achieves hyperspectral image classification by minimizing the following objective function:

[0033]

[0034] Formula (9) is a non-smooth objective function, where , It is a pixel The indicator vector; λ>0 is the Lagrange multiplier. These are orthogonal constraint terms, and L is the Laplace matrix. It is the trace of the matrix, and F represents the Frobenius norm;

[0035] S32. Set a label prediction function for a subset of anchor structure samples, where the anchor structure samples are obtained through a certain sampling interval s, and the subset... The label prediction function f(.) is shown in the following formula, where for:

[0036]

[0037] Where Z is the similarity matrix between all samples and the selected anchor structure samples. By relaxing the discretization conditions and considering non-negativity and orthogonality constraints, Z is substituted into... and To update and Formula (10) can be rewritten as:

[0038] LY+2λYY T Y-2λY=QP=(Y+2λYY T Y)-(2λY+ZΔ -1 Z T Y) (11)

[0039] in , According to the standard non-negative matrix factorization algorithm, the minimization of the objective function in formula (9) is obtained by updating Y:

[0040]

[0041] wherein and represent element multiplication and element division, respectively, The objective function formula (9) converges to obtain the final result of classification.

[0042] The homogeneous region is obtained by the entropy rate superpixel segmentation method; the spatial redundant information in the homogeneous region is removed based on the principal component analysis of the superpixel; the redundant information in the principal component domain is optimized by the two-dimensional singular spectrum analysis method, the spectral features are enhanced, and finally the unsupervised classification framework based on the anchor point graph clustering is used to realize the unsupervised classification of large-scale hyperspectral images. The present application is closer to the actual engineering application compared with the existing supervised classification method, and can process larger image scale compared with the existing unsupervised classification method, and has the advantages of no need for prior information reference, high classification precision, fast classification speed and the like. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 is a system block diagram of the unsupervised hyperspectral image classification method based on mixed spatial-spectral information according to the embodiment of the present application.

[0044] Figure 2 is the data set test result of the unsupervised hyperspectral image classification method based on mixed spatial-spectral information according to the embodiment of the present application.

[0045] Figure 3 is the data set test result of the unsupervised hyperspectral image classification method based on mixed spatial-spectral information according to the embodiment of the present application.

[0046] Figure 4 is the segmentation result of different superpixel methods according to the embodiment of the present application.

[0047] Figure 5 is the clustering result on three public data sets according to the embodiment of the present application.

[0048] Figure 6 is the clustering result of five self-collected data sets according to the embodiment of the present application. DETAILED DESCRIPTION

[0049] Hereinafter, embodiments of the present application will be described with reference to the accompanying drawings. In the following description, the same modules are denoted by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, detailed descriptions thereof will not be repeated.

[0050] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not constitute a limitation on the present application.

[0051] Figure 1 The application system block diagram provided by the embodiment of the present application is shown.

[0052] As shown in Figure 1 , the application system block diagram provided by the embodiment of the present application mainly includes the following steps:

[0053] Before superpixel segmentation, the average value of all dimensional images is obtained to extract the main information of the hyperspectral image.

[0054] S1, obtain a binary segmentation map based on the principal component image through the entropy rate superpixel segmentation algorithm; apply the binary segmentation map on the original hyperspectral image to obtain a segmented superpixel block, convert the input hyperspectral image into multiple homogeneous regions based on superpixel segmentation, remove redundant information, and guide data purification.

[0055] The data purification method in step S1 is to convert the input hyperspectral image into multiple homogeneous regions through superpixel segmentation based on the entropy rate superpixel segmentation method. The entropy rate superpixel segmentation method not only removes redundant information, but also helps to combine fragmented image information into homogeneous regions, which is beneficial to subsequent classification. Step S1 specifically includes the following steps:

[0056] S11, the entropy rate superpixel segmentation method extracts homogeneous regions. By comparing the performance results of various superpixel segmentation methods, the entropy rate superpixel segmentation method is selected as the most suitable method for extracting homogeneous regions. The algorithm of entropy rate superpixel segmentation constructs a graph structure , the vertex V is the pixel of the image to be segmented, and the edge E is composed of the similarity weight between pairs of pixels; by selecting a subset of edges , the graph structure is divided into connected subgraphs, and the obtained subgraph structure containing small connected components , the objective function of the entropy rate superpixel segmentation method is as follows:

[0057]

[0058] where represents the trace of the matrix, H(A) is the entropy rate term obtained based on random walk in the constructed subgraph structure, which is used as a standard to obtain compact and uniform clustering; B(A) is the balance term, which is defined as a monotone increasing and submodular function with similar size on cluster distribution, used to reduce the number of unbalanced superpixels, is the weight of the balance term, argmax represents taking the maximum value, and s.t represents under the constraint condition.

