A hyperspectral image clustering method based on dynamic sparse graph constrained autoencoder

Abstract

This application discloses a hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder, relating to the field of hyperspectral image processing. The method includes: dimensionality reduction and superpixel segmentation of the hyperspectral image to extract superpixel-level node feature matrices; calculating distances based on the node feature matrices and constructing an initial sparse adjacency matrix through sparse regularization; inputting the feature matrix and the initial adjacency matrix into a dynamic graph autoencoder to extract latent representations and reconstruct connected distributions, dynamically updating the adjacency matrix using an exponential moving average strategy; calculating a soft clustering assignment matrix based on the latent representations, iteratively optimizing network parameters and graph topology by combining graph reconstruction loss and clustering loss; and finally outputting the clustering results based on the soft assignment matrix. This application overcomes the shortcomings of traditional methods, such as rigid graph structure and redundant edges, through dynamic sparse graph constraints and a joint optimization mechanism, achieving adaptive evolution of the graph topology and significantly improving the accuracy and computational efficiency of hyperspectral image clustering.

Description

Technical Field

[0001] This application relates to the field of hyperspectral image processing, and in particular to a hyperspectral image clustering method based on a dynamic sparse graph constrained autoencoder. Background Technology

[0002] Hyperspectral image (HSI) clustering is a core unsupervised learning task with wide applications in precision agriculture, environmental monitoring, and urban planning. In recent years, deep graph clustering methods have shown great potential in this field, effectively improving feature representation capabilities by capturing the topological relationships between data through graph neural networks (GNNs).

[0003] However, existing depth map clustering methods have the following significant drawbacks when processing hyperspectral images: First, existing methods typically employ a fixed graph network structure throughout the training process. This rigid design limits the ability of the initial graph topology to adaptively adjust based on clustering performance, causing the network to be unable to correct erroneous connections in the initial graph structure later in training based on learned deep semantic features.

[0004] Second, common graph construction strategies (such as those based on K-nearest neighbors or fully connected graphs) often generate suboptimal node relationships, introducing too many redundant edges and compromising the sparsity of the graph. Hyperspectral images exhibit high local clustering of similar land features; dense graphs not only increase computational complexity but also introduce noisy edges, leading to feature confusion between different land feature categories and limiting the upper limit of clustering performance.

[0005] Therefore, how to design a graph topology that can adaptively evolve and maintain sparsity during training to improve the accuracy and efficiency of hyperspectral image clustering is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this application is to provide a hyperspectral image clustering method based on a dynamic sparse graph constrained autoencoder. By using dynamic sparse graph constraints and a joint optimization mechanism, the method achieves adaptive evolution of the graph topology, thereby improving the clustering accuracy and robustness.

[0007] To achieve the above objectives, this application provides the following solution: This application provides a hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder, including: Acquire the raw hyperspectral image; The original hyperspectral image is subjected to dimensionality reduction and superpixel segmentation. The average spectral features of pixels in each superpixel region are extracted to obtain a superpixel-level node feature matrix. Based on the superpixel-level node feature matrix, calculate the Euclidean distance between nodes; Based on the Euclidean distance, the conditional probability is solved by minimizing the loss with sparse regularization. Construct an initial sparse adjacency matrix based on the conditional probabilities; The superpixel-level node feature matrix and the initial sparse adjacency matrix are input into a dynamic graph autoencoder. The dynamic graph autoencoder includes a graph embedding convolutional encoder and a dynamic graph decoder. The latent representation is extracted through the graph embedding convolutional encoder, the reconstructed connectivity distribution is calculated through the dynamic graph decoder and the latent representation, and the reconstruction loss is calculated based on the reconstructed connectivity distribution. The initial sparse adjacency matrix is ​​dynamically updated using an exponential moving average strategy to obtain the dynamic adjacency matrix and the latent representation of the current iteration. Based on the potential representation of the current iteration, calculate the soft clustering assignment matrix and the auxiliary target distribution; The clustering loss is constructed based on the soft clustering assignment matrix and the auxiliary target distribution; The total loss function is constructed by combining the reconstruction loss and clustering loss. The network parameters and dynamic adjacency matrix of the dynamic graph autoencoder are iteratively updated based on the total loss function until the preset convergence condition is met, and the final soft clustering assignment matrix is ​​obtained. Based on the final soft clustering assignment matrix, the maximum probability class label of each superpixel node is determined, and the final clustering result of the hyperspectral image is output.

