Webpage classification method and system based on Delaunay triangulation double-graph neural network
By constructing shadow graphs through Delaunay triangulation and performing graph convolution operations, the problems of oversmoothing and over-crushing in existing graph neural networks for web page classification are solved, improving the model's expressive power and robustness, and achieving more accurate web page classification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING INST OF TECH
- Filing Date
- 2026-01-28
- Publication Date
- 2026-05-12
- Estimated Expiration
- Not applicable · inactive patent
AI Technical Summary
Existing graph neural networks suffer from oversmoothing and overcrowding issues in web page classification, making it difficult to effectively capture the global structure and deep semantic relationships of graphs. Furthermore, existing graph reconnection methods are prone to introducing spurious relationships, reducing the interpretability and robustness of the model.
We construct shadow graphs using Delaunay triangulation, and obtain local structural information and global relational information through graph convolution operations. We then fuse the information without destroying the semantics of the original graph structure to form a dual-graph structure for classification.
It effectively alleviates the problems of oversmoothing and over-crushing, improves the expressive power and information dissemination efficiency of web page classification, and enhances the robustness and classification effect of the model.
Smart Images
Figure CN122019908A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of network classification technology, specifically relating to a web page classification method and system based on Delaunay triangulation dual-graph neural network. Background Technology
[0002] Large websites contain massive amounts of web page data. Web page classification refers to the task of dividing web pages into different categories based on features such as content, theme, or link structure, thereby achieving systematic organization and management of web pages and supporting more accurate search recommendations or content distribution. However, due to the large scale of websites, the vast number of web pages, and the complex link relationships, Graph Neural Networks (GNNs) are typically used for automatic classification based on the links and content associations between web pages. But existing GNN models generally suffer from over-smoothing and over-squashing problems, making it difficult for the models to effectively capture the global structure and deep semantic relationships of the graph, thus hindering the further development and application of web page classification technology in real-world large-scale scenarios.
[0003] To alleviate the aforementioned problems, some existing technologies propose graph rewiring, which modifies the edge structure of the original graph to enhance information propagation capabilities. However, existing graph rewiring methods are mostly based on heuristic rules or random strategies, which can easily introduce spurious relationships, disrupt the semantic structure of the original graph, and reduce the interpretability and robustness of the model. Summary of the Invention
[0004] This invention addresses the shortcomings of existing technologies by providing a webpage classification method and system based on a Delaunay triangulation dual-graph neural network. This method effectively enhances the graph's expressive power and information dissemination efficiency, thereby improving webpage classification performance, without compromising the semantics of the original graph structure.
[0005] This invention provides the following technical solution:
[0006] Firstly, a webpage classification method based on a Delaunay triangulation bigraph neural network is provided, including: Step S1: Obtain the original graph and node features of the web page classification; the original graph includes several nodes and directed edges between the nodes, the nodes are web pages, the directed edges are hyperlinks between web pages, and the node features are web page content; Step S2: Reduce the dimensionality of the node features to two-dimensional space, and construct the shadow map using the Delaunay triangulation method; Step S3: Perform graph convolution operations on the original graph and the shadow graph respectively to obtain the local structure information and global relationship information of the nodes; Step S4: Fuse local structural information and global relational information to generate the final node representation, and classify all nodes based on the final node representation using a neural network classifier.
[0007] Optionally, step S2 specifically includes: Step S21: Use the UMAP algorithm or PCA algorithm to reduce the dimensionality of all node features to a two-dimensional space, obtain the two-dimensional coordinates of the nodes, and put them into the coordinate set. In, among them, Represents a node Two-dimensional coordinates, Indicates the number of nodes; Step S22: Construct an initial triangle that can enclose all elements of the coordinate set, place the initial triangle into the triangle set, and initialize the edge set of the shadow graph. ; Step S23: Iterate through each element of the coordinate set in sequence. Locate the current triangle containing the element from the set of triangles. If it is located inside the current triangle, then use the element... Divide the current triangle into three new triangles for each vertex, and then update the triangle set after performing local optimization on the new triangles through a flipping operation; Step S24: Remove all triangles in the triangle set that contain the vertices of the initial triangle, and extract the edges from the remaining triangle set to obtain the edge set of the shadow graph. The final shadow graph is formed by combining the node set of the original graph.