[0059] S12, Set the original hyperspectral image data The size is Where M, N, and B represent the width, height, and dimension of the HSI, respectively. Before superpixel segmentation, the average value of all dimensions of the image is obtained to extract the size. Key information ,based on A binary segmentation map Y is obtained through ERS segmentation, where 1 represents the edge of a superpixel and 0 represents a non-edge pixel. Y is then applied to the hyperspectral image. The above method can segment the input image into superpixels, as shown below:

[0060]

[0061] in It is the i-th superpixel, n is the number of superpixels, and s j This represents the j-th superpixel, where i and j do not overlap and their intersection is empty. To reduce the computational burden caused by complex pixel distributions, this invention generates multiple homogeneous regions based on over-segmented superpixel blocks. Specifically, the superpixel blocks are calculated... The average spectral information of all pixels within the superpixel block is used to replace the pixel information within the original superpixel block.

[0062] S13. The input hyperspectral image is processed using the following formula. Purification to obtain :

[0063]

[0064] The elements in the array are smooth, homogeneous regions. This operation allows subsequent calculations to be performed on synthetic data with less noise and greater consistency, thereby reducing computational complexity and burden.

[0065] S2. Principal component analysis based on superpixels is used to reduce the dimensionality of the spectral data to obtain principal component components, while suppressing noise and intra-class inconsistency. The obtained principal component components are then enhanced with spatial spectral characteristics and noise removed using 2D metaspectral analysis. For the image... Joint enhancement of spatial spectral features based on principal component domain two-dimensional heterogeneous spectral analysis.

[0066] To further enhance the separability of hyperspectral images and the adaptability of unsupervised classification methods to different data, the two-dimensional singular spectrum analysis method strategy is introduced into the unsupervised hyperspectral classification problem; in the process of generating homogeneous regions, all pixel values in each superpixel block are simultaneously set to the average pixel value of the block; to save calculation time, instead of operating on each individual pixel, the superpixel-based principal component analysis method is used to reduce the dimensionality of spectral data.

[0067] For the principal component components extracted by the principal component analysis method, the two-dimensional singular spectrum analysis method is applied in the principal component domain for spatial spectral feature enhancement. Step S2 specifically includes the following steps:

[0068] S21, after performing principal component analysis in the principal component domain, the number of spectral bands is reduced from B to , wherein ( is set to 15, and B is more than one hundred), by combining the reduced superpixel blocks together, a new image is obtained as follows

[0069]

[0070] S22, for each spectral band in , the two-dimensional singular spectrum analysis method is applied to further enhance the features and remove noise, and the hyperspectral image after feature enhancement is used for hyperspectral image classification:

[0071]

[0072] S23, the two-dimensional singular spectrum analysis method removes noise and improves the signal-to-noise ratio to improve classification accuracy: for an image with a single spectral band size of h x w, set the size of the embedding window to u x v (where 1≤u≤h and 1≤v≤w), move from the top left corner to the bottom right corner to construct a trajectory matrix G, the pixels in the window are unfolded and connected as column vectors of the matrix trajectory , as shown below:

[0073]

[0074] The eigenvalues and corresponding eigenvectors of are represented as and

[0075]

[0076] According to formulas (5-8), for the image , the two-dimensional singular spectrum analysis method based on the principal component domain is used for joint spatial-spectral feature enhancement, and the two-dimensional singular spectrum analysis method based on the principal component domain is used for joint spatial-spectral feature enhancement ; wherein and are the empirical orthogonal functions and the principal components of G, respectively, the two-dimensional singular spectrum analysis method extracts different components of the input image, including trends , oscillations and noise, thus obtaining smoothed and denoised data; here, we choose as the approximation of G, mainly because it contains the most important spatial information that is beneficial for classification; finally, by a two-step diagonal averaging process, the is converted again into a new image of size h x w; by simultaneously considering local and global spatial information, the two-dimensional singular spectrum analysis method can effectively reduce image noise, and the reconstructed image can show strong noise robustness.

[0077] S3, based on the anchor graph structure spectral clustering algorithm, realizing the unsupervised classification of large-scale hyperspectral images.

[0078] Step S3 specifically comprises the following steps:

[0079] S31, for the input hyperspectral image data , the data purification strategy first converts it into , and then obtains a new image through a feature enhancement strategy; the image will be input into the anchor graph structure spectral clustering framework for classification to obtain the final result, and this simple and effective strategy is also applicable to other unsupervised classification frameworks.

[0080] Based on the anchor graph structure spectral clustering method, the input hyperspectral image is represented as an undirected graph, where each pixel is regarded as a vertex of the anchor graph structure, and the similarity between pairs of vertices is regarded as the edge of the anchor graph structure; by minimizing the following objective function, the hyperspectral image classification is realized:

[0081]

[0082] Formula (9) is a non-smooth objective function, which introduces an anchor graph structure, wherein , is the indicator vector of pixel ; λ>0 is the Lagrange multiplier, is the orthogonal constraint term, L is the Laplacian matrix, is the trace of the matrix, and F represents the Frobenius norm.