[0008] Optionally, the original hyperspectral image is subjected to dimensionality reduction and superpixel segmentation processing. The average spectral features of pixels within each superpixel region are extracted to obtain a superpixel-level node feature matrix, specifically including: Principal component analysis (PCA) was used to reduce the dimensionality of the original hyperspectral image. The simple linear iterative clustering (SLIC) algorithm is used to segment the dimensionality-reduced image and generate superpixel regions. The average value of the spectral feature vectors of all original pixels within each superpixel region is calculated to obtain the superpixel-level node feature matrix.

[0009] Optionally, based on the superpixel-level node feature matrix, the Euclidean distance between nodes is calculated using the following formula: ; in, and All represent nodes With nodes The square of the Euclidean distance between them; This represents the mapping function that maps node features to the latent space; Indicates the first The feature vector of each node; Indicates the first The feature vector of each node; express The square of the norm is the square of the Euclidean distance.

[0010] Optionally, based on the Euclidean distance, the conditional probability is solved by minimizing the loss with sparse regularization using the following formula: ;in, Represents a given node At that time, node The conditional probability associated with it; Represents a node Of the distances to all other nodes, the first... Small distance value; Represents a node To the The distance to the nearest neighbor; Indicates hyperparameters; Indicates a positive operation; Indicates the index number; This represents the upper limit of the summation of the denominators. This represents a placeholder, indicating any real number expression.

[0011] Optionally, the initial sparse adjacency matrix is ​​constructed based on the conditional probability using the following formula: ; in, Represents the initial sparse adjacency matrix The Middle Line 1 The elements of a column, i.e., nodes With nodes Weights of undirected edges between them; Represents a given node At that time, node The conditional probability associated with it.

[0012] Optionally, the latent representation is extracted via the graph embedding convolutional encoder using the following formula: ; in, Indicates the final potential representation; This indicates the number of layers in the graph embedding convolutional encoder; Indicates the first Activation function of the layer; Represents a symmetric normalized adjacency matrix. ; Indicates the first Activation function for layer -1; This represents the activation function of the first layer; Represents spectral features at the superpixel level; This represents the trainable weight parameter matrix of the first graph convolutional layer; Indicates the first The trainable weight parameter matrix of a layered graph convolutional layer; This represents the adjacency matrix after adding self-loops; express The degree matrix is ​​a diagonal matrix.

[0013] Optionally, the reconstructed connected distribution is calculated using the following formula through the dynamic graph decoder and the latent representation: ; in, Indicates the reconstructed connected distribution; Represents a node and The square of the Euclidean distance in the latent space; Represents the normalization factor, summed over all nodes, ensuring ; The exponent represents the negative distance; the smaller the distance, the larger the exponent value, indicating a higher probability of connection.

[0014] Optionally, the reconstruction loss is calculated based on the reconstructed connectivity distribution using the following formula: ; in, Indicates the reconstruction loss; Indicates the Kullback-Leibler divergence; This represents the estimated conditional connectivity distribution reconstructed by the graph autoencoder in the latent space; Represents a given node At that time, node The conditional probability associated with it is the conditional probability of the original sparse graph. Indicates the reconstructed connected distribution; This represents the total number of nodes in the graph.