[0008] Optionally, in step S23, the triangle set is updated after locally optimizing the new triangle through a flipping operation, specifically as follows: Step e1: [The text appears to be incomplete and contains several grammatical errors and inconsistencies. A more accurate When creating new triangles for vertices, the edges generated are added to the queue to be optimized. The three newly created triangles are then added to the triangle set, and the elements are deleted. The current triangle in which it is located at the time of positioning; Step e2: Remove an edge from the queue to be optimized. Find the shared edge Two triangles and ; Step e3: Opposite edge Perform an empty circumcircle test. If the test fails, then the edge... Violating the circumcircle rule, flipping the edge. Generate edges This forms two optimized triangles. and And remove the original two triangles from the triangle set. and And adding triangles and If the test is successful, then... Satisfies the empty circumcircle criterion, so no processing is required for the triangle set; Step e4: Remove edges from the queue to be optimized If the queue to be optimized is empty, output the updated triangle set; if the queue to be optimized is not empty, return to step e2.
[0009] Optionally, in step S3, two graph neural networks are used to perform graph convolution operations on the original graph and the shadow graph, respectively.
[0010] Optionally, in step S4, the fusion of local structural information and global relational information includes: splicing and linearly transforming the local structural information and global relational information.
[0011] Secondly, a web page classification system based on a Delaunay triangulation bigraph neural network is provided, including: The data acquisition module is used to acquire the original graph and node features of web page classification; the original graph includes several nodes and directed edges between nodes, the nodes are web pages, the directed edges are hyperlinks between web pages, and the node features are web page content. The shadow graph construction module is used to reduce the dimensionality of node features to two-dimensional space and construct the shadow graph using the Delaunay triangulation method. The shadow graph and the original graph form a bi-graph structure. A two-level message passing module is used to perform graph convolution operations on the original graph and the shadow graph respectively to obtain the local structure information and global relationship information of the nodes; The dual-fusion module is used to fuse local structural information and global relational information to generate the final node representation; The classification module is used for the final node-based representation, employing a neural network classifier to classify all nodes.
[0012] Thirdly, a computer device is provided, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the steps of the web page classification method based on the Delaunay triangulation dual-graph neural network as described in any one of the first aspects.
[0013] Fourthly, a computer-readable storage medium is provided for storing a computer program; when executed by a processor, the computer program implements the steps of the web page classification method based on the Delaunay triangulation dual-graph neural network as described in any one of the first aspects.
[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention constructs a shadow graph through Delaunay triangulation, generating edges based on geometric structures to enhance global connectivity and avoid introducing spurious relationships. Furthermore, this invention performs graph convolution on both the original graph and the shadow graph, providing multi-view information propagation paths and improving expressive power. This effectively alleviates the oversmoothing and over-crushing problems caused by existing graph neural network technologies when processing graph-structured data for web page classification. The shadow graph effectively enhances graph expressive power and information propagation efficiency without destroying the semantics of the original graph structure, thereby improving web page classification results. Attached Figure Description
[0015] Figure 1 This is a flowchart of the web page classification method based on Delaunay triangulation dual-graph neural network of the present invention; Figure 2 This is a flowchart of the process for constructing the shadow graph according to the present invention; Figure 3 This is a block diagram of the web page classification system based on the Delaunay triangulation dual-graph neural network of the present invention. Detailed Implementation
[0016] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be used to limit the scope of protection of the present invention. It should be noted that the term "comprising" and any variations thereof in the specification, claims and the above-mentioned drawings of the present invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or devices.
[0017] Example 1 like Figure 1 As shown, a web page classification method based on a Delaunay triangulation bigraph neural network includes: Step S1: Obtain the original graph and node features of the web page classification.