[0083] S32, setting a label prediction function for a subset of anchor structure samples, wherein the anchor structure samples are obtained through a certain sampling interval s; the label prediction function f(.) of the subset is shown in the following formula, wherein For anchor samples

[0084]

[0085] where Z is the similarity matrix between all samples and selected anchor samples, by relaxing the discrete condition and considering non-negative and orthogonal constraints, formula (10) is rewritten as:

[0086] LY+2λYY T Y-2λY=Q-P=(Y+2λYY T Y)-(2λY+ZΔ -1 Z T Y) (11)

[0087] where , According to the standard non-negative matrix factorization algorithm, the minimization of the non-smooth objective function in formula (9) is obtained by updating Y:

[0088]

[0089] where and represent element multiplication and element division, respectively, The convergence of the non-smooth objective function formula (9) can obtain the classification result, since only one element in each row of the indicator matrix Y is positive and all other elements are close to zero, it can be considered as a perfect indicator matrix for clustering.

[0090] Figures 2-3 The data set test results of the unsupervised hyperspectral image classification method based on mixed spectral information provided by the embodiment of the application are shown.

[0091] As Figures 2-3 shown, the algorithm test on the three public test data sets and five self-collected data sets provided by the embodiment of the application is performed by gradually adding the proposed strategy, i.e., the baseline (B), the baseline and data optimization (B+DO), the baseline and data determination (B+DD), and the program results of the complete version of the proposed method.

[0092] In order to make a comprehensive comparison, the test is performed on the labeled pixels and unlabeled pixels of the hyperspectral image data set, Figure 2 The top of is the Salinas original image, the middle is the Salinas A original image, and the bottom is the Indian Pines original image, the ground truth and the classification result.

[0093] Figure 3 The original images of the self-collected data sets SC-1 to SC-5, their ground truths and classification results under different strategies are shown, and all results are only for labeled pixels except the last column of results.

[0094] Figure 4 The segmentation results of different superpixel methods provided according to embodiments of the present invention are shown.

[0095] like Figure 4 As shown in the figure, the segmentation results of different superpixel methods for the Salinas A, Salinas, and Indian Pines datasets provided in this embodiment of the invention are shown from top to bottom.

[0096] Data optimization strategies can be applied not only to hyperspectral image classification problems, but also to the classification of ordinary RGB images. They can be applied to hyperspectral image classification under both unsupervised and supervised frameworks.

[0097] Figure 5 The following diagram illustrates clustering results on three public datasets provided according to embodiments of the present invention, such as... Figure 5 As shown, "NaN" indicates that no classification results were generated due to insufficient memory, "-" indicates that there are no results to refer to, bold indicates the best result among all methods, and underline indicates the best result of the unsupervised method.

[0098] Figure 6 The following diagram illustrates the clustering results of five self-collected datasets provided according to embodiments of the present invention, such as... Figure 6 As shown, "NaN" indicates that there are no classification results due to insufficient memory, "-" indicates that there are no results to refer to, bold indicates the best result of all methods, and underline indicates the best performance of unsupervised methods.

[0099] This invention enables classification on larger hyperspectral images:

[0100] Figures 5-6 The results shown are the quantitative results of various indicators on the public test dataset and the self-collected dataset. On datasets larger than 500*500 (Salinas, SC-1 to SC-5), other similar methods may experience memory overflow or fail to obtain good classification results, while the algorithm of this invention can obtain the best classification results.

[0101] In the description of the specification, the description of the terms "one embodiment", "some embodiments", "an example", "a specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Also, the specific features, structures, materials or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, different embodiments or examples described in the specification and the features of different embodiments or examples can be combined and combined by those skilled in the art without contradiction.

[0102] Although the embodiments of the present application have been shown and described above, it is understood that the above-described embodiments are exemplary and are not to be construed as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-described embodiments within the scope of the present application.

[0103] The above specific embodiments of the present application do not constitute a limitation on the scope of protection of the present application. Any various other corresponding changes and modifications made in accordance with the technical concept of the present application shall be included in the scope of protection of the claims of the present application.