[0015] Optionally, the clustering loss is constructed based on the soft clustering assignment matrix and the auxiliary target distribution using the following formula: ; in, Represents the clustering loss; Indicates the Kullback-Leibler divergence; Indicates the target distribution; Represents the soft clustering assignment matrix; Represents nodes in the target distribution Belongs to cluster The probability of; Indicates the nodes in the current soft allocation Belongs to cluster The probability of.

[0016] Optionally, the expression for the total loss function is as follows: ; in, Indicates the total loss; Represents the clustering loss; Indicates the reconstruction loss; This represents the balancing hyperparameter.

[0017] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder, which has the following significant advantages: Adaptive Graph Topology Evolution: This application introduces a dynamic graph decoder and an exponential moving average (EMA) strategy, enabling the graph's adjacency matrix to be iteratively updated as deep semantic features are learned. This closed-loop evolution mechanism overcomes the rigidity of traditional static graphs, allowing the graph structure to adaptively conform to the real-world distribution of features.

[0018] Efficient sparse graph construction: In the initial graph construction stage, a conditional probability truncation mechanism with L1 norm regularization is used to forcibly retain the most representative similarity connections of land features and remove redundant and noisy edges. This not only ensures the high-quality sparsity of the graph but also significantly reduces the computational complexity in the graph convolution process.

[0019] Joint optimization enhances clustering performance: By jointly optimizing the graph structure reconstruction loss and the self-training clustering loss based on the Student t-distribution, the algorithm becomes robust to outlier spectra during probability allocation, resulting in more compact intra-class superpixel embeddings and clearer inter-class separation, significantly improving the overall accuracy and stability of hyperspectral image clustering. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of a hyperspectral image clustering method based on a dynamic sparse graph constrained autoencoder in one embodiment of this application; Figure 2This is a flowchart illustrating a hyperspectral image clustering method based on a dynamic sparse graph constrained autoencoder, provided as an embodiment of this application. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] In one exemplary embodiment, such as Figure 1 As shown, the Dynamic Graph Autoencoder (DSGC) framework comprises four key components: local region generation, sparse graph construction, dynamic graph autoencoder, and joint optimization mechanism. Initially, the local region generation stage transforms image pixels into spatially coherent regions, preserving the integrity of local structures. Simultaneously, sparse graph construction builds an initial sparse graph structure to represent the relationships between regions. The dynamic graph autoencoder is used to discover latent feature representations from the sparse graph, supporting hyperspectral image clustering tasks. During training iterations, this component progressively optimizes the sparsity of the graph by updating edge connections, thereby enhancing the discovery of sparse patterns. Finally, the joint optimization module ensures structural consistency and promotes graph sparsity while coordinating network training. This integrated approach maintains consistency between graph representations and systematically optimizes the entire architecture to improve clustering performance.

[0025] like Figure 2 As shown, a hyperspectral image clustering method based on a dynamic sparse graph constrained autoencoder is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method includes the following steps: Step 101: Obtain the raw hyperspectral image.

[0026] Step 102: Perform dimensionality reduction and superpixel segmentation on the original hyperspectral image, extract the average spectral features of pixels in each superpixel region, and obtain the superpixel-level node feature matrix.