[0018] The original graph consists of several nodes and directed edges between them. The nodes are web pages, and the directed edges are hyperlinks between web pages. The node features are the content of the web pages. The method of obtaining it can refer to existing technologies. Represents a set of nodes. Let be the edge set of the original graph.
[0019] Step S2: Reduce the dimensionality of the node features to two-dimensional space and construct the shadow map using the Delaunay triangulation method.
[0020] like Figure 2 As shown, step S2 specifically includes: Step S21: Use the UMAP algorithm or PCA algorithm to reduce the dimensionality of all node features to a two-dimensional space, obtain the two-dimensional coordinates of the nodes, and put them into the coordinate set. In, among them, Represents a node Two-dimensional coordinates, Indicates the number of nodes.
[0021] Step S22: Construct an initial triangle that can enclose all elements of the coordinate set, place the initial triangle into the triangle set, and initialize the edge set of the shadow graph. .
[0022] edge set of shadow graph Initially empty, the triangle set initially contains only the initial triangle.
[0023] Step S23: Iterate through each element of the coordinate set in sequence. Locate the current triangle containing the element from the set of triangles. If it is located inside the current triangle, then use the element... Divide the current triangle into three new triangles for each vertex, and then update the triangle set after performing local optimization on the new triangles through a flip operation.
[0024] Step S23 is as follows: Process each element of the coordinate set sequentially. Perform the following operations on it: Step S231: Locate the triangle. In the triangle set, find the triangle containing... The current triangle.
[0025] Step S232: When element If it is located inside the current triangle, then use the element... Divide the current triangle into three new triangles using vertices.
[0026] When element If an element is located inside the current triangle, it is considered to be outside the boundary. Located on the boundary, this is a degenerate phenomenon. In this case, assume the element If a point is located exactly on the side ab of a triangle, it cannot be divided into a single triangle as if the point were inside the triangle. Because the point is on the side, it is necessary to divide the two adjacent triangles (the two triangles sharing this side) together. Refer to existing technologies for specific division methods.
[0027] Step S233: Update the triangle set after locally optimizing the new triangle through a flip operation.
[0028] Step S233 specifically includes: Step e1: [The text appears to be incomplete and contains several grammatical errors and inconsistencies. A more accurate When creating new triangles for vertices, the edges generated are added to the queue to be optimized. The three newly created triangles are then added to the triangle set, and the elements are deleted. The current triangle in which it is located at the time of positioning; Step e2: Remove an edge from the queue to be optimized. Find the shared edge Two triangles and ; Step e3: Opposite edge Perform an empty circumcircle test. If the test fails, then the edge... Violating the circumcircle rule, flipping the edge. Generate edges This forms two optimized triangles. and And remove the original two triangles from the triangle set. and And adding triangles and If the test is successful, then... Satisfies the empty circumcircle criterion, so no processing is required for the triangle set; Step e4: Remove edges from the queue to be optimized If the queue to be optimized is empty, output the updated triangle set; if the queue to be optimized is not empty, return to step e2.
[0029] In this embodiment, we take edge ab as an example to illustrate a local optimization of the triangle set. Specifically, we take edge ab from the queue to be optimized and find the two triangles that share edge ab. and Perform an empty circumcircle test on side ab. If vertex d is located in triangle... If the edge ab is inside the circumcircle, then the empty circumcircle rule is violated. Flipping edge ab generates edge cd, forming two new triangles. and Add to the triangle set, then delete the original triangle. and If vertex d is located in triangle If the triangle is outside the circumcircle, then side ab satisfies the empty circumcircle criterion. Therefore, the original triangle... and Retain the edge ab in the triangle set; remove edge ab from the queue to be optimized, and perform an empty circumcircle test on the next edge of the queue to be optimized, until the queue to be optimized is empty, then the element... The insertion operation is complete, and the next element in the coordinate set is... Execute steps S231-S233 until all element insertion operations are completed.
