Hyperspectral image classification method based on nonlinear weighted graph convolution and classification model training method

Abstract

The invention discloses a hyperspectral image classification method based on nonlinear weighted graph convolution and a classification model training method, and belongs to the technical field of hyperspectral remote sensing image classification. The objective of the invention is to solve the problem of poor classification performance of a model caused by insufficient mining of high-dimensional information of a hyperspectral image in an existing hyperspectral image classification method. According to the method, a hyperspectral image is clustered into superpixels, a superpixel feature matrix is generated by utilizing internal image convolution, weights are determined based on superpixel nodes and similarity between adjacent superpixel nodes, and weights of adjacent edges of the superpixels are combined into an adjacent matrix of the whole hyperspectral image; performing local information aggregation on the superpixel feature matrix according to an adjacent matrix by external image convolution, and generating a depth feature matrix based on image convolution processing so as to realize classification; in a classification model training process, a curvature regular strategy and an intrinsic dimension regular strategy are utilized to constrain a nonlinear weighted graph convolution layer, so that manifold local information measurement is more accurate, and interference of redundant information on the model is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of hyperspectral remote sensing image classification, and relates to a hyperspectral image classification method based on graph convolution and a training method for its classification model. Background Art

[0002] Spectral features are obtained by measuring the intensity of the emitted, reflected, or transmitted light of the observed material, and contain rich discriminant information. Hyperspectral images are composed of spectral features and spatial features, and can be widely applied to multiple fields such as mineral exploration, resource management, and fine classification of crops. Hyperspectral image classification is a technique that uses the fine spectral resolution of hyperspectral images to classify each pixel into different categories. Currently, thanks to the research results of deep learning, hyperspectral image classification technology has been developed. However, existing deep learning methods do not fully exploit the high-dimensional information of hyperspectral images when there are few labeled samples of hyperspectral images, resulting in poor classification performance of the model. Summary of the Invention

[0003] The present invention aims to solve the problem that existing hyperspectral image classification methods do not fully exploit the high-dimensional information of hyperspectral images, resulting in poor classification performance of the model.

[0004] A hyperspectral image classification method based on non-linear weighted graph convolution, for a hyperspectral image X, uses a classification model based on non-linear weighted graph convolution for image classification; the processing process of the classification model based on non-linear weighted graph convolution includes:

[0005] Using the simple linear iterative clustering algorithm to cluster the hyperspectral image into n superpixels, and the pixels within the superpixels share features; then using the non-linear weighted graph convolution module, the non-linear weighted graph convolution module includes internal graph convolution and external graph convolution processing;

[0006] The internal graph convolution generates the k-th shared feature based on graph convolution The shared features s corresponding to n superpixels k constitute the superpixel feature matrix S = [s1,..., s k ,..., s n ∈ R n×d ; where is the degree matrix of the internal graph convolution, is the adjacency matrix, W in is the learnable parameter matrix, pool mean [·] is the average pooling operation; X k represents the feature matrix of the pixels within the k-th superpixel, and d is the number of spectral channels;

[0007] Based on the superpixel node s i and all adjacent superpixel nodes sj Determine s based on the similarity between them i and s j The normalized weight a of the corresponding edge ij ; The weight combinations of all adjacent edges of n superpixels form the adjacency matrix of the entire hyperspectral image External graph convolution is based on the adjacency matrix Perform local information aggregation on the input superpixel feature matrix S, and finally generate the depth feature matrix Z based on graph convolution processing;

[0008] Feed the generated feature matrix Z into a linear classifier for classification to obtain the hyperspectral image classification result

[0009] Furthermore, during the process of clustering the hyperspectral image into n superpixels using the simple linear iterative clustering algorithm, the hyperspectral image is segmented into graph-structured data composed of nodes and edges through the simple linear iterative clustering algorithm, and each node represents a superpixel

[0010] Furthermore, s i and s j The normalized weight of the corresponding edge where cos<·,·> represents the cosine similarity operation

[0011] Furthermore, the adjacency matrix All the main diagonal elements of the adjacency matrix have a +1 operation