[0027] In hyperspectral images, pixels of the same category tend to cluster in statistically uniform regions. Current research highlights the effectiveness of superpixel segmentation in revealing the comprehensive spectral-spatial properties of hyperspectral images, facilitating better localization of data homogeneity in advanced analytical workflows. To achieve this, this embodiment first performs dimensionality reduction on the original hyperspectral image using Principal Component Analysis (PCA), generating compact and representative images for subsequent tasks. Then, the Simple Linear Iterative Clustering (SLIC) algorithm is used to dynamically segment these dimensionality-reduced outputs into irregularly shaped regions, i.e., superpixel regions, to accommodate spatial heterogeneity and texture complexity. Finally, the consistency of feature representation is ensured by averaging the spectral features of individual superpixels to obtain a superpixel-level node feature matrix, i.e.: ; ; in, Represents superpixel-level spectral features, with dimensions of Each row corresponds to the average spectral vector of a superpixel, reflecting the distribution of the average reflectance of ground features in that area with different bands. The total number of nodes in the graph is automatically generated by the SLIC algorithm based on the image complexity. This represents the spectral feature dimension, i.e., the number of effective bands retained after PCA dimensionality reduction (e.g., 30~100 principal components). Indicates the first The spectral feature vectors of each superpixel have a length of [missing information]. , as the initial feature of a node in a graph network; Indicates transpose; Indicates the first The number of original pixels contained in a superpixel (i.e., the spatial scale of the region). Indicates the first Spectral feature vector of a pixel; Indicates the first Within the first superpixel The spectral vector of each original pixel (raw pixel reflectance values ​​without averaging).

[0028] Step 103: Calculate the Euclidean distance between nodes based on the superpixel-level node feature matrix.

[0029] The specific formula is as follows: ; in, and All represent nodes With nodes The square of the Euclidean distance between them; This represents the mapping function that maps node features to the latent space; Indicates the first The feature vector of each node; Indicates the first The feature vector of each node; express The square of the norm is the square of the Euclidean distance.

[0030] Step 104: Based on the Euclidean distance, solve for the conditional probability by minimizing the loss with sparse regularization.

[0031] Step 105: Construct an initial sparse adjacency matrix based on the conditional probabilities.

[0032] For each node This application aims to define a distribution , used to represent nodes Connect to node The probability of connection between nodes. Ideally, nodes that are close to each other in the feature space should have a high connection probability, while nodes that are far apart should have a probability close to zero. However, if these probabilities are set directly based on the pairwise distances between nodes, the resulting graph will be dense. Therefore, the true connection distribution is... Treat them as unknowns to be estimated, and impose constraints that the graph structure should remain sparse and conducive to clustering. If the nodes Near the node So, the expectation is: ; in, Represents a mapping function; Represents the total number of nodes in the graph; Represents the conditional probability distribution The mathematical expectation; Represents a given node At that time, node The conditional probability associated with it.

[0033] To address this challenge, a direct solution remains impractical because it relates to... The subproblem has a trivial solution, that is... (for )and A widely adopted strategy is to minimize the regularization loss, whose objective function is expressed as: ; in, Let represent the regularization term, and let . As a prior distribution, It can be broken down into: ; in, It is a hyperparameter used to control the strength of the regularization term; This represents the true connectivity distribution to be estimated; This represents the prior distribution. In the absence of prior knowledge, a uniform distribution is usually chosen. As a priori. Function This is used to quantify the difference between two discrete distributions. Although the Kullback-Leibler divergence is a commonly used choice, this application proposes a simpler form of metric. This metric has the following advantageous properties. ; in, Let represent a row vector consisting of all optimal sparse probabilities. It is a with Irrelevant constants Represents a given node At that time, node The conditional probability associated with it; This indicates a prior uniform distribution. Therefore, the objective simplifies to: ; in, Control sparsity. If ,in Represents a node The distance to all other nodes is the first If there are a minimum value, then the solution to this optimization problem is guaranteed to have exactly one minimum value. Non-zero entries (i.e.) -Sparseness). This yields a closed-ended solution: ; in, This represents a hyperparameter used to determine the out-degree (number of non-zero edges) of each node. This represents a virtual index variable used in the summation process; This indicates the upper limit of the summation of the denominators. This design has two motivations: First, - Sparsity aligns with the goals of graph-based clustering, as the probability of nodes in different clusters should approach zero. Secondly, compared to alternative methods requiring extensive parameter tuning, the sparse graph construction module has only one hyperparameter. The optimization process has been simplified. It is a node The distance to all other nodes is the first Small distance value; It is the first Short distance. This design has two motivations: first, - Sparsity aligns with the goal of graph clustering—the connection probability of nodes in different clusters should approach zero; second, this sparse graph construction step only requires adjusting one hyperparameter. Compared to alternative methods that require extensive parameter tuning, this significantly simplifies the optimization process.

