Graph neural network feature and label propagation method for multi-view data

Abstract

The invention discloses a graph neural network feature and label propagation method for multi-view data, and the method comprises the following steps: S1, initializing a model optimization variable, and evaluating adjacent matrixes of all graphs through employing a kernel method; s2, according to node features in the multi-view data, spreading the node features in the multi-view data in a graph structure by using a message passing mechanism of a graph neural network; s3, according to selection of parallel or cooperative training of feature and label propagation, label information is propagated in a graph structure through different multi-view label propagation rules; and S4, predicting the label of the test sample in combination with the results of the feature propagation and the label propagation. According to the method, information can be effectively integrated in multi-view data, the accuracy of label prediction is improved, and the method is suitable for complex graph structure data processing tasks.

Description

Technical Field

[0001] The present invention relates to the fields of graph neural networks and multi-view learning, and in particular to a graph neural network feature and label propagation method for multi-view data. Background Art

[0002] In practical applications, multi-view data is widely available. The same object can often be described from multiple views, each providing unique information dimensions. Comprehensive analysis facilitates a more comprehensive understanding of the object. For example, user data on social media platforms encompasses multiple dimensions, including text posts, visual uploads, and social connections. This facilitates in-depth analysis and decision-making for targeted marketing and personalized content recommendations. Multi-view learning has emerged as a result, achieving significant progress in fields such as data mining, machine learning, and computer vision.

[0003] Multi-view semi-supervised learning aims to address the resource-intensive, expert-required, and resource-intensive challenges of labeling multi-view data, leveraging multi-view data with limited labels. Among the many multi-view methods, graph-based approaches hold great promise. They analyze sample similarities to uncover implicit connections and learn consistency and complementarity between views. However, many graph-based multi-view semi-supervised classification methods are shallow models that struggle to effectively integrate graph structure information with intrinsic properties.

[0004] In recent years, deep graph learning methods have attracted much attention. Graph Convolutional Networks (GCNs) have become a powerful tool for extracting complex semantic information from graph data. Numerous effective variants have promoted the development of fields such as link prediction, anomaly detection, and recommendation systems. They have also prompted researchers to apply them to multi-view semi-supervised classification and achieve certain results.

[0005] Graph Convolutional Networks (GCNs), proposed by Kipf and Welling, are a powerful feature propagation method for processing complex graph data. They can leverage the structural information of graphs to learn robust node representations. Due to the effectiveness of GCNs, numerous variants have been explored. For example, Li et al. improved GCNs by using joint training and self-training methods to alleviate the over-smoothing problem; Chiang et al. developed an efficient training algorithm that leveraged graph clustering to improve the storage and computational efficiency of large-scale graphs; Chen et al. proposed a model that merged local and global feature interactions before graph convolution to enhance the initial node representation of classification features; Zhao et al. introduced a neighborhood class consistency metric to optimize graph topology to enhance node classification performance; and Huang et al. enhanced GCNs by integrating the petal Laplacian operator in a simplex complex to effectively capture high-order interactions. However, existing GCN models perform well on single-view graph data but still face significant challenges in effectively processing multi-view data.

[0006] Multi-view learning aims to extract valuable information by mining the consistency and complementarity between different data views. With the development of multimedia technology, this field has attracted much attention from researchers. In terms of traditional methods, Nie et al. optimized graph construction to process noisy data and automatically determined the ideal view weights; Huang et al. used the joint optimization of embedding regularizers and shared prediction label matrices to process multi-view data with limited labels; Wan et al. developed a six-step iterative optimization algorithm to fuse coefficient matrices of different dimensions into the best consensus matrix and converge to a unique low-dimensional space. In the exploration based on deep learning, Qin et al. introduced a noise-aware incomplete multi-view learning network to enhance robustness and consistency by processing inherent noise and evaluating data quality; Lin et al. solved cross-view errors by optimizing mutual information and conditional entropy. Figure 1 In recent years, researchers have focused on the problem of consistency and lost view recovery. Xu et al. designed a method to handle conflicting instances of multi-view data by learning view-specific evidence and aggregating it into reliable decision opinions. Inspired by GCN, Li et al. created a multi-view semi-supervised learning model that adaptively exploits multi-view graph information by combining Laplacian matrices. These studies highlight the advantages of multi-view learning over single-view learning and demonstrate its effectiveness in extracting more comprehensive and accurate insights from diverse datasets.

