Three-dimensional object classification method of hypergraph wavelet neural network based on smooth spline

Abstract

The invention is suitable for the technical field of three-dimensional object classification, and provides a three-dimensional object classification method of a hypergraph wavelet neural network based on a smooth spline, and the method comprises the following steps: inputting and preprocessing data; constructing a hypergraph and scoring node importance; optimizing node features by applying a smooth spline; and carrying out multi-scale feature extraction, feature fusion and classification through a hypergraph wavelet neural network based on a smooth spline. According to the invention, by introducing a smooth spline method and a node importance scoring mechanism, the robustness of the model to noise is enhanced, and the smoothness of features is improved; the integrated feature fusion strategy effectively fuses different features, more meaningful information is captured, and node embedding representation with higher discrimination is obtained. Experimental results show that the model provided by the invention is superior to an existing 3D object classification model in classification accuracy, and verifies the effectiveness of the hypergraph wavelet neural network based on the smooth spline and the adopted fusion strategy.

Description

Technical Field

[0001] The present invention belongs to the technical field of three-dimensional object classification, and particularly relates to a three-dimensional object classification method based on a smooth spline hypergraph wavelet neural network. Background Art

[0002] Three-dimensional object classification, as a core topic in the fields of computer vision and graphics, is widely applied to scenarios such as robot navigation, autonomous driving, virtual reality, and medical diagnosis. Existing mainstream methods mainly include strategies based on voxels, point clouds, and multi-views. Among them, the multi-view method extracts features from 2D views taken from different angles and fuses them to achieve the recognition of 3D objects. However, multi-view feature fusion still faces challenges such as how to make full use of complementary information between different perspectives and reduce redundant noise.

[0003] Current 3D object classification methods, such as convolutional neural networks (CNNs) and graph neural networks (GNNs), mainly focus on pairwise relationships between nodes, that is, simple edge connections. When dealing with complex 3D data, these methods cannot fully capture high-order relationships and multi-modal associations in the data, resulting in insufficient understanding of the complex relationships between objects by the model. In 3D data, multiple objects may be associated with each other simultaneously to form high-order relationships, which contain rich structural information and are crucial for accurate classification. Ignoring high-order relationships may cause the model to fail to fully understand the overall structure and associations of objects. In addition, when fusing different feature representations, many existing methods often adopt simple splicing, averaging, or weighting methods, and fail to fully explore the complementarity and correlation between different features, resulting in the inability to make full use of the rich information in multi-modal data. Therefore, the hypergraph structure has received attention, and each hyper-edge of it can connect multiple nodes simultaneously, which is more conducive to capturing the collaborative relationships between multi-modalities and multi-views. Through hypergraph neural networks (HGNNs), researchers have achieved good results in tasks such as three-dimensional object classification, retrieval, and segmentation.

[0004] However, in a hypergraph environment, if there is noise in node features, the iterative propagation of high-order associations often amplifies the influence of noise, thereby affecting the performance of the model. At the same time, in existing hypergraph neural networks, the high-frequency oscillation features between nodes are also prone to overfitting and feature degradation problems. In addition, 3D data often has noise, missing values, or measurement errors. For example, point cloud data may generate noise due to sensor accuracy or environmental interference. Existing neural network models are sensitive to this noise, which may lead to inaccurate feature extraction and thus affect the classification performance. In view of the above problems, the present invention proposes a three-dimensional object classification method based on a smooth spline hypergraph wavelet neural network. Summary of the Invention

[0005] The object of the present invention is to provide a three-dimensional object classification method based on a smoothed spline hypergraph wavelet neural network, aiming to solve the problems raised in the above-mentioned background technology.