[0034] Then you can define the nodes in the original graph. and The connection between them is ,Right now: .

[0035] Step 106: Input the superpixel-level node feature matrix and the initial sparse adjacency matrix into a dynamic graph autoencoder; the dynamic graph autoencoder includes a graph embedding convolutional encoder and a dynamic graph decoder; extract latent representations through the graph embedding convolutional encoder, calculate the reconstructed connectivity distribution through the dynamic graph decoder and the latent representation, and calculate the reconstruction loss based on the reconstructed connectivity distribution; and dynamically update the adjacency matrix using an exponential moving average strategy to obtain the dynamic adjacency matrix and the latent representation of the current iteration.

[0036] The latent representation is obtained through iterations of spectral graph convolutional layers, the th... The output of the layer is controlled by the following operations: ; in, and They represent the first The input and output feature matrices of the layer, This represents the trainable parameter matrix optimized during network training. Let represent the initial sparse adjacency matrix, and GCN denote a graph convolutional layer. Initial feature matrix. Set to equal to the input node attribute According to the graph convolution formula, the mathematical definition of the graph convolution operation at each layer is: ; in, Indicates the activation function; express The degree matrix; This represents the adjacency matrix after adding self-loops. , It is an identity matrix.

[0037] By stacking The final latent representation generated by each convolutional layer The calculation is as follows: ; in, Indicates the final potential representation; This indicates the number of layers in the graph embedding convolutional encoder; Indicates the first Activation function of the layer; Represents a symmetric normalized adjacency matrix. ; Indicates the first Activation function for layer -1; This represents the activation function of the first layer; Represents spectral features at the superpixel level; This represents the trainable weight parameter matrix of the first graph convolutional layer; Indicates the first The trainable weight parameter matrix of a layered graph convolutional layer; This represents the adjacency matrix after adding self-loops; express The degree matrix is ​​a diagonal matrix.

[0038] Step 107: Based on the latent representation of the current iteration, calculate the soft clustering assignment matrix and the auxiliary target distribution.

[0039] Step 108: Construct clustering loss based on the soft clustering assignment matrix and auxiliary target distribution.

[0040] Unlike existing adaptive graph methods, which either maintain a fixed graph topology or learn dense edge weights, the decoder in this application aims to dynamically adjust edge weights and the underlying sparse topology based on the clustering objective. Traditional methods typically use inner products to reconstruct... To achieve the decoding process, resulting in It remains unchanged throughout the training process. In this application, the distribution of connections between nodes is calculated. To obtain the adjacency matrix Specifically, the updated adjacency matrix The calculation is as follows: ; in, It is iteration time matrix, It is a smoothing factor that controls the update rate. This ensures that the graph structure evolves gradually, maintaining stability while adapting to the learned feature representations.

[0041] To extract deep features from a graph autoencoder, it is necessary to recover the original conditional probability distribution. Therefore, the definition To represent potential representations Distance: in, yes The Column vectors. Then, normalization is used to reconstruct the connection distribution, i.e.: ; This process can be explained as... This is achieved through a SoftMax layer, which is part of the decoder in a Dynamic Graph Auto-Encoder. It's worth noting that the smaller... Generate a large This indicates that similarity is determined by Euclidean distance, rather than the inner product commonly used in dynamic graph autoencoders (GAEs). To quantify the difference between the two distributions, the Kullback-Leibler (KL) divergence is employed, which modulates the objective function... The expression is as follows: ; By using During network training, the adjacency matrix can be adaptively adjusted according to different clustering tasks. This involves adjusting the connection values ​​between different nodes to change the sparsity of the graph, thereby improving clustering accuracy. KL divergence loss. The graph is used to guide the reconstruction of the connection distribution, but the actual graph update is explicitly performed using the moving average strategy defined above. This avoids trivial solutions and stabilizes the training.