[0012] Furthermore, based on the adjacency matrix The method of performing local information aggregation on the input superpixel feature matrix S is as follows

[0013]

[0014] Furthermore, external graph convolution is based on the adjacency matrix The process of performing local information aggregation on the input superpixel feature matrix S and finally generating the depth feature matrix Z based on graph convolution processing includes

[0015] Denote the corresponding to the λ-th layer of external graph convolution as Denote the superpixel feature matrix S as S 0 Perform graph convolution processing with it as the input of external graph convolution, and the processing of the features generated by the λ-th layer of external graph convolution is expressed as

[0016]

[0017] where relu is the activation function and BN is the batch normalization layer; is a trainable matrix is the adjacency matrix corresponding to the λ-th layer of external convolution S λ is the output feature matrix of the λ-th layer of external convolution;

[0018] The output of the last layer of external graph convolution is the generated deep feature matrix Z.

[0019] Furthermore, the non-linear weighted graph convolution module performs two layers of external convolution processing.

[0020] A training method for a classification model based on non-linear weighted graph convolution, which trains a classification model based on non-linear weighted graph convolution in a hyperspectral image classification method based on non-linear weighted graph convolution. The training process includes:

[0021] For each hyperspectral image in the hyperspectral image training set, generate the deep feature matrix Z and classify it using a linear classifier; the deep feature matrix Z lies on the low-dimensional manifold surface in the high-dimensional space Let be the N samples on the manifold t z i is the central sample selected for calculating the curvature of the manifold surface is the Nz i neighborhood samples of r then the local manifold subspace of z i is μ i is the mean obtained by averaging the N i neighborhood samples of z r by feature dimension. Perform singular value decomposition on M i to obtain is a rectangular diagonal matrix generated by singular value decomposition, and the non-negative values on its diagonal are arranged in descending order; the neighboring nodes of z i also have a local manifold subspace M j centered on itself. Perform singular value decomposition to obtain Let Perform singular value decomposition to obtain Based on obtain the curvature of the manifold surface at the l-th training iteration

[0022] Use the curvature to determine the regularization term constraint where τ1 is the weight for controlling the curvature regularization term; L1 is the classification loss function, represents L1 at the l-th training iteration; represents the integer division operation, that is L1 is divided by an integer, and the remainder is not retained;

[0023] On the surface of the feature manifold , is N samples on the manifold r Let represent a set of noises on the manifold . Based on the intrinsic dimension of z i , obtain the global intrinsic dimension of Z t ,

[0024] The intrinsic dimension of the said z i is as follows:

[0025]

[0026] where z i is the central sample selected for calculating the intrinsic dimension of the manifold surface ; z r ∈Z t is another sample on the manifold surface ; z j ∈Z t is located within the neighborhood of z i , indicating that this neighborhood does not include the noise z k . r(z i ) is the radius of the neighborhood circle centered at z i and containing z r ; Matrix operation where v and w represent the two inputs for matrix operation;

[0027] Furthermore, obtain the loss function at the l-th iteration where τ2 is used to control the weight of the intrinsic dimension regularization term; Based on complete the training of the model.

[0028] Furthermore, the curvature of the manifold surface at the l-th training iteration

[0029] Furthermore, z j ∈Z t being located within the neighborhood of z i is achieved through the following steps:

[0030] Within the neighborhood of z i , calculate the distances to all neighborhood samples z j and sort them in ascending order, and take the first ten samples as z i within the neighborhood of z j .

[0031] The hyperspectral image classification method proposed by the present invention uses non-linear weighted graph convolution to aggregate information between superpixel nodes, obtaining deeper non-linear local and global information, and can effectively solve the problem that the high-dimensional information of hyperspectral images is not fully mined, resulting in poor classification performance of the model. In addition, during the training process of the model, non-linear weighted graph convolution aggregates information between superpixel nodes, obtains deeper non-linear local and global information, generates a high-dimensional feature manifold surface, and improves the classification performance of the model by performing manifold geometric regularization on the feature manifold surface, including a manifold curvature regularization term for improving the accuracy of local information measurement and an intrinsic dimension regularization term for reducing the interference of redundant information to the model. This enables the present invention to actually achieve classification using the generated regular features, ensuring that the entire classification model generates the final classification result. Therefore, it can better extract the non-linear spatial-spectral joint information of hyperspectral images and improve the classification performance of the model. Through experimental analysis, the method proposed in this experiment can obtain OA values of 0.9468, 0.9596, and 0.8651 on three datasets respectively. Description of the Drawings

[0032] Figure 1 It is a flowchart of the hyperspectral image classification method based on manifold geometric regularization and non-linear weighted graph convolution.