[0007] Although the above-mentioned related research has achieved many results, there is still a lack of perfect solutions for effectively applying GCN to multi-view data processing, and there is room for further research and innovation. Summary of the Invention

[0008] The purpose of the present invention is to provide a graph neural network feature and label propagation method for multi-view data. Through the parallel or collaborative training mode of feature propagation and label propagation, the feature propagation and label propagation processes are optimized, which can effectively integrate information in multi-view data and improve the accuracy of label prediction. It is suitable for complex graph structure data processing tasks.

[0009] The technical solution adopted in the present invention is:

[0010] A graph neural network feature and label propagation method for multi-view data, comprising the following steps:

[0011] Step S1, acquiring multi-view data to construct a graph network and initializing model parameters of a graph neural network suitable for extracting node features of multi-view data, and using a Gaussian kernel method to evaluate and calculate the adjacency matrix of the multi-view data;

[0012] Step S2: Based on the node features in the multi-view data, the message passing mechanism of the graph neural network is used to propagate the node features in the multi-view data in the graph structure;

[0013] Step S3: Based on the selection of parallel or collaborative feature and label propagation training, the label information is propagated in the graph structure using different multi-view label propagation rules to obtain the corresponding predicted label matrix;

[0014] Step S4: Combine the results of feature propagation and label propagation to predict the label of the test sample.

[0015] Furthermore, step S1 includes the following steps:

[0016] Step S1-1, obtain multi-view data to build a graph network in, is a node set, and Indicates that there are N samples; ε is the edge set, and |ε| = M indicates that there are M edges; X∈R N×D is the node feature matrix, i.e., multi-view data; A∈R N×N is the adjacency matrix between nodes;

[0017] Step S1-2, initialize model parameters α, β, and Ω, where α and β are learnable weight vectors for evaluating the importance of multi-view and label propagation, respectively, Θ (l,v) is the weight matrix connecting the l-1th layer and the lth layer in the graph neural network, and Ω is the parameter of the multilayer perceptron (MLP);

[0018] Step S1-3, use the Gaussian kernel method to calculate the adjacency matrix of multi-view data Among them A v The calculation formula for (i,j) is:

[0019]

[0020] Among them, A v (i, j) represents the adjacency matrix between nodes i and j in the vth view; X v (i) and X v (j) are the eigenvectors of nodes i and j in the vth view, respectively, and σ is the bandwidth parameter of the Gaussian kernel.

[0021] Furthermore, step S2 includes the following steps:

[0022] Step S2-1: label the first n samples of the multi-view data to obtain a zero-filled label matrix Y∈R N×C , where n<<N, N represents the number of samples, and C represents the number of categories;

[0023] Step S2-2, propagating node features through a graph neural network based on the graph neural network message passing mechanism, is expressed as:

[0024]

[0025] Among them, H (l,v) is the output representation of the lth layer of the vth view, and l∈[L] and v∈[V], initially H (0,v) =X v ;H (l-1,v) is the output representation of the l-1th layer of the vth view; Θ (l,v) is the weight matrix connecting the hidden representations of the l-1th layer and the lth layer; σ is the bandwidth parameter of the Gaussian kernel; is the normalized adjacency matrix with self-loops added to the v-th view; the diagonal elements D of the v-th view v The calculation formula is:

[0026] Step S2-3, L-th output representation based on graph neural network Use the attention mechanism to adaptively adjust the weight of each view data, expressed as:

[0027]

[0028] Where α=[α1,…,α V ] is a learnable weight vector used to evaluate the importance of multiple views; H (L) is the fusion node feature matrix used to represent the predicted label of the test sample;

[0029] H (L) It is given by the following formula:

[0030]

[0031] Step S2-4, collect predicted labels H (L) and training labels Y, using cross entropy loss to evaluate the difference between predicted labels and true labels The calculation expression is:

[0032]

[0033] Where n is the number of labeled samples and C is the number of categories;

[0034] In step S2-5, the output of the last network layer is aligned with the given label information, and the process is iterated until the cross entropy loss or model convergence occurs.