[0042] To address the unsupervised node clustering problem in graph representation learning, this application combines a dynamic graph autoencoder with self-supervised training. While the encoder generates latent graph embeddings through dimensionality reduction, traditional methods neglect clustering-oriented optimization during representation learning. A key obstacle in unsupervised scenarios is the lack of supervisory signals for model training. To bridge this gap, this application implements a self-training paradigm that utilizes iterative label refinement to guide cluster formation. The clustering objective employs Kullback-Leibler divergence: ; in Indicates the target distribution. This represents the soft assignment derived from node-cluster similarity, i.e., the soft clustering assignment matrix. Specifically, it uses the student... - The distribution serves as the kernel function for probability allocation: ; in, Describing the degrees of freedom of the distribution. Represents a node Belongs to cluster jThe soft assignment probabilities. These assignments form a matrix. To enhance cluster compactness, auxiliary target distribution is used. Sharpen the distribution using the following formula: ; in, Represents nodes in the target distribution i Belongs to cluster j The probability of; This represents a virtual index variable used in mathematical summation.

[0043] Step 109: Construct the total loss function by combining the reconstruction loss and clustering loss.

[0044] minimize By making Denser clustering promotes intra-cluster cohesion and inter-cluster separation. Minimizes clustering loss. This will cause the soft allocation matrix to be used. The distribution becomes more concentrated and deterministic (each node belongs to a cluster with a high probability), thereby enhancing intra-cluster compactness and increasing inter-cluster distance. The composite optimization function combines reconstruction and clustering objectives: .

[0045] Step 110: Iteratively update the network parameters and dynamic adjacency matrix of the dynamic graph autoencoder based on the total loss function until the preset convergence condition is met, and obtain the final soft clustering assignment matrix.

[0046] Step 111: Based on the final soft clustering assignment matrix, determine the maximum probability class label for each superpixel node and output the final clustering result of the hyperspectral image.

[0047] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0048] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder, characterized in that, The hyperspectral image clustering method based on dynamic sparse graph-constrained autoencoders includes: Acquire the raw hyperspectral image; The original hyperspectral image is subjected to dimensionality reduction and superpixel segmentation. The average spectral features of pixels in each superpixel region are extracted to obtain a superpixel-level node feature matrix. Based on the superpixel-level node feature matrix, calculate the Euclidean distance between nodes; Based on the Euclidean distance, the conditional probability is solved by minimizing the loss with sparse regularization. Construct an initial sparse adjacency matrix based on the conditional probabilities; The superpixel-level node feature matrix and the initial sparse adjacency matrix are input into a dynamic graph autoencoder. The dynamic graph autoencoder includes a graph embedding convolutional encoder and a dynamic graph decoder. The latent representation is extracted through the graph embedding convolutional encoder, the reconstructed connectivity distribution is calculated through the dynamic graph decoder and the latent representation, and the reconstruction loss is calculated based on the reconstructed connectivity distribution. The initial sparse adjacency matrix is ​​dynamically updated using an exponential moving average strategy to obtain the dynamic adjacency matrix and the latent representation of the current iteration. Based on the potential representation of the current iteration, calculate the soft clustering assignment matrix and the auxiliary target distribution; The clustering loss is constructed based on the soft clustering assignment matrix and the auxiliary target distribution; The total loss function is constructed by combining the reconstruction loss and clustering loss. The network parameters and dynamic adjacency matrix of the dynamic graph autoencoder are iteratively updated based on the total loss function until the preset convergence condition is met, and the final soft clustering assignment matrix is ​​obtained. Based on the final soft clustering assignment matrix, the maximum probability class label of each superpixel node is determined, and the final clustering result of the hyperspectral image is output.

2. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 1, characterized in that, The original hyperspectral image is subjected to dimensionality reduction and superpixel segmentation. The average spectral features of pixels within each superpixel region are extracted to obtain a superpixel-level node feature matrix, specifically including: Principal component analysis (PCA) was used to reduce the dimensionality of the original hyperspectral image. The simple linear iterative clustering (SLIC) algorithm is used to segment the dimensionality-reduced image and generate superpixel regions. The average value of the spectral feature vectors of all original pixels within each superpixel region is calculated to obtain the superpixel-level node feature matrix.

3. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 1, characterized in that, Based on the superpixel-level node feature matrix, the Euclidean distance between nodes is calculated using the following formula: ； in, and All represent nodes With nodes The square of the Euclidean distance between them; This represents the mapping function that maps node features to the latent space; Indicates the first Feature vectors of each node; Indicates the first Feature vectors of each node; express The square of the norm is the square of the Euclidean distance.

4. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 3, characterized in that, Based on the Euclidean distance, the conditional probability is solved by minimizing the loss with sparse regularization using the following formula: ;in, Represents a given node At that time, node The conditional probability associated with it; Represents a node The distance to all other nodes is the first Small distance value; Represents a node To the The distance to the nearest neighbor; Indicates hyperparameters; Indicates a positive operation; Indicates the index number; This indicates the upper limit of the summation of the denominators; This represents a placeholder, indicating any real number expression.

5. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 4, characterized in that, The initial sparse adjacency matrix is ​​constructed based on the aforementioned conditional probabilities using the following formula: ； in, Represents the initial sparse adjacency matrix The Middle Line number The elements of a column, i.e., nodes With nodes Weights of undirected edges between them; Represents a given node At that time, node The conditional probability associated with it.

6. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 1, characterized in that, The latent representation is extracted using the graph embedding convolutional encoder using the following formula: ； in, Indicates the final potential representation; This indicates the number of layers in the graph embedding convolutional encoder; Indicates the first Activation function of the layer; Represents a symmetric normalized adjacency matrix. ; Indicates the first Activation function for layer -1; This represents the activation function of the first layer; Represents spectral features at the superpixel level; This represents the trainable weight parameter matrix of the first graph convolutional layer; Indicates the first The trainable weight parameter matrix of a layered graph convolutional layer; This represents the adjacency matrix after adding self-loops; express The degree matrix is ​​a diagonal matrix.

7. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 1, characterized in that, The reconstructed connected distribution is specifically calculated using the following formula through the dynamic graph decoder and the latent representation: ； in, Indicates the reconstructed connected distribution; Represents a node and The square of the Euclidean distance in the latent space; Represents the normalization factor, summed over all nodes, ensuring ; The exponent represents the negative distance; the smaller the distance, the larger the exponent value, indicating a higher probability of connection.

8. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 7, characterized in that, The reconstruction loss is calculated based on the reconstructed connectivity distribution using the following formula: ; in, Indicates the reconstruction loss; Indicates the Kullback-Leibler divergence; This represents the estimated conditional connectivity distribution reconstructed by the graph autoencoder in the latent space; Represents a given node At that time, node The conditional probability associated with it; Indicates the reconstructed connected distribution; This represents the total number of nodes in the graph.

9. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 1, characterized in that, The clustering loss is constructed based on the soft clustering assignment matrix and the auxiliary target distribution using the following formula: ； in, Represents the clustering loss; Indicates the Kullback-Leibler divergence; Indicates the target distribution; Represents the soft clustering assignment matrix; Represents nodes in the target distribution Belongs to cluster The probability of; Indicates the nodes in the current soft allocation Belongs to cluster The probability of.

10. The hyperspectral image clustering method based on a dynamic sparse graph-constrained autoencoder according to claim 1, characterized in that, The expression for the total loss function is as follows: ； in, Indicates the total loss; Represents the clustering loss; Indicates the reconstruction loss; This represents the balancing hyperparameter.

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