A Graph Neural Network Node Classification Application Model with Enhanced Node Association

Abstract

This study combines the present stage of the node classification problem with the fact that there is frequent noise in the graph structure of the graph convolution calculation, which can lead to the omission of some of the actual edge relations between nodes and the appearance of numerous isolated nodes. In this paper, we propose the graph neural network model ENode-GAT for improving the accuracy of small sample node classification using the method of external referencing of similar word nodes, combined with Graph Convolutional Neural Network (GCN), Graph Attention Network (GAT), and the early stop algorithm. In order to demonstrate the applicability of the model, this paper employs two distinct types of node datasets for its investigations. The first is the Cora dataset, which is widely used in node classification at this time, and the second is a small-sample Stock dataset created by Eastern Fortune’s stock prospectus of the Science and Technology Board (STB). The experimental results demonstrate that the ENode-GAT model proposed in this paper obtains 85.1% classification accuracy on the Cora dataset and 85.3% classification accuracy on the Stock dataset, with certain classification advantages. It also verifies the future applicability of the model to the fields of stock classification, tender document classification, news classification, and government announcement classification, among others.

1. Introduction

In recent years, with the advancements in computer technology, artificial intelligence, and other related industries, there has been a growing focus on graph neural network algorithms based on deep learning. The development stages of graph neural networks have led to unprecedented progress in the learning of graph structure. One of the most common tasks is semi-supervised node classification [1,2], in which many nodes lack corresponding labels, and the labels of unlabeled nodes must therefore be determined using the topological complementary information of the nodes in the graph [3]. Social network analysis, protein interoperation network analysis, recommender systems, inter-document classification, and inter-paper classification [4] are just a few of the fields in which GCN’s semi-supervised node classification has been widely applied. Node classification based on graph neural networks has yielded outstanding results in previous research, and these methods boil down to the aggregation of features using the graph structure (the corresponding adjacency matrix is indirectly understood as the presence of edge connections) [5]. Moreover, among the existing classification models for graph neural networks, the existing models are too homogeneous to simultaneously account for the types of problems each would bring under various conditions [6,7]. This paper proposes an innovative graph neural network node classification model named ENode-GAT. Through a review of relevant literature and materials, we enhance the interconnectivity between nodes by integrating the classification properties of the graph neural network model and the inherent connectivity of the graph structure formed by the dataset prior to performing convolution computation in the convolution layer.. It is also confirmed that this model can be applied in the future to duties such as the classification of papers, stocks, tender documents, and announcements issued by various local governments.

Unlike the conventional node classification model, this model reconstructs the graph structure prior to the calculation of convolution by introducing external nodes of similar terms. This process focuses on the effect of virtual edge relationships between nodes because a large number of nodes are in relative isolation and the graph structure required by the model is unconnected, which can have a significant impact on the experimental results [8,9]. Take, for instance, the graph structure of a citation network, in which the vertices represent individual papers, and the edges represent the citation relationships between the papers. Evidently, a paper cites another paper with the same topic, but a paper cannot cite all related papers, which would demonstrate that edge relations play a significant role in the node classification task. A node classification task appears to require a focus on the edge relationship between nodes, and it can be demonstrated that the model proposed in this paper has high application value.

In this paper, a model applicable to the node classification of graph neural networks is proposed to resolve the shortcomings of the existing node-level classification model of graph neural networks. This model employs a graph convolutional neural network coupled with a graph attention mechanism and incorporates an early stop algorithm when overfitting occurs to finish the classification model design, which is used to finish semi-supervised node classification in graph neural networks. The feasibility of the model is confirmed by the common dataset as well as the small sample dataset that is established. The following are the principal contributions of this paper:

• ENode-GAT is a node classification model for graph neural networks that improves the connections between nodes. This model is applicable to several emerging disciplines, including the classification of citation networks, stocks, tender documents, news, and government announcements;
• By introducing similar terms to external nodes, the graph structure at the input side of the model is reconstructed and a small sample classification dataset is generated;
• The model effectively combines a graph convolutional neural network, a graph attention mechanism, an early stop algorithm, and a Dropout algorithm, and uses the reconstructed graph structure as model input for classification experiments, which demonstrate that ENode-GAT has distinct advantages over other classification models.

2. Related Work

2.1. Graph Neural Network

Graph neural networks play a crucial role in the application of non-Euclidean data in deep learning. The use of graph structures interpretable on traditional Bayesian causal networks has attracted significant interest from readers [10]. A graph neural network is a model that employs graph data to perform end-to-end learning, thereby attaining an efficient combination of graph data and deep learning [11]. In the development phase of graph neural networks, Gori et al. [12] first proposed the concept of graph neural networks, and he summarized and designed a network model that can be used to process graph structures as well as graph data by drawing on neural network research. This resulted in the conception of graph neural networks, which laid the groundwork for their subsequent technological advancement. Scarselli et al. [13] subsequently summarized and elaborated the graph neural network models proposed at that time, and also prompted a large number of new models of graph neural networks to be widely proposed, and the application fields of graph neural networks began to expand gradually. Bruna et al. [14] were motivated by their predecessors to incorporate convolution into graph neural networks for the first time, which was an audacious endeavor and a challenge. However, it was demonstrated through experimental data, and the proposed model attained unprecedented success and garnered widespread interest from industry researchers. Subsequently, successive high-caliber articles were consistently distributed. Zhang et al. [15] reviewed deep learning techniques based on graph structures from semi-supervised and unsupervised perspectives, thereby strengthening the relevant theoretical foundation for such research. Bai et al. [16] provided a systematic review of graph neural networks based on graph structure, adequately introduced the spatial and spectral approaches to graph convolutional neural networks, and elucidated the role played by graph neural networks in a variety of classification applications as well as future directions. Ma et al. [17] conducted a comprehensive analysis of graph neural network models and their applications. In terms of spectral domain, spatial domain, and pooling, three aspects are described, after which a self-encoder model based on attention mechanism is used to experiment with graph neural networks and various methods for implementing graph neural networks are introduced. For the existing knowledge of graph neural networks, Wang et al. [18] provide a systematic elaboration of graph neural networks, a more comprehensive introduction to the specific application form of graph neural networks and the future development direction, as well as a detailed outlook for the future. Zhao et al. [19] provide a review of large-scale neural network systems, demonstrating that graph neural networks are effective and correspondingly explanatory for point classification, graph classification, and link prediction by combining graph broadcast operations with deep learning algorithms that involve both graph structure information and vertex attribute information during the learning process.