[0006] The object of the present invention is achieved through the following technical solutions: A three-dimensional object classification method based on a smoothed spline hypergraph wavelet neural network includes the following steps: Step 1: Data input and preprocessing; Two multi-view feature extraction methods, namely a multi-view convolutional neural network and a group-view convolutional neural network, are used to generate two sets of feature vectors with different dimensions for each 3D object. Step 2: Hypergraph construction and node importance scoring, including: Step 21: Hypergraph construction: A method combining far-point sampling and ball query is used to generate hyperedges. Step 22: Node importance scoring: Learnable weights are used to combine three scores, namely degree centrality, closeness centrality, and self-attention of nodes, to obtain the final importance score of each node. Step 3: Apply smoothed splines to optimize node features; The smoothed spline method is introduced into the hypergraph wavelet neural network to preprocess node features. The smoothed spline method realizes the smoothness and regularity of node features by minimizing the objective function; the natural cubic spline function is used for feature enhancement, and the high-dimensional features are reduced back to an appropriate dimension through a fully connected layer. Step 4: Perform multi-scale feature extraction, feature fusion, and classification through the hypergraph wavelet neural network based on smoothed splines; The hypergraph wavelet neural network includes a hypergraph wavelet convolutional layer, a feature fusion module based on the attention mechanism, and a classification layer; The unsmoothed features and the smoothed features are input into the hypergraph wavelet convolutional layer for feature extraction; the features obtained by extracting the unsmoothed features through the hypergraph wavelet neural network, the features obtained by extracting the smoothed features through the hypergraph wavelet neural network, and the smoothed features are fused in the feature fusion module based on the attention mechanism; finally, the fused feature vector is sent to the classification layer for the classification task of 3D objects.

[0007] Further, the specific process of Step 1 is as follows: Arrange 12 virtual cameras around the 3D object, rotate them once every 30°, generate 12 views at different angles in total, each camera captures a 2D view, convert the 3D point cloud data into the corresponding 2D image, and finally generate two groups of feature vectors with different dimensions for each 3D object, which come from the multi-view convolutional neural network and the group-view convolutional neural network respectively.

[0008] Further, the specific process of step 21 is as follows: Far point sampling: Randomly select a vertex from the vertex set as the initial point, calculate the distances between this vertex and all other vertices, select the vertex with the farthest distance as the next sampling point, and repeat the steps until the predetermined number of sampling points is reached; Ball query: For each sampling point, construct a sphere with a radius of R, and group all the vertices located within this sphere into a hyperedge; Finally, obtain the incidence matrix of the hypergraph H .

[0009] Further, in step 22, the final importance score of each node is calculated as follows: ) ; where , and are learnable parameters; is the self-attention score; is the degree centrality score; is the closeness centrality score.

[0010] Further, in step 3, the calculation formula of the objective function is as follows: ; where is the regularized residual sum of squares; is the number of nodes; is the index of the node; is the expected output; is the mapping function at the prediction output of the node; is the regularization coefficient, used to balance the two parts of the formula; is the dimension of the input feature; is the index of the feature dimension; is the j-th feature of the input feature; is the multi-dimensional input vector.

[0011] Further, in step 4, the formula of the hypergraph wavelet convolutional layer is as follows: Z = ([( )I-2 Xθ; Among them, Z is the feature after hypergraph convolution; and are the wavelet low-frequency approximation coefficient and the wavelet high-frequency detail coefficient respectively; I is the identity matrix; are the node degree matrix and the hyperedge degree matrix respectively, used for regularization; is the incidence matrix of the hypergraph; W is the identity matrix; is the transpose of the incidence matrix of the hypergraph; X is the input feature; θ is the learnable parameter.