[0030] Step S24: Remove all triangles in the triangle set that contain the vertices of the initial triangle, and extract the edges from the remaining triangle set to obtain the edge set of the shadow graph. The final shadow graph is formed by combining the node set of the original graph. The specific pseudocode is as follows:
[0031] The original graph and the shadow graph form a bi-graph structure. The original graph module preserves the original topology of the input graph, while the shadow graph module constructs a new graph structure based on node features. The original graph and the shadow graph have the same node set.
[0032] Step S3: Perform graph convolution operations on the original graph and the shadow graph respectively to obtain the local structure information and global relationship information of the nodes.
[0033] In this embodiment, two graph neural networks are used to perform graph convolution operations on the original graph and the shadow graph, respectively. Specifically, the first graph neural network is used to perform graph convolution operations on the original graph to learn the local structure information and explicit information of the nodes, and the second graph neural network is used to perform graph convolution operations on the shadow graph to learn the global relational information and implicit information of the nodes. The specific formula is as follows:
[0034]
[0035]
[0036]
[0037] in, For the first Layer shadow diagram The nodes in the representation, No. Original layer diagram The nodes in the representation, It is the adjacency matrix of the shadow graph. , It is the identity matrix. yes The angle matrix, It is the first Layer trainable weight matrix. , , Layer trainable weight matrix, It is the node feature matrix.
[0038] Step S4: Fuse local structural information and global relational information to generate the final node representation, and classify all nodes based on the final node representation using a neural network classifier.
[0039] Fusion involves both splicing and linear transformation. The fusion process adaptively integrates characteristic and structured information through node-to-node mapping. Specifically, nodes... The fusion is represented as follows:
[0040] in , It is a trainable fusion matrix. For concatenation operations (i.e., concatenating vectors or matrices), and It is a column vector consisting entirely of one elements.
[0041] By encoding the graph structure data through steps S3 and S4 to generate a node fusion representation, and then classifying the node fusion representation through a classification layer to output the web page classification result, the problem of oversmoothing and overcrushing caused by existing graph neural network technology in processing network-related graph structure data can be effectively alleviated, the classification effect can be improved, the model's expressive power and robustness can be enhanced, and it has good versatility and scalability.
[0042] Example 2 This paper provides a specific example of using the webpage classification method based on the Delaunay triangulation dual-graph neural network of this application for classification.
[0043] Simulation experiments were conducted on six benchmark datasets for web page classification tasks: Chameleon, Squirrel, Cornell, Texas, Wisconsin, and Actor. The Chameleon dataset contains information related to online communities; each node represents a web page, and each edge represents a hyperlink between two web pages. The main task of this dataset is to classify nodes based on their features and graph structure. The Squirrel dataset originates from a social network and contains web pages (nodes) and hyperlinks (edges). The goal of this dataset is to classify nodes based on their features and graph structure. The Cornell dataset is used to evaluate and test the performance of GNN models in node classification tasks; each node represents a web page. Each web page has a feature vector, typically represented using a bag-of-words model. The Texas dataset is specifically designed for node classification tasks, classifying web pages based on their content and link structure; each node represents a web page; each web page has a feature vector, typically represented by a bag-of-words model; each edge represents a hyperlink from one web page to another; and edges are directed, meaning hyperlinks have directionality. The Wisconsin dataset consists of academic papers or web pages, with each paper or web page considered a node and citations or links considered edges. This dataset contains nodes of five categories, each with a feature vector and label. The main task of this dataset is to classify nodes based on their features and graph structure. The Actor dataset contains multiple actor nodes and the relationships between actors. Each node (actor) has a corresponding feature vector and category label. The main task of this dataset is to classify nodes based on their features and graph structure.
[0044] Table 1 shows detailed statistics for the benchmark datasets of six web page classification tasks.
[0045] The method of the present invention is compared with the following methods.
[0046] GCN: A deep learning model specifically designed for processing graph-structured data. By defining graph convolution operations, it can effectively handle the irregularity and dynamism of graph data.