Claims

1. An unsupervised hyperspectral image classification method based on mixed spatial-spectral information, characterized in that, Includes the following steps: S1. The principal component image is segmented into a binary image using the entropy rate superpixel segmentation method; the binary segmentation image is applied to the original hyperspectral image to obtain segmented superpixel blocks; multiple homogeneous regions are generated based on the segmented superpixel blocks, and redundant information is removed to guide data purification; step S1 includes the following sub-steps: S11. Construct a graph structure using the entropy rate superpixel segmentation algorithm. Vertices V are the pixels of the image to be segmented, and edges E consist of similarity weights between pairs of pixels. A subset of edges is selected... The graph structure is divided into connected subgraphs to obtain subgraph structures containing preset connected components. The objective function for the entropy rate superpixel segmentation is as follows: in H(A) represents the trace of the matrix and is the structure of the constructed subgraph. The entropy rate term, obtained based on random walks, is used as a standard for obtaining compact and uniform clusters; B(A) is a balance term, defined as a monotonically increasing submodular function with similar sizes on the cluster distribution, used to reduce the number of imbalanced superpixels. These are the weights of the balancing terms; argmax indicates taking the maximum value; and st indicates under the constraints. S12, Assume the original hyperspectral image data The size is Where M, N, and B represent the width, height, and dimension of the hyperspectral image, respectively. Before the entropy rate superpixel segmentation, the average value of the image across all dimensions is obtained to extract the size. Key information ,based on A binary segmentation map Y is obtained through the entropy rate superpixel segmentation, where 1 represents the edge of a superpixel and 0 represents a non-edge pixel. Y is then applied to... The input image can be segmented into superpixels, as shown below: in It is the i-th superpixel, and n is the number of superpixels. The specific calculation of the superpixels... The average spectral information of all pixels within the block is used to replace the information of the pixels within the original superpixel block. j Let i represent the j-th superpixel, where i and j do not overlap and their intersection is empty; S13, The two-dimensional metaspectral analysis method includes... Transform into : The elements in the array are smooth, homogeneous regions; S2. Principal component analysis (PCA) is used to reduce the dimensionality of the segmented superpixel blocks to obtain principal component components. The spatial spectral characteristics of the obtained principal component components are enhanced and noise is removed using Divergence metaspectral analysis. Step S2 includes the following sub-steps: S21. After performing principal component analysis within the principal component domain, the number of spectral segments decreased from B to [missing information]. ,in , With B set to 15 and B greater than 100, a new image is obtained by combining the dimensionality-reduced superpixel blocks. as follows: S22, For For each spectral band within the image, the aforementioned two-dimensional metaspectral analysis method is applied to enhance spatial spectral characteristics and remove noise, resulting in a feature-enhanced hyperspectral image. Used for hyperspectral image classification: S23. For an image with a single spectral band size of h×w, let the size of the embedding window be u×v (where 1≤u≤h and 1≤v≤w). Move the window from the top left corner to the bottom right corner of the image to construct the trajectory matrix G. The pixels in the window are expanded and concatenated to form the column vector of the matrix trajectory. As shown below: The eigenvalues ​​and corresponding eigenvectors are represented as ( )and( The trajectory matrix can be represented by the following formula: in and These are the empirical orthogonal function and the principal component components of G, respectively. The two-dimensional heterospectral analysis method extracts different components of the input image, including trends. The data is processed by removing oscillations and noise to obtain smoothed and denoised data. Finally, a two-step diagonal averaging process is used to... Convert it again to a new image of size h×w; S3. Based on the principal component components that enhance spatial spectral characteristics, the anchor point map clustering unsupervised classification method is used to achieve unsupervised classification of large-scale hyperspectral images.

2. The unsupervised hyperspectral image classification method based on mixed spatial-spectral information according to claim 1, characterized in that: Step S3 includes the following sub-steps: S31, Image The input hyperspectral image is classified using an anchor point graph structure spectrum clustering method; the anchor point graph structure spectrum clustering method will classify the input hyperspectral image. Represented as an undirected graph, where each pixel is considered a vertex of the anchor graph structure, and the similarity between pairs of vertices is considered an edge of the anchor graph structure, the spectral clustering method of the anchor graph structure achieves hyperspectral image classification by minimizing the following objective function: Formula (9) is a non-smooth objective function, where , It is a pixel The indicator vector; λ>0 is the Lagrange multiplier. These are orthogonal constraint terms, and L is the Laplace matrix. It is the trace of the matrix, and F represents the Frobenius norm; S32. Set a label prediction function for a subset of anchor structure samples, wherein the anchor structure samples are obtained through a certain sampling interval s, and the subset... The label prediction function f(.) is shown in the following formula, where for: Where Z is the similarity matrix between all samples and the selected anchor structure sample, substituted into the equation by relaxing the discrete conditions and considering nonnegativity and orthogonality constraints. and To update and Formula (10) can be rewritten as: LY+2λYY T Y-2λY=Q-P=(Y+2λYY T Y)-(2λY+ZΔ -1 Z T Y) (11) in , According to the standard nonnegative matrix factorization algorithm, the minimization of the nonsmooth objective function in formula (9) is obtained by updating Y: in and These represent element-wise multiplication and element-wise division, respectively. The final classification result can be obtained when the non-smooth objective function formula (9) converges.

Images