[0012] Furthermore, the classification task is modeled as a regularization problem, including an empirical loss term and a regularization term. The final cost function in the framework is as follows: ; Among them, L represents the overall loss function; represents the cross-entropy loss function; represents the global smoothing regularization term; represents the local smoothing regularization term; and are the regularization coefficients, controlling the intensity of global smoothing and local sparsity respectively; Z represents the final output of the network; represents the feature matrix obtained from the features extracted from the last hypergraph wavelet convolution layer in the hypergraph wavelet neural network; For the empirical loss term , the cross-entropy error of all labeled examples is evaluated: ; Among them, is the index of the labeled sample; is the set of indices of the labeled vertices; is the class index; is the total number of classes; is the true label matrix; is the predicted probability of the model for the node; The term is used to promote the global smoothness of the labels on the hypergraph and is defined as follows: ; Among them, is the Laplacian matrix of the hypergraph; The term is the wavelet coefficient L1-norm regularization factor, used to improve the smoothness of the features extracted from the last hypergraph wavelet convolution layer, and is defined as follows: ; Among them, are wavelet coefficients.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: By introducing the smoothing spline method and the node importance scoring mechanism, the present invention enhances the robustness of the model to noise and improves the smoothness of features; the integrated feature fusion strategy effectively fuses different features, captures more meaningful information, and obtains a more discriminative node embedding representation. The present invention significantly improves the accuracy and robustness of 3D object classification, and has broad application prospects and practical value. Experimental results on two public 3D datasets, ModelNet40 and NTU, show that the model of the present invention is superior to existing 3D object classification models in terms of classification accuracy, verifying the effectiveness of the hypergraph wavelet neural network based on smoothing splines and the fusion strategy adopted. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flowchart of the method of the present invention.

[0015] Figure 2 is a data conversion flowchart of 3D objects.

[0016] Figure 3 is a node importance scoring graph.

[0017] Figure 4 is a network structure diagram of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0018] In order to have a clearer understanding of the technical features, objectives, and beneficial effects of the present invention, the technical solution of the present invention will be described in detail below, but it should not be construed as a limitation on the scope of implementation of the present invention.

[0019] The present invention performs multi-scale feature extraction based on the Hypergraph Wavelet Neural Network (HGWNN), uses wavelet transform to capture the local and global features of 3D objects at different scales, effectively models the high-order relationships between nodes, and enhances the richness and accuracy of feature representation. On this basis, a smoothing spline method is introduced to optimize the extracted node features, reduce noise interference through smoothing, and enhance the continuity and consistency of features, thereby improving the generalization ability and noise resistance of the model. To further improve the model performance, the present invention designs a node importance scoring mechanism dedicated to hypergraphs. This mechanism combines multi-dimensional scoring methods and adaptively evaluates and selects the nodes that are most important for the classification task based on the topological structure and node features of the hypergraph, ensuring that the information of key nodes is fully retained and utilized during the feature optimization process. In addition, an attention mechanism is used to fuse the smoothed features with the original unsmoothed features, dynamically adjust the weights of different features, and achieve effective integration of information, further enhancing the expression ability and classification performance of the network.

[0020] The following describes the specific implementation of the present invention in detail with specific embodiments.

[0021] An embodiment of the present invention provides a three-dimensional object classification method based on a hypergraph wavelet neural network with a smoothing spline, and its flowchart is as Figure 1 shown, and the method includes the following steps: Step 1: Data input and preprocessing; The input of the 3D object classification task is usually 3D point cloud data. A point cloud is a set of a large number of points distributed in three-dimensional space, and each point contains its coordinate information in space. Point cloud data can intuitively represent the shape and structure of an object and is an important data form in the field of 3D computer vision. However, there are the following challenges in directly processing the original point cloud data. Point cloud data usually contains thousands of points, has a high dimension, and a large computational complexity. The points in the point cloud do not have a fixed order, making it difficult to directly apply traditional Convolutional Neural Networks (CNNs). The actually acquired point cloud data may contain noise and irregular distributions, affecting the robustness of the model.