[0047] GAT: A neural network architecture based on graph-structured data that optimizes the shortcomings of traditional graph convolutional neural networks by introducing an attention mechanism.
[0048] GIN: A graph neural network architecture based on the Weisfeiler-Lehman test, designed to maximize graph representation capabilities and effectively distinguish non-isomorphic graphs.
[0049] SDRF: A graph reconnection method based on graph curvature, designed to alleviate the information overload problem during message passing. Its core objective is to eliminate edges that cause bottlenecks in information transmission by adjusting the graph's topology.
[0050] GTR: A graph structure optimization algorithm based on the Effective Resistance metric. It treats the edges in the graph as resistors and enhances the connectivity of the graph by minimizing the total effective resistance between pairs of nodes.
[0051] DR: A rewire method that completely skips the original graph topology and directly utilizes node features to construct a "Delaunay triangulation graph" in the embedding space.
[0052] CoBFormer: A graph neural network model that suppresses over-globalization by using "graph clustering + intra-cluster / inter-cluster double-layer attention" and integrates local GCN and global Transformer through collaborative training.
[0053] By comparing seven state-of-the-art methods, including graph neural networks, graph reconnection, and graphtransformer, on six datasets and using Micro-F1 and Macro-F1 evaluation metrics, the excellent classification performance and robustness of the web page classification method in this application are fully demonstrated, as shown in Tables 2 and 3.
[0054] Table 2 shows the experimental results of the Micro-F1 algorithm for the web page classification node task.
[0055] Table 3 shows the experimental results of the Macro-F1 webpage classification node task.
[0056] As shown in Tables 2 and 3, the webpage classification performance of this invention is the best, comprehensively outperforming all other models and achieving optimal results on all datasets. This invention effectively alleviates the oversmoothing and over-crushing problems caused by existing graph neural network techniques in processing graph-structured data for webpage classification by reducing node features and constructing a Delaunay triangulation shadow graph, employing a dual-graph structure for message passing and information fusion, thus improving the model's expressive power and robustness.
[0057] Example 3 like Figure 3 As shown, a web page classification system based on a Delaunay triangulation bigraph neural network includes: The data acquisition module is used to acquire the original graph and node features of web page classification; the original graph includes several nodes and directed edges between nodes, the nodes are web pages, the directed edges are hyperlinks between web pages, and the node features are web page content. The shadow graph construction module is used to reduce the dimensionality of node features to two-dimensional space and construct the shadow graph using the Delaunay triangulation method. The shadow graph and the original graph form a bi-graph structure. A two-level message passing module is used to perform graph convolution operations on the original graph and the shadow graph respectively to obtain the local structure information and global relationship information of the nodes; The dual-fusion module is used to fuse local structural information and global relational information to generate the final node representation; The classification module is used for the final node-based representation, employing a neural network classifier to classify all nodes.
[0058] For more specific details about the above modules, please refer to the corresponding content disclosed in the foregoing embodiments, which will not be repeated here.
[0059] Example 4 The present invention provides a computer device, including a processor and a memory; wherein, when the processor executes a computer program stored in the memory, it implements the steps of the above-described web page classification method based on Delaunay triangulation dual-graph neural network.
[0060] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.
[0061] Example 5 This invention provides a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, it implements the steps of the above-described web page classification method based on a Delaunay triangulation dual-graph neural network.
[0062] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.
[0063] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The systems, devices, and storage media disclosed in the embodiments are described simply because they correspond to the methods disclosed in the embodiments; relevant details can be found in the method section.
[0064] Those skilled in the art will clearly understand that the techniques in the embodiments of the present invention can be implemented using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.
[0065] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.
Claims
1. A webpage classification method based on a Delaunay triangulation bigraph neural network, characterized in that, include: Step S1: Obtain the original graph and node features of the web page classification; the original graph includes several nodes and directed edges between the nodes, the nodes are web pages, the directed edges are hyperlinks between web pages, and the node features are web page content; Step S2: Reduce the dimensionality of the node features to two-dimensional space, and construct the shadow map using the Delaunay triangulation method; Step S3: Perform graph convolution operations on the original graph and the shadow graph respectively to obtain the local structure information and global relationship information of the nodes; Step S4: Fuse local structural information and global relational information to generate the final node representation, and classify all nodes using a neural network classifier based on the final node representation.