[0035] Furthermore, in step S3, when feature and label propagation are selected for parallel training, a label propagation process is performed independently of the feature propagation process. The label propagation process includes the following steps:

[0036] Step S3-1-1, calculate and obtain the random walk model propagation matrix of the vth label;

[0037]

[0038] Among them, Q (0,v) ∈R N×C is the initial distribution, γ v ∈R N×C represents the restart weight, which is used to control the restart probability of label propagation, Q (k,v) is the propagation matrix of the v-th view at the k-th step; is a normalized adjacency matrix with self-loops added to the diagonal elements; the diagonal elements D v The calculation formula is: N represents the number of samples, and C represents the number of categories;

[0039] Step S3-1-2, use the attention mechanism to normalize the label propagation results of multiple views in a parameter-free manner to obtain the fused label matrix Q (K) The calculation process is as follows:

[0040]

[0041] Where β=[β1,…,β V ] is an attention weight vector; here, the fusion label matrix Q (K) is the weighted sum of multi-view label indicators:

[0042] In step S3-1-3, in the parallel training of feature and label propagation, the optimization goal is to minimize the empirical expectation. The expression for minimizing the empirical expectation is:

[0043]

[0044] where f(x,y;Θ) is parameterized by Θ and consists of multi-view features and training labels y to feed the neural network, represents the actual data distribution, Indicates that x obeys

[0045] Step S3-1-4, obtain the fusion label matrix Q through the above steps (K) Then, the fusion representation H obtained in step S2 is combined (L) , the overall predicted label indicator matrix is ​​expressed as:

[0046]

[0047] Furthermore, in step S3, when feature and label propagation collaborative training is selected, the label propagation process and the feature propagation process are carried out collaboratively. The label propagation process includes the following steps:

[0048] In step S3-2-1, a parameterized model is constructed using a multi-layer perceptron (MLP) for label propagation. The calculation process is as follows:

[0049]

[0050] Where MLP(·) is a multilayer perceptron parameterized by Ω. When MLP(·) is simplified to a linear layer, the parameter Ω∈R C×C A learnable weight matrix shared by all multiple views, which indicates class-level correlation;

[0051] Step S3-2-2, the fusion representation H of the predicted labels obtained by the collaborative feature propagation process (L) , the overall predicted label indicator matrix is ​​expressed as:

[0052]

[0053] Step S3-2-3 calculates the overall training loss of the collaborative propagation of fusion features and labels. The specific expression is:

[0054]

[0055] Where n is the number of labeled samples, C is the number of categories, and Y ij is the element in row i and column j of the labeled label matrix, is the element in the i-th row and j-th column of the prediction label matrix;

[0056] Step S3-2-4, continue to iterate until the overall training loss or model converges.

[0057] Specifically, the way to obtain prediction labels through parallel training is the same as the way to obtain prediction labels through collaborative training, both of which are obtained by fusing the node feature matrix H (L) And the fusion label matrix Q (K) Make an overall prediction label indicator matrix Calculation; finally, the predicted label corresponding to each sample i is obtained.

[0058] It should be noted that the collaborative and parallel training method of the present invention is only for Q (K) In terms of computation, in parallel training, Q (K) Completely independent of H (L) The propagation process is calculated and Q is updated by random walk. (K) ; In the collaborative training method, Q (K) With H(L) The main collaborative point is that the loss function of the collaborative training process also includes Q (K) With H (L) .