[0022] To more effectively capture the shape and structure information of 3D objects, the present invention adopts two advanced multi-view feature extraction methods, namely the Multi-View Convolutional Neural Network (MVCNN) and the Group-View Convolutional Neural Network (GVCNN). The overall data conversion process is as Figure 2 shown. By arranging virtual cameras around the object, multiple two-dimensional views of the object are captured from different angles. Specifically, 12 virtual cameras are arranged around the 3D object, and it rotates once every 30°, generating a total of 12 views at different angles. Each camera captures a two-dimensional view, converting the 3D point cloud data into the corresponding 2D image. These views retain the appearance information of the 3D object in different directions.

[0023] Through the above method, two sets of feature vectors with different dimensions are generated for each 3D object, which are from MVCNN and GVCNN respectively. These feature vectors will serve as the basis for subsequent hypergraph construction and feature fusion.

[0024] Step 2: Hypergraph construction and node importance scoring; (1) Hypergraph construction; To effectively model the high-order relationships between 3D objects, a hypergraph structure is adopted, where each vertex represents a 3D object and hyperedges connect multiple vertices, indicating the complex relationships between them. The present invention uses the method of farthest point sampling (FPS) combined with ball query to generate hyperedges. The specific process of farthest point sampling is as follows: randomly select a vertex from the vertex set as the initial point, calculate the distances between this vertex and all other vertices, select the vertex with the farthest distance as the next sampling point, and repeat the above steps until a predetermined number of sampling points is reached. This method can effectively capture the global distribution of the vertex set and ensure that the sampling points cover the entire data space. Then, for each sampling point obtained by farthest point sampling, a ball query operation is performed. The specific process is as follows: for each sampling point, a sphere with a radius of R is constructed, and all vertices located within this sphere are grouped into one hyperedge. This method can ensure that each hyperedge can effectively cover the local structure while maintaining the diversity and coverage between hyperedges. Through the above steps, the incidence matrix of the hypergraph is finally obtained. H .

[0025] (2) Node importance scoring; As Figure 3 shown, to further optimize feature selection, the present invention designs a node importance scoring mechanism, which combines the degree centrality, closeness centrality, and self-attention score of the node. The above three scores are combined using learnable weights to obtain the final importance score of each node. : ) ; where , and are learnable parameters; is the self-attention score; is the degree centrality score; is the closeness centrality score.

[0026] Step 3: Apply smoothing splines to optimize node features; In the Hypergraph Wavelet Neural Network (HGWNN), to reduce the sensitivity of the feature mapping function to noise and maintain feature smoothness, we introduce the smoothing spline method to preprocess the node features. In the first layer of the hypergraph wavelet convolution, after the node features undergo a linear transformation, the mapping function may be overly sensitive to noise due to noise or non-smoothness, and this sensitivity will be amplified during subsequent propagation and convolution processes, affecting the model performance. To alleviate this problem before training, the smoothing spline method is introduced to preprocess the node features, so that the mapping function already has better smoothness and noise resistance before entering the network. being overly sensitive to noise, and this sensitivity will be amplified during subsequent propagation and convolution processes, affecting the model performance. To alleviate this problem before training, the smoothing spline method is introduced to preprocess the node features, so that the mapping function already has better smoothness and noise resistance before entering the network.

[0027] The smoothing spline method realizes the smoothness and regularity of node features by minimizing an objective function. The specific formula of this objective function is as follows: ; where is the regularized sum of squared residuals; is the number of nodes; is the index of the node; is the desired output; is the mapping function is the predicted output of the mapping function at the node; is the regularization coefficient; is the dimension of the input features; is the index of the feature dimension; is the j-th feature of the input features; is the multi-dimensional input vector. By minimizing the objective function, it can be ensured that the data in each feature dimension has a certain degree of smoothness and regularity, thereby reducing the sensitivity to noise.