[0033] Figure 2 It is the false color image, ground truth image, and classification result image of Dataset I; among them, (a) is the false color image, (b) is the ground truth image, and (c) is the classification image.

[0034] Figure 3 It is the false color image, ground truth image, and classification result image of Dataset II; among them, (a) is the false color image, (b) is the ground truth image, and (c) is the classification image.

[0035] Figure 4 It is the false color image, ground truth image, and classification result image of Dataset III; among them, (a) is the false color image, (b) is the ground truth image, and (c) is the classification image.

[0036] Figure 5 It is the influence curve of the selection of the number of neighborhood samples of the intrinsic dimension on the classification performance of the model.

[0037] Figure 6 It is the influence curve of the selection of the coefficient of the curvature regularization term on the classification performance of the model.

[0038] Figure 7 It is the influence curve of the selection of the coefficient of the intrinsic dimension regularization term on the classification performance of the model. Detailed Implementation Manner

[0039] Aiming at the problems existing in the background art, the present invention proposes a hyperspectral image classification method based on non-linear weighted graph convolution, which can better extract the non-linear spatial-spectral joint information of hyperspectral images and improve the classification performance of the model. The present invention first uses a non-linear weighted graph convolution module based on the graph-in-graph network structure to obtain the non-linear spatial-spectral information of hyperspectral images, and uses a curvature regularization strategy to constrain the non-linear weighted graph convolution layer to generate a flatter feature manifold, making the local information metric of the manifold more accurate; in addition, the present invention uses an intrinsic dimension regularization strategy to embed the noise in the feature space into the manifold surface with a lower intrinsic dimension, reducing the interference of redundant information on the model. The present invention will be further described below in conjunction with specific embodiments.

[0040] Specific Embodiment 1: In combination with Figure 1 describe this embodiment,

[0041] This embodiment is a hyperspectral image classification method and a classification model training method based on non-linear weighted graph convolution, which mainly includes a non-linear weighted graph convolution module, a manifold curvature regularization module, and a manifold intrinsic dimension regularization module.

[0042] The hyperspectral image X∈R w×h×c , first passes through a simple linear iterative clustering algorithm, and adjacent pixel nodes with similar features are clustered together to form n superpixels, that is, X = [X1,..., X k ,..., X n . Then, the superpixel graph is sent into the non-linear weighted graph convolution module. The non-linear weighted graph convolution includes an external graph convolution and an internal graph convolution. The features generated by the internal graph convolution shared among the n superpixels constitute the superpixel feature matrix S = [s1,..., s k ,..., s n ∈R n ×d , where d is the number of spectral channels; the cosine similarity is calculated between superpixels, and the external graph convolution dynamically weights different edges according to the cosine similarity to perform information aggregation to obtain long-distance semantic information, generating the feature representation Z = [z1,..., z k ,..., z n ∈R n×d lying on a low-dimensional manifold surface in a high-dimensional space , where the feature Z is a matrix composed of discrete feature nodes, while represents a continuous manifold surface.

[0043] In the training stage, the model needs to perform manifold geometric regularization on the manifold surface where the feature representation Z is located, including two items: a manifold curvature regularization term and a manifold intrinsic dimension regularization term. The two losses are nested to form the final loss Lfinal The generated features are fed into a linear classifier to obtain the classification result graph. In the test phase, the trained non-linear weighted graph convolution module directly extracts the high-dimensional non-linear features of the superpixels and feeds them into the linear classifier to obtain the classification result.