[0059] Furthermore, in step S4, based on the predicted label matrix Calculate the predicted label of the i-th sample starting from the n+1th without label Get the predicted label set containing the predicted label for each sample Predicted Label The expression is:

[0060]

[0061] Where j represents The index corresponding to the maximum value of the Cth element in the i-th row;

[0062] That is, in In the Cth element of the i-th row (representing the possibility that the sample belongs to C different categories), find the index j corresponding to the element with the largest value. This index j is the predicted label of sample i Thus, the predicted label set containing the predicted label of each sample can be obtained

[0063] Using this multi-view graph neural network feature and label propagation algorithm, through the parallel or collaborative training mode of feature propagation and label propagation, the feature propagation and label propagation processes are optimized, which can effectively integrate information in multi-view data and improve the accuracy of label prediction. It is suitable for complex graph structure data processing tasks.

[0064] The present invention adopts the above technical solution. Compared with the existing technology, the beneficial effect of the present invention is as follows: an end-to-end graph convolutional network framework is proposed, which effectively integrates the feature propagation and label propagation representation of multi-view semi-supervised classification tasks. By introducing optimization-inspired objective functions and execution solution methods, a model-interpretable graph neural network transparent architecture is constructed. A lightweight label propagation component is introduced into the multi-view graph convolutional network to reduce the impact of feature noise in the original data space on model training. The algorithm can well integrate effective information in complex multi-view data, improve the accuracy of label prediction, and can be used in fields such as multi-view learning and graph neural networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments;

[0066] Figure 1This is a flow chart of a graph neural network feature and label propagation method for multi-view data according to the present invention;

[0067] Figure 2 This is a schematic diagram of the model structure used in an embodiment of the present invention. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0069] like Figure 1 As shown in FIG2 , the present invention discloses a graph neural network feature and label propagation method for multi-view data, comprising the following steps:

[0070] Step S1: Initialize the model optimization variables and evaluate the adjacency matrix of all graphs using the kernel method;

[0071] Step S2: Based on the node features in the multi-view data, the message passing mechanism of the graph neural network is used to propagate the node features in the multi-view data in the graph structure;

[0072] Step S3: Based on the choice of parallel or co-training of feature and label propagation, the label information is propagated in the graph structure through different multi-view label propagation rules;

[0073] Step S4: Combine the results of feature propagation and label propagation to predict the label of the test sample.

[0074] In this embodiment, the step S1 initializes the model optimization variables and uses the kernel method to evaluate the adjacency matrix of all graphs. The specific method is:

[0075] Assume a property graph in, is a node set, and Indicates that there are N samples; ε is the edge set, and |ε| = M indicates that there are M edges; X∈R N×D is the node feature matrix; A∈R N×N is the adjacency matrix between nodes;

[0076] Initialize model parameters α, β, and Ω, where α and β are learnable weight vectors for evaluating the importance of multi-view and label propagation, respectively, Θ (l,v) is the weight matrix connecting the l-1th layer and the lth layer in the graph neural network, and Ω is the parameter of the multilayer perceptron (MLP);

[0077] Computing graph adjacency matrix using Gaussian kernel method Among them A vThe calculation formula for (i,j) is:

[0078]

[0079] Among them, X v (i) and X v (j) are the eigenvectors of nodes i and j in the vth view, respectively, and σ is the bandwidth parameter of the Gaussian kernel.

[0080] In this embodiment, step S2 propagates the node features in the multi-view data in the graph structure using the message passing mechanism of the graph neural network according to the node features in the multi-view data. The specific method is as follows:

[0081] For a given graph and its associated multi-view data Without loss of generality, assume that the first n samples are labeled and n<<N. At the same time, the zero-filled label matrix is ​​represented as Y∈R N×C , where N represents the number of samples and C represents the number of categories. For each view v∈V, a graph neural network based on the V message passing mechanism is used to propagate node features. This process is expressed as:

[0082]

[0083] in, is a normalized adjacency matrix with self-loops added to the diagonal elements; the diagonal elements D v The calculation formula is: For any l∈[L] and v∈[V], H (l,v) is the output representation of the lth layer of the vth network. Initially, H (0,v) =X v ,Θ (l,v) is the weight matrix connecting the hidden representations of layer l-1 and layer l;