2. The webpage classification method based on Delaunay triangulation dual-graph neural network according to claim 1, characterized in that, Step S2 specifically includes: Step S21: Use the UMAP algorithm or PCA algorithm to reduce the dimensionality of all node features to a two-dimensional space, obtain the two-dimensional coordinates of the nodes, and put them into the coordinate set. In, among them, Represents a node Two-dimensional coordinates, Indicates the number of nodes; Step S22: Construct an initial triangle that can enclose all elements of the coordinate set, place the initial triangle into the triangle set, and initialize the edge set of the shadow graph. ; Step S23: Iterate through each element of the coordinate set in sequence. Locate the current triangle containing the element from the set of triangles. If it is located inside the current triangle, then use the element... Divide the current triangle into three new triangles for each vertex, and update the triangle set after local optimization of the new triangles by flipping them. Step S24: Remove all triangles in the triangle set that contain the vertices of the initial triangle, and extract the edges from the remaining triangle set to obtain the edge set of the shadow graph. The final shadow graph is formed by combining the node set of the original graph.
3. The webpage classification method based on Delaunay triangulation dual-graph neural network according to claim 2, characterized in that, In step S23, the triangle set is updated after local optimization of the new triangle through a flipping operation, specifically as follows: Step e1: (The last part is incomplete and likely refers to a specific element or process.) When creating new triangles for vertices, the edges generated are added to the queue to be optimized. The three newly created triangles are then added to the triangle set, and the elements are deleted. The current triangle in which it is located at the time of positioning; Step e2: Remove an edge from the queue to be optimized. Find the shared edge Two triangles and ; Step e3: Opposite edge Perform an empty circumcircle test. If the test fails, then the edge... Violating the circumcircle rule, flipping the edge. Generate edges This forms two optimized triangles. and And remove the original two triangles from the triangle set. and And adding triangles and ; If the test is successful, then... Satisfies the empty circumcircle criterion, so no processing is required for the triangle set; Step e4: Remove edges from the queue to be optimized If the queue to be optimized is empty, output the updated triangle set; if the queue to be optimized is not empty, return to step e2.
4. The webpage classification method based on Delaunay triangulation dual-graph neural network according to claim 1, characterized in that, In step S3, two graph neural networks are used to perform graph convolution operations on the original graph and the shadow graph, respectively.
5. The webpage classification method based on Delaunay triangulation dual-graph neural network according to claim 1, characterized in that, In step S4, the local structural information and global relational information are fused, including splicing and linearly transforming the local structural information and global relational information.
6. A web page classification system based on a Delaunay triangulation bigraph neural network, characterized in that, include: The data acquisition module is used to acquire the original graph and node features of web page classification; the original graph includes several nodes and directed edges between nodes, the nodes are web pages, the directed edges are hyperlinks between web pages, and the node features are web page content. The shadow graph construction module is used to reduce the dimensionality of node features to two-dimensional space and construct the shadow graph using the Delaunay triangulation method. The shadow graph and the original graph form a bi-graph structure. A two-level message passing module is used to perform graph convolution operations on the original graph and the shadow graph respectively to obtain the local structure information and global relationship information of the nodes; The dual-fusion module is used to fuse local structural information and global relational information to generate the final node representation; The classification module is used for the final node-based representation, employing a neural network classifier to classify all nodes.
7. A computer device, characterized in that, It includes a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the steps of the web page classification method based on the Delaunay triangulation dual-graph neural network as described in any one of claims 1-5.
8. A computer-readable storage medium, characterized in that, Used to store computer programs; when executed by a processor, the computer programs implement the steps of the web page classification method based on the Delaunay triangulation dual-graph neural network as described in any one of claims 1-5.