[0044] Specifically, the image classification model training method and the image classification method described in this embodiment include the following steps:

[0045] S1. Non-linear weighted graph convolution:

[0046] The hyperspectral image is first segmented into graph structure data composed of nodes and edges by the simple linear iterative clustering algorithm (SLIC algorithm). Each node represents a superpixel, and the number of pixels within the superpixel is determined by the compactness set by humans. The pixels within the superpixel share features.

[0047] The graph convolution method based on superpixels can obtain the non-linear spatial information of hyperspectral image data. By integrating the neighbor node information, the feature representation ability of the model is improved while the smoothness of the classification result is enhanced.

[0048] Existing graph convolution methods for hyperspectral images equally integrate all neighborhood node information, resulting in the features of the central superpixel node being masked by the neighborhood node features. The high spatial resolution of hyperspectral images makes the spectral characteristics of adjacent superpixels differ greatly. Equally weighting and integrating neighborhood information will lead to a significant decline in the classification performance of the model in the case of small samples. To address this problem, the present invention proposes a non-linear weighted graph convolution module, which includes an internal graph convolution and an external graph convolution; the pixels within the superpixel share the features generated by the internal graph convolution, and the features between superpixels are aggregated through the non-linearly weighted external graph convolution. The weights are dynamically integrated from adjacent superpixels by normalizing based on the cosine similarity of the edges, enabling the external convolution to pay more attention to the central superpixel features and the features of more similar adjacent superpixel nodes when integrating information.

[0049] X k represents the feature matrix of the pixels within the k-th superpixel. The internal graph convolution generates the k-th shared feature s based on the classical graph convolution theory k ∈R 1×d The operation can be expressed as:

[0050]

[0051] Among them, is the degree matrix of the internal graph convolution, is the adjacency matrix, W in is the learnable parameter matrix, and pool mean [·] is the average pooling operation.

[0052] Shared feature s corresponding to n superpixels k Construct the superpixel feature matrix S = [s1,..., s k ,..., s n ∈ R n×d , where d is the number of spectral channels;

[0053] Dynamically assign weights to the adjacent edges between superpixels through cosine similarity measurement. The input is the superpixel node s i and all adjacent superpixel nodes s j , and the output is the normalized weight a i of the edge between s j and s ij . The formula for calculating the cosine similarity normalized weight of the edge is:

[0054]

[0055] where cos<·,·> represents the cosine similarity operation, and a ij ∈ [0, 1].

[0056] Based on formula (2), the nodes within the local neighborhood of the superpixels are dynamically assigned different weights according to the similarity of features. The weight combination of all adjacent edges of the n superpixels is the adjacency matrix of the entire hyperspectral image, denoted as:

[0057]

[0058] where, for the main diagonal elements of the adjacency matrix, a +1 operation is performed, which helps the non-linear weighted graph convolution module to assign higher weights to the central node information during feature aggregation. Different from the traditional graph convolution methods for hyperspectral images, in formula (3), a ij ≠ a ji . The external graph convolution aggregates local information based on the adjacency matrix for the input superpixel feature matrix S, and the external graph convolution finally generates the deep feature matrix Z;

[0059] The operation of aggregating information by the external graph convolution can be expressed as:

[0060]

[0061] Denote the corresponding to the λ-th layer of external graph convolution as Denote the superpixel feature matrix S as S 0 As the input of the external graph convolution for graph convolution processing, the features generated by the λ-th layer of external graph convolution are processed and expressed as:

[0062]

[0063] Among them, relu is the activation function, and BN is the batch normalization layer; is a trainable matrix, is the adjacency matrix corresponding to the external convolution of the λ-th layer S λ is the output feature matrix of the external convolution of the λ-th layer;

[0064] The output of the last layer of external graph convolution is the generated deep feature matrix Z.

[0065] Based on the operations of formulas (4) and (5), the non-linear graph convolution module dynamically aggregates neighborhood and long-range abstract information to generate more discriminative non-linear spatial spectral features. In this embodiment, the non-linear weighted graph convolution module performs two layers of external convolution processing, that is, λ = 0, 1, and the obtained S 2 is the generated deep feature matrix Z; setting two layers of external convolution processing in this embodiment can capture long-range features without degrading the model performance.