[0084] L-th output representation based on multi-view graph neural network Use the attention mechanism to adaptively adjust the weight of each view data, expressed as:

[0085]

[0086] Where α=[α1,…,α V ] is a learnable weight vector used to evaluate the importance of multiple views; here, it is used to represent the fusion representation H of the predicted label of the test sample (L) It is given by the following formula:

[0087]

[0088] Collect predicted labels H (L) And given the training label Y, the cross entropy loss is used to evaluate the difference between the predicted label and the true label, which is defined as:

[0089]

[0090] Where n is the number of labeled samples, C is the number of categories, and the output in the last network layer is aligned with the given label information, and the iteration continues until the cross entropy loss or model converges.

[0091] In this embodiment, step S3 propagates label information in the graph structure using different multi-view label propagation rules based on the selection of parallel or collaborative feature and label propagation training. The specific method is as follows:

[0092] When feature and label propagation are selected for parallel training, the label propagation process is independent of the feature propagation process; for a given graph and its associated multi-view data Without loss of generality, assume that the first n samples are labeled and n<<N. At the same time, the zero-filled label matrix is ​​represented as Y∈R N×C , where N represents the number of samples and C represents the number of categories. Specifically, the propagation rule of the random walk model for the vth label is as follows:

[0093]

[0094] Among them, Q (0,v) ∈R N×C is the initial distribution, γ v ∈R N×C represents the restart weight, which is used to control the restart probability of label propagation, Q (k,v) is the propagation matrix of the v-th view at the k-th step; is a normalized adjacency matrix with self-loops added to the diagonal elements; the diagonal elements D v The calculation formula is:

[0095] Next, the attention mechanism is used to normalize the label propagation results of multiple views in a parameter-free manner to obtain the fused label matrix Q (K) The calculation process is as follows:

[0096]

[0097] Where β=[β1,…,β V ] is an attention weight vector; here, the fusion label matrix Q (K) can be interpreted as a weighted sum of multi-view label indicators:

[0098]

[0099] In the parallel training of feature and label propagation, the above propagation method, combined with feature and label propagation, aims to minimize the following empirical expectation:

[0100]

[0101] where f(x,y;Θ) is parameterized by Θ and consists of multi-view features and training labels y to feed the neural network, represents the actual data distribution, Indicates that x obeys

[0102] The fusion label matrix Q is obtained through the above steps (K) Then, the fusion representation H obtained in step S2 is combined (L) , the overall predicted label indicator matrix is ​​expressed as:

[0103]

[0104] When feature and label propagation are selected for collaborative training, the label propagation process and the feature propagation process are carried out in coordination. Different from the above parameter-free label propagation model, a parameterized model is constructed using a multi-layer perceptron (MLP) for label propagation. The calculation process is as follows:

[0105]

[0106] Where MLP(·) is a multilayer perceptron parameterized by Ω. When MLP(·) is simplified to a linear layer, the parameter Ω∈R C×C can be interpreted as a learnable weight matrix shared by all multiple views, which indicates the class-level correlation;

[0107] Next, the fusion representation H of the predicted labels obtained by the collaborative feature propagation process (L) , the overall predicted label indicator matrix can be expressed as:

[0108]

[0109] Therefore, the overall training loss for collaborative propagation of fused features and labels is defined as:

[0110]

[0111] Where n is the number of labeled samples, C is the number of categories, and Y ij is the element in row i and column j of the labeled label matrix, It is the element in the i-th row and j-th column of the prediction label matrix, and iterates continuously until the overall training loss or model converges.