[0028] To enhance the discriminative ability of features and the robustness of the model, the present invention introduces a spline function to preprocess the node features. The feature vector of each node is mapped by the spline function to map the low-dimensional features to a high-dimensional space to capture more complex non-linear relationships. The natural cubic spline function is used for feature enhancement to ensure that the mapped features have good smoothness and noise resistance. However, since the spline function mapping will cause the expansion of the feature dimension, to avoid overfitting, after mapping, the high-dimensional features are reduced back to an appropriate dimension through a fully connected layer. At the same time, important base nodes are selected as the nodes of the spline function through a node importance scoring mechanism to reduce the computational complexity and avoid over-smoothing.

[0029] Step 4: Perform multi-scale feature extraction, feature fusion, and classification through SWHNN (Smoothing Spline-based Hypergraph Wavelet Neural Network); The hypergraph wavelet neural network includes a hypergraph wavelet convolution layer, a feature fusion module based on an attention mechanism, and a classification layer; As shown Figure 4 below, the unsmoothed features and the smoothed features are input into the hypergraph wavelet convolutional layer for feature extraction. The formula of the hypergraph wavelet convolutional layer is as follows: Z = ([( )I - 2 )Xθ; where Z is the feature after hypergraph convolution; are the wavelet low-frequency approximation coefficient and the wavelet high-frequency detail coefficient respectively; I is the identity matrix; are the node degree matrix and the hyperedge degree matrix respectively, which are used for regularization; is the incidence matrix of the hypergraph; W is the identity matrix; is the transpose of the incidence matrix of the hypergraph; X is the input feature; θ is the learnable parameter.

[0030] To make full use of the information from different feature extraction methods, the present invention designs a feature fusion module based on the attention mechanism. The features obtained by feature extraction of the unsmoothed features through the hypergraph wavelet neural network, the features obtained by feature extraction of the smoothed features through the hypergraph wavelet neural network, and the smoothed features are fused. The fused feature vector synthesizes the information from different feature extraction methods and improves the discriminative ability of the features.

[0031] Finally, the fused feature vector is fed into the classification layer for the classification task of 3D objects, and the classification layer finally outputs the classification result of the 3D objects.

[0032] The classification task in the present invention can be modeled as a regularization problem, which usually includes two parts: the empirical loss term and the regularization term. The final cost function in the framework is as follows: ; where, L represents the overall loss function; represents the cross-entropy loss function; represents the global smoothing regularization term; represents the local smoothing regularization term; and are the regularization coefficients, which control the intensity of global smoothing and local sparsity respectively; Z represents the final output of the network; represents the feature matrix obtained after wavelet transformation of the features extracted from the last hypergraph wavelet convolutional layer in the hypergraph wavelet neural network.

[0033] For the empirical loss term , the cross-entropy error of all labeled examples is evaluated: ; Among them, is the labeled sample index; is the index set of the marked vertices; is the class index; is the total number of classes; is the true label matrix; is the predicted probability of the model for the nodes; The term is used to promote the global smoothness of the labels on the hypergraph, and the detailed definition is as follows: ; Among them, is the Laplacian matrix of the hypergraph; The term is the wavelet coefficient L1-norm regularization factor, which is used to improve the smoothness of the features extracted from the last hypergraph wavelet convolutional layer, and the definition is as follows: ; Among them, is the wavelet coefficient.

[0034] Example 1: 3D object classification of ModelNet40 and NTU datasets; Two publicly available 3D datasets, ModelNet40 and NTU, are selected as the evaluation benchmarks. The ModelNet40 dataset contains 12,311 3D objects, which are divided into 40 common classes. According to the division, 9,843 objects are used for training and 2,468 objects are used for testing. The NTU dataset contains 2,012 3D shapes, distributed in 67 classes, including boats, bombs, books, cars, chairs, guitars, guns, hats, and helicopters, etc. There are two division methods for this dataset: the first division method uses 1,639 objects for training and 373 objects for testing; the second method evenly divides the dataset into two parts, with 50% for training and 50% for testing.