[0066] The proposed non-linear weighted graph convolution module can obtain non-linear spatial information through internal and external convolutions of superpixels, and extract non-linear spectral information by dynamically weighting and normalizing the adjacency matrix. Then, the generated feature matrix Z is fed into a linear classifier for classification to obtain the hyperspectral image classification result. In the training stage, the output of the linear classifier needs to be calculated with the cross-entropy loss with the label and used for the calculation of the popular curvature regularization term and the intrinsic dimension regularization term. In actual applications, the output of the linear classifier is directly converted into the probabilities of each known class, and the class name with the highest probability is taken as the prediction result.

[0067] S2. Design manifold curvature regularization:

[0068] To measure the local information similarity more accurately, manifold curvature regularization is proposed as one of the constraint terms to constrain the non-linear weighted graph convolution module and shape a flatter feature representation manifold. A flatter feature representation manifold means projecting the features on the original surface onto a smooth manifold surface with a more accurate metric. Let be the manifold with N t samples on it, and z i be the central sample selected for calculating the curvature of the manifold surface ; is the N i neighborhood samples of z r , then the local manifold subspace of z i is defined as μ i is the mean value obtained by averaging the N i neighborhood samples of z r in the feature dimension, for Mi Do singular value decomposition to get is a rectangular diagonal matrix generated by singular value decomposition, with non-negative values ​​on the diagonal arranged in descending order; z i The neighboring nodes also have a local manifold subspace M with itself as the center point j , perform singular value decomposition to get make Do singular value decomposition to get

[0069] The manifold surface at the lth iteration The curvature is as follows:

[0070]

[0071] Formula (6) shows that for each point z i , calculate the mean of its value with all neighboring points The final mean of all points is the overall curvature of the manifold.

[0072] In order to achieve a flatter feature manifold representation in the construction of nonlinear weighted graph convolution models, a manifold curvature regularization module is proposed. This module constrains the model by using the manifold curvature as a regularization term to reduce the curvature of the feature manifold. The calculation method at the lth training iteration of the model training is:

[0073]

[0074] Among them, τ1 is a hyperparameter set artificially, which is used to control the weight of the curvature regularization term. The larger τ1 is, the smaller the influence of the curvature regularization term is; L1 is the classification loss function, which is obtained by calculating the difference between the predicted value and the true value. represents L1 at the lth training iteration. represents the integer division operation, that is Dividing L1 without retaining the remainder aims to keep them in the same order of magnitude. In the later stages of model training, the training loss will drop to a lower order of magnitude, and the manifold curvature regularization term needs to be aligned with it to prevent a sudden deterioration in model performance.

[0075] S3. Design the manifold intrinsic dimension regularization:

[0076] In order to reduce the interference of redundant information in high-dimensional space on the similarity measurement of local information, the manifold intrinsic dimension regularization is proposed. On the surface, except for the characteristic sample Z t In addition, there is noise with complex distribution patterns. In order to eliminate redundant information in the representation process of the training model, the present invention proposes a regularization term to constrain the model. This regularization term reduces the manifold surface The intrinsic dimension p, where p < d, reduces the interference of redundant high-dimensional information on the model. is a manifold with N r samples on it. Let represent a set of noises on the manifold . The intrinsic dimension of z i is:

[0077]

[0078] where z i is the central sample selected for calculating the intrinsic dimension of the manifold surface . z r ∈ Z t is another sample on the manifold surface . z j ∈ Z t is located within a minimal neighborhood of z i . This minimal neighborhood is formed by calculating the distances to all neighboring z j and sorting them in ascending order, taking the top ten samples. indicates that this minimal neighborhood does not include the noise z k , because of the difference between the noise and the samples at the spectral feature level, the noise can be excluded through the constraint of the minimal neighborhood. r(z i ) is defined as the radius of the neighborhood circle centered at z i and containing z r . The matrix operation is defined as:

[0079]

[0080] where v and w represent the two inputs for the matrix operation;

[0081] The global intrinsic dimension of Z t is defined as:

[0082]

[0083] During the l-th iteration of model training, a feature manifold surface is formed, and is used to measure the intrinsic dimension of the training feature samples on this surface. To constrain the model to compress the noise onto the low-dimensional manifold surface and thus eliminate redundant information, the proposed manifold intrinsic dimension regularization can be expressed at the l-th iteration as:

[0084]

[0085] where substituting formula (7) into L l, that is, the curvature regularization and the intrinsic dimension regularization are in a nested relationship. τ2 is a hyperparameter set by humans and is used to control the weight of the intrinsic dimension regularization term. The larger τ2 is, the smaller the influence of the intrinsic dimension regularization term is. is the constraint loss finally used in the l-th iteration of the training of the proposed model.