[0112] In this embodiment, step S4 combines the results of feature propagation and label propagation to predict the label of the test sample. The specific method is:

[0113] After getting the predicted label matrix Then, for the i-th sample starting from n+1, its predicted label It is obtained by the following formula:

[0114]

[0115] That is, in In the Cth element of the i-th row (representing the possibility that the sample belongs to C different categories), find the index j corresponding to the element with the largest value. This index j is the predicted label of sample i Thus, the predicted label set containing the predicted label of each sample can be obtained

[0116] Specifically, the way to obtain prediction labels through parallel training is the same as the way to obtain prediction labels through collaborative training, both of which are obtained by fusing the node feature matrix H (L) And the fusion label matrix Q (K) Make an overall prediction label indicator matrix Calculation; finally, the predicted label corresponding to each sample i is obtained.

[0117] It should be noted that the collaborative and parallel training method of the present invention is only for Q (K) In terms of computation, in parallel training, Q (K) Completely independent of H (L) The propagation process is calculated and Q is updated by random walk. (K) ; In the collaborative training method, Q (K) With H (L) The main collaborative point is that the loss function of the collaborative training process also includes Q (K) With H (L) .

[0118] The present invention adopts the above technical solution. Compared with the existing technology, the beneficial effect of the present invention is as follows: an end-to-end graph convolutional network framework is proposed, which effectively integrates the feature propagation and label propagation representation of multi-view semi-supervised classification tasks. By introducing optimization-inspired objective functions and execution solution methods, a model-interpretable graph neural network transparent architecture is constructed. A lightweight label propagation component is introduced into the multi-view graph convolutional network to reduce the impact of feature noise in the original data space on model training. The algorithm can well integrate effective information in complex multi-view data, improve the accuracy of label prediction, and can be used in fields such as multi-view learning and graph neural networks.

[0119] Obviously, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments. In the absence of conflict, the embodiments in the present application and the features in the embodiments can be combined with each other. The components of the embodiments of the present application generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of the present application is not intended to limit the scope of the application for protection, but merely represents the selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

Claims

1. A graph neural network feature and label propagation method for multi-view data, characterized by: It includes the following steps: Step S1, acquiring multi-view data to construct a graph network and initializing model parameters of a graph neural network suitable for extracting node features of multi-view data, and using a Gaussian kernel method to evaluate and calculate the adjacency matrix of the multi-view data; Step S2: Based on the node features in the multi-view data, the message passing mechanism of the graph neural network is used to propagate the node features in the multi-view data in the graph structure; Step S3: Based on the selection of parallel or collaborative feature and label propagation training, the label information is propagated in the graph structure using different multi-view label propagation rules to obtain the corresponding predicted label matrix; Step S4: Combine the results of feature propagation and label propagation to predict the label of the test sample.

2. The method for graph neural network feature and label propagation of multi-view data according to claim 1, characterized in that: Step S1 includes the following steps: Step S1-1, obtain multi-view data to build a graph network in, is a node set, and Indicates that there are N samples; ε is the edge set, and |ε| = M indicates that there are M edges; X∈R N×D is the node feature matrix, i.e., multi-view data; A∈R N×N is the adjacency matrix between nodes; Step S1-2, initialize model parameters α, β, and Ω, where α and β are learnable weight vectors for evaluating the importance of multi-view and label propagation, respectively, Θ (l,v) is the weight matrix connecting the l-1th layer and the lth layer in the graph neural network, and Ω is the parameter of the multilayer perceptron (MLP); Step S1-3, use the Gaussian kernel method to calculate the adjacency matrix of multi-view data Among them A v The calculation formula for (i,j) is: Among them, A v (i, j) represents the adjacency matrix between nodes i and j in the vth view; X v (i) and X v (j) are the eigenvectors of nodes i and j in the vth view, respectively, and σ is the bandwidth parameter of the Gaussian kernel.