[0035] To effectively represent each 3D object, we adopt two advanced multi-view convolutional neural network feature extraction methods: MVCNN and GVCNN. These two methods are selected because they perform excellently in capturing rich 3D shape information. Specifically, these two methods arrange 12 virtual cameras at intervals of 30° around each 3D object, thus generating 12 views at different angles. Subsequently, the 4,096-dimensional MVCNN features and 2,048-dimensional GVCNN features of each object are extracted using their respective methods. After training the model using the above training set, the segmentation prediction of the final model is shown in the following table: Table 1 Classification results of ModelNet40 dataset Method Input Accuracy VoxNet Voxel 83.00% PC-GAN Voxel 92.70% PointNet Point Cloud 89.20% PointNet++ Point Cloud 90.70% MVCNN Multi-View 90.10% GVCNN Multi-View 93.10% tMHL Multi-View Hypergraph 96.20% HGNN Multi-View Hypergraph 96.70% CDMH Multi-View Hypergraph 96.76% HGAT Multi-View Hypergraph 97.10% iMHL Multi-View Hypergraph 97.16% TDHNN Multi-View Hypergraph 97.52% HGWNN Multi-View Hypergraph 97.81% SWHNN Multi-View Hypergraph 97.97% Table 2 Classification Results of NTU Dataset Dataset Split Method Input Accuracy HGNN Multi-View Hypergraph 84.20% CDMH Multi-View Hypergraph 84.45% MHGNN Multi-View Hypergraph 85.50% 1639 / 373 HGAT Multi-View Hypergraph 85.50% TDHNN Multi-View Hypergraph 86.05% HGWNN Multi-View Hypergraph 86.20% SWHNN Multi-View Hypergraph 86.59% MVCNN Multi-View 74.95% GVCNN Multi-View 74.40% MVCNN+SVM Multi-View 77.58% GVCNN+SVM Multi-View 78.90% 1006 / 1006 tMHL Multi-View Hypergraph 86.26% HGNN Multi-View Hypergraph 89.76% iMHL Multi-View Hypergraph 90.33% HGWNN Multi-View Hypergraph 91.30% Ours Multi-View Hypergraph 92.15% Experimental results on two publicly available 3D datasets, ModelNet40 and NTU, show that the model of the present invention is superior to existing 3D object classification models in terms of classification accuracy, which verifies the effectiveness of the hypergraph wavelet neural network based on smooth splines and the adopted fusion strategy.

[0036] The above is only the preferred embodiment of the present invention. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicability of the patent.

Claims

1. A three-dimensional object classification method based on a smoothed spline hypergraph wavelet neural network, characterized in that, It includes the following steps: Step 1: Data input and preprocessing; Two multi-view feature extraction methods, namely the multi-view convolutional neural network and the group-view convolutional neural network, are used to generate two sets of feature vectors with different dimensions for each 3D object; Step 2: Hypergraph construction and node importance scoring, including: Step 21: Hypergraph construction: A method combining far-point sampling and ball query is used to generate hyperedges; Step 22: Node importance scoring: The degree centrality, closeness centrality, and self-attention scores of the nodes are combined using learnable weights to obtain the final importance score for each node; Step 3: Apply smoothing splines to optimize node features; The smoothing spline method is introduced in the hypergraph wavelet neural network to preprocess the node features. The smoothing spline method realizes the smoothness and regularity of the node features by minimizing the objective function; the natural cubic spline function is used for feature enhancement, and the high-dimensional features are reduced back to an appropriate dimension through a fully connected layer; Step 4: Perform multi-scale feature extraction, feature fusion, and classification through the hypergraph wavelet neural network based on smoothing splines; The hypergraph wavelet neural network includes a hypergraph wavelet convolutional layer, a feature fusion module based on the attention mechanism, and a classification layer; The unsmoothed features and the smoothed features are input into the hypergraph wavelet convolutional layer for feature extraction; the features obtained by extracting the unsmoothed features through the hypergraph wavelet neural network, the features obtained by extracting the smoothed features through the hypergraph wavelet neural network, and the smoothed features are fused in the feature fusion module based on the attention mechanism; finally, the fused feature vector is fed into the classification layer for the classification task of 3D objects.