[0086] S4. Based on the constraint loss After the model training is completed, the trained model is used for hyperspectral image classification.

[0087] The hyperspectral image classification algorithm proposed by the present invention uses non-linear weighted graph convolution to aggregate information between superpixel nodes, obtains deeper non-linear local and global information, and generates a high-dimensional feature manifold surface. By performing manifold geometry regularization on the feature manifold surface, including a manifold curvature regularization term for improving the accuracy of local information measurement and an intrinsic dimension regularization term for reducing the interference of redundant information on the model, the classification performance of the model is improved. A linear classifier is used to classify the generated regular features to generate the final classification result map.

[0088] Three hyperspectral data are used to illustrate the effect of the hyperspectral image classification method based on manifold geometry regularization and non-linear weighted graph convolution proposed by the present invention. The detailed information of the three data used is listed in Table 1. The overall accuracy (OA) is used as the evaluation index for the experimental results. The higher the value of OA, the better the detection effect.

[0089] Table 1 Detailed information of the hyperspectral images used

[0090]

[0091] For different data, the parameter analysis of the method of the present invention is shown by Figures 5 - 7 As shown, the selection of different parameters has little influence on the classification performance of the model. The language environment is Python 3.9.12, and the experimental hardware platform is NVIDIA GeForce RTX3090 GPU, and the CUDA version is 11.1.

[0092] The false color maps, ground truth maps and classification result maps of Dataset I to Dataset III are as shown in Figures 2 - 4 As shown. Through experimental analysis, the method proposed in this experiment can obtain OA values of 0.9468, 0.9596 and 0.8651 on the three datasets respectively.

[0093] The above numerical examples of the present invention are only for explaining in detail the calculation model and calculation process of the present invention, rather than limiting the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation manners here. Any obvious changes or modifications derived from the technical solutions of the present invention still fall within the protection scope of the present invention.

Claims

1. A hyperspectral image classification method based on nonlinear weighted graph convolution, characterized in that: For the hyperspectral image X, a classification model based on nonlinear weighted graph convolution is used for image classification; The classification model processing process based on nonlinear weighted graph convolution includes: A simple linear iterative clustering algorithm is used to cluster the hyperspectral image into n superpixels, and the pixels within the superpixels share features. Then a nonlinear weighted graph convolution module is used, which includes internal graph convolution and external graph convolution processing. The internal graph convolution generates the kth shared feature based on the graph convolution The shared features s corresponding to n superpixels k Construct super pixel feature matrix S = [s1,...,s k ,...,s n ]∈R n×d ;in, is the degree matrix of the inner graph convolution, is the adjacency matrix, W in is the learnable parameter matrix, pool mean [·] is the average pooling operation; X k represents the feature matrix of the pixels inside the kth superpixel, and d is the number of spectral channels; Based on superpixel nodes i and all neighboring superpixel nodes s j The similarity between them is determined by i and j The normalized weight a of the corresponding edge ij ; The weights of all adjacent edges of n superpixels are combined into the adjacency matrix of the entire hyperspectral image External graph convolution based on adjacency matrix Perform local information aggregation on the input superpixel feature matrix S, and finally generate the deep feature matrix Z based on graph convolution processing; The generated feature matrix Z is sent to the linear classifier for classification to obtain the hyperspectral image classification result.

2. The hyperspectral image classification method based on nonlinear weighted graph convolution according to claim 1, characterized in that: In the process of clustering the hyperspectral image into n superpixels using a simple linear iterative clustering algorithm, the hyperspectral image is segmented into graph structure data consisting of nodes and edges by a simple linear iterative clustering algorithm, and each node represents a superpixel.