3. The graph neural network feature and label propagation method for multi-view data according to claim 1, characterized in that: Step S2 includes the following steps: Step S2-1: label the first n samples of the multi-view data to obtain a zero-filled label matrix Y∈R N×C , where n<<N, N represents the number of samples, and C represents the number of categories; Step S2-2, propagating node features through a graph neural network based on the graph neural network message passing mechanism, is expressed as: Among them, H (l,v) is the output representation of the lth layer of the vth view, and l∈[L] and v∈[V], initially H (0,v) =X v ;H (l -1,v) is the output representation of the l-1th layer of the vth view; Θ (l,v) is the weight matrix connecting the hidden representations of the l-1th layer and the lth layer; σ is the bandwidth parameter of the Gaussian kernel; is the normalized adjacency matrix with self-loops added to the v-th view; the diagonal elements D of the v-th view v The calculation formula is: Step S2-3, L-th output representation based on graph neural network Use the attention mechanism to adaptively adjust the weight of each view data, expressed as: Where α=[α1,…,α V ] is a learnable weight vector used to evaluate the importance of multiple views; H (L) is the fusion node feature matrix representing the predicted label of the test sample; H (L) It is given by the following formula: Step S2-4, collect predicted labels H (L) and training labels Y, using cross entropy loss to evaluate the difference between predicted labels and true labels The calculation expression is: Where n is the number of labeled samples and C is the number of categories; In step S2-5, the output of the last network layer is aligned with the given label information, and the process is iterated until the cross entropy loss or model convergence occurs.

4. The method for graph neural network feature and label propagation of multi-view data according to claim 1, characterized in that: In step S3, when feature and label propagation are selected for parallel training, a label propagation process is performed independently of the feature propagation process. The label propagation process includes the following steps: Step S3-1-1, calculate and obtain the random walk model propagation matrix of the vth label; Among them, Q (0,v) ∈R N×C is the initial distribution, γ v ∈R N×C represents the restart weight, which is used to control the restart probability of label propagation, Q (k,v) is the propagation matrix of the v-th view at the k-th step; is a normalized adjacency matrix with self-loops added to the diagonal elements; the diagonal elements D v The calculation formula is: N represents the number of samples, and C represents the number of categories; Step S3-1-2, use the attention mechanism to normalize the label propagation results of multiple views in a parameter-free manner to obtain the fused label matrix Q (K) The calculation process is as follows: Where β=[β1,…,β V ] is an attention weight vector; fusion label matrix Q (K) is the weighted sum of multi-view label indicators: In step S3-1-3, in the parallel training of feature and label propagation, the optimization goal is to minimize the empirical expectation. The expression for minimizing the empirical expectation is: where f(x,y;Θ) is parameterized by Θ and consists of multi-view features and training labels y to feed the neural network, represents the actual data distribution, Indicates that x obeys Step S3-1-4, obtain the fusion label matrix Q through the above steps (K) Then, the fusion representation H obtained in step S2 is combined (L) , the overall predicted label indicator matrix is ​​expressed as:

5. The method for graph neural network feature and label propagation of multi-view data according to claim 1, characterized in that: In step S3, when feature and label propagation collaborative training is selected, the label propagation process and the feature propagation process are carried out collaboratively. The label propagation process includes the following steps: In step S3-2-1, a parameterized model is constructed using a multi-layer perceptron (MLP) for label propagation. The calculation process is as follows: Where MLP(·) is a multilayer perceptron parameterized by Ω. When MLP(·) is simplified to a linear layer, the parameter Ω∈R C×C A learnable weight matrix shared by all multiple views; Step S3-2-2, the fusion representation H of the predicted labels obtained by the collaborative feature propagation process (L) , the overall predicted label indicator matrix is ​​expressed as: Step S3-2-3 calculates the overall training loss of the collaborative propagation of fusion features and labels. The specific expression is: Where n is the number of labeled samples, C is the number of categories, and Y ij is the element in row i and column j of the labeled label matrix, is the element in the i-th row and j-th column of the prediction label matrix; Step S3-2-4, continue to iterate until the overall training loss or model converges.

6. The method for graph neural network feature and label propagation of multi-view data according to claim 1, characterized in that: In step S4, based on the predicted label matrix Calculate the predicted label of the i-th sample starting from the n+1th without label Get the predicted label set containing the predicted label for each sample Predicted Label The expression is: Among them, j represents The index of the element with the maximum value in the Cth element of the i-th row.

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