2. The three-dimensional object classification method of the hypergraph wavelet neural network based on smoothing splines according to claim 1, wherein, The specific process of the above Step 1 is as follows: Twelve virtual cameras are arranged around the 3D object and rotated once every 30°, generating a total of 12 views at different angles. Each camera captures a two-dimensional view, and the 3D point cloud data is converted into the corresponding 2D image. Finally, two sets of feature vectors with different dimensions are generated for each 3D object, which come from the multi-view convolutional neural network and the group-view convolutional neural network respectively.

3. The three-dimensional object classification method based on a smoothed spline hypergraph wavelet neural network according to claim 1, characterized in that, The specific process of the above Step 21 is as follows: Far-point sampling: Randomly select a vertex from the vertex set as the initial point, calculate the distances between this vertex and all other vertices, select the vertex with the farthest distance as the next sampling point, and repeat the steps until the predetermined number of sampling points is reached; Ball query: For each sampling point, construct a sphere with a radius of R, and group all the vertices located within this sphere into one hyperedge; Finally, the incidence matrix of the hypergraph is obtained H .

4. The three-dimensional object classification method of the hypergraph wavelet neural network based on smoothing splines according to claim 1, characterized in that In the said step 22, the final importance score of each node is calculated as follows: ) ； Among them, , and are learnable parameters; is the self-attention score; is the degree centrality score; is the closeness centrality score.

5. The three-dimensional object classification method of the hypergraph wavelet neural network based on smoothing splines according to claim 1, characterized in that, In the above Step 3, the calculation formula of the objective function is as follows: ； Among them, is the regularized sum of squared residuals; is the number of nodes; is the index of the node; is the expected output; is the mapping function is the predicted output at the node; is the regularization coefficient, used to balance the two parts of the formula; is the dimension of the input features; is the index of the feature dimension; is the j-th feature of the input features; is the multi-dimensional input vector.

6. The three-dimensional object classification method of the hypergraph wavelet neural network based on smoothing splines according to claim 3, characterized in that In the above Step 4, the formula of the hypergraph wavelet convolutional layer is as follows: Z=[( )I - 2 Xθ; Among them, Z is the feature after hypergraph convolution; and are the wavelet low-frequency approximation coefficient and the wavelet high-frequency detail coefficient respectively; I is the identity matrix; are the node degree matrix and the hyperedge degree matrix respectively, used for regularization; is the incidence matrix of the hypergraph; W is the identity matrix; is the transpose of the incidence matrix of the hypergraph; X is the input feature; θ is the learnable parameter.

7. The 3D object classification method based on a smoothed spline-based hypergraph wavelet neural network according to claim 1, wherein Model the classification task as a regularization problem, including an empirical loss term and a regularization term. The final cost function in the framework is as follows: ； Among them, L represents the overall loss function; represents the cross-entropy loss function; represents the global smoothing regularization term; represents the local smoothing regularization term; and are regularization coefficients that control the intensity of global smoothing and local sparsity respectively; Z represents the final output feature of the network; represents the feature matrix obtained from the features extracted from the last hypergraph wavelet convolutional layer in the hypergraph wavelet neural network; For the empirical loss term , the cross-entropy error for all labeled examples is evaluated: ； Among them, is the labeled sample index; is the index set of the marked vertices; is the class index; is the total number of classes; is the true label matrix; is the predicted probability of the model for the nodes; The item is used to promote the global smoothness of labels on the hypergraph and is defined as follows: ； Among them, is the Laplacian matrix of the hypergraph; The item is the L1 norm regularization factor of wavelet coefficients, which is used to improve the smoothness of the features extracted from the last-layer hypergraph wavelet convolution layer and is defined as follows: ； Among them, are wavelet coefficients.

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