3. The hyperspectral image classification method based on nonlinear weighted graph convolution according to claim 1 or 2, characterized in that: s i and j The normalized weight of the corresponding edge Among them, cos<·,·> represents the cosine similarity operation.

4. The hyperspectral image classification method based on nonlinear weighted graph convolution according to claim 3 is characterized in that: Adjacency Matrix There is a +1 operation on all the main diagonal elements of the adjacency matrix.

5. The hyperspectral image classification method based on nonlinear weighted graph convolution according to claim 4 is characterized in that: According to the adjacency matrix The way to aggregate local information of the input superpixel feature matrix S is as follows:

6. The hyperspectral image classification method based on nonlinear weighted graph convolution according to claim 5, characterized in that: External graph convolution based on adjacency matrix The process of aggregating local information of the input superpixel feature matrix S and finally generating the deep feature matrix Z based on graph convolution processing includes: The corresponding external graph convolution of the λth layer Recorded as The superpixel feature matrix S is denoted as S 0 As the input of the external graph convolution, the graph convolution is processed, and the features generated by the λth layer external graph convolution are processed and expressed as: Among them, relu is the activation function, and BN is the batch normalization layer; is a trainable matrix, is the adjacency matrix corresponding to the outer convolution of the λth layer S λ is the output feature matrix of the λth layer outer convolution; The output of the last layer of outer graph convolution generates the deep feature matrix Z.

7. The hyperspectral image classification method based on nonlinear weighted graph convolution according to claim 6, characterized in that: The nonlinear weighted graph convolution module performs two layers of outer convolution processing.

8. A training method for a classification model based on nonlinear weighted graph convolution, characterized in that: The classification model based on nonlinear weighted graph convolution in the hyperspectral image classification method based on nonlinear weighted graph convolution according to any one of claims 1 to 7 is trained, and the training process includes: For each hyperspectral image in the hyperspectral image training set, a deep feature matrix Z is generated and classified using a linear classifier; the deep feature matrix Z is located on a low-dimensional manifold surface in a high-dimensional space. on; set It is a manifold N t samples, z i The selected manifold surface is used to calculate The center sample of curvature, Yes i N r neighborhood samples, then z i The local manifold subspace of μ i For z i N r The average of the neighborhood samples according to the feature dimension is the mean of M i Do singular value decomposition to get is a rectangular diagonal matrix generated by singular value decomposition, with non-negative values ​​on the diagonal arranged in descending order; z i The neighboring nodes also have a local manifold subspace M with itself as the center point j , perform singular value decomposition to get make Do singular value decomposition to get based on Get the manifold surface at the lth training iteration Curvature Using curvature Determine the regularization constraints Among them, τ1 is the weight used to control the curvature regularization term; L1 is the classification loss function, represents L1 at the lth training iteration; represents the integer division operation, that is Divide L1 without leaving a remainder; On the characteristic manifold On the surface, It is a manifold N r Samples, set Representing manifolds A set of noises on z i The intrinsic dimension of Get Z t The global intrinsic dimension of The z i The intrinsic dimension of is: Among them, z i The selected manifold surface is used to calculate The center sample of the intrinsic dimension; z r ∈Z t It is a manifold surface Another sample on z j ∈Z t Located in i In the neighborhood of Indicates that the neighborhood does not include noise z k , r(z i ) is z i The center contains z r The radius of the neighborhood circle; matrix operations Among them, v and w represent two inputs for matrix operations; Then we get the loss function at the lth iteration: Among them, τ2 is used to control the weight of the regularization term of the intrinsic dimension; based on Complete the model training.

9. The training method of a classification model based on nonlinear weighted graph convolution according to claim 8, characterized in that: The manifold surface at the lth training iteration Curvature 10. According to the training method of the classification model based on nonlinear weighted graph convolution according to claim 9, j ∈Z t Located in i This is achieved by following the steps in the neighborhood: In z i In the neighborhood of j Calculate the distance and sort it in increasing order, taking the first ten samples as z i z in the neighborhood of j .

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