2.2. Classification of Graph Neural Network Nodes

With the rise of deep learning and the development of graph neural networks, the problem of node classification based on graph data has gained widespread application in the real world. Gradually, semi-supervised node classification of graph neural networks has emerged as a primary focus of research. In recent years, graph-based semi-supervised learning has been a popular area of study, where learning can be performed with a small number of labels by exploiting the graph or stream structure of the data. Li et al. [20] validated the benefits of semi-supervised learning of graph convolutional neural networks, trained the graph convolution using joint training and self-training methods, and achieved good classification results for semi-supervised classification of graph convolutional neural networks with fewer labels, thereby validating their proposed theory. Hu et al. [21] proposed a new deep hierarchical graph convolutional network (H-GCN) for semi-supervised node classification on a common node classification dataset. The proposed method outperformed the then-current state-of-the-art methods and improved the accuracy by 5.9% with a small sample size, which served as a good inspiration for the subsequent researchers. On the study of node classification, Zeng et al. [22] introduced the current characteristics of node classification in graph neural networks and proposed a node embedding enhancement model along with a comprehensive analysis of the graph structure of graph neural networks. By introducing the DSM model and mining the concealed connections between nodes, extensive experiments were conducted on a public dataset, and the results demonstrated that the proposed model was superior to the conventional model. At this juncture, Guo et al. [23] proposed an integrated model of Bagging to address the issue of unbalanced classification of graph neural network nodes. The primary classifier of the model is a graph convolutional neural network, and majority voting is used to complete the integration. Extensive experiments demonstrate that the model is capable of classifying nodes with an imbalance. Jang et al. [24] combined graph neural networks and natural language processing flawlessly to study an RF-EMF model of radio frequency electromagnetic field in order to complete the classification of scientific literature. They obtained promising experimental results and demonstrated the future applicability of the technology to text classification. Gong et al. [25] discovered that graph edge features contain important information, and in this paper, a new framework for partial graph neural networks is developed to enable them to conduct focused computations on graph edge features. In addition to graph node classification of multiple citation networks, the new model is also applied to full graph classification and regression of multiple molecular datasets. It is shown that the proposed model outperforms the then-advanced graph neural network classification models, demonstrating the significance of edge features in graph neural networks. Yang et al. [26] propose a novel model for node and edge feature learning in graph neural networks based on a hierarchical two-layer attention mechanism. They note that most of the state-of-the-art graph learning methods to date only focus on node features, ignoring rich relationship information contained in edge features. The authors demonstrate that node and edge embeddings can mutually enhance each other by training the model on different datasets and validating its feasibility. CensNet, the edge-node switching convolutional graph neural network, was proposed by Jiang et al. [27] for semi-supervised classification and regression of graph-structured data with node and edge features. CensNet is a general framework for graph embedding that embeds nodes and edges within a latent feature space. Experimental findings on realistic academic citation networks and quantum chemical maps demonstrate that the method performs at or near the cutting edge. Xiao et al. [28] proposed a hypergraph convolutional neural network called HGCNN for the classification of irregular citation network data at the node level. Unique advantages are provided by this model, which converts feature vectors of nodes into predicted labels and validates them on multiple datasets. Huang et al. [29] enhanced the classification of citation networks by employing the knowledge of graph neural network node classification and powerful deep learning techniques to achieve improved classification results. The classification of nodes for graph neural networks is successfully accomplished. Qiang et al. [30] classified the tender documents using the small sample classification of graph neural networks. This study makes extensive use of node classification knowledge and an effective graph neural network model to achieve the desired results. This experiment will serve as an invaluable resource for future researchers in this field. Xu et al. [31] effectively introduced graph neural networks to the financial industry and completed the classification of small sample nodes for graph neural networks, paving the way for graph neural networks to be implemented across different domains. Li et al. [32] effectively extended the graph neural network node classification problem to course learning, which is a significant breakthrough and a new application area for the future growth of graph neural networks.

ENode-GAT is a novel graph neural network node classification model introduced in this study. The model uses external similar word node referencing to strengthen the connections between nodes and reconstruct the graph structure, thereby achieving the classification task for nodes. After experimental validation on the Cora dataset and the self-developed Stock dataset, the ENode-GAT model exhibits accurate and efficient classification results. In the future, the model will be extended to several emerging fields, such as tender document classification, news classification, and government announcement classification, in order to improve the precision and dependability of this type of classification task.

3. Model Analysis

3.1. ENode-GAT Model

In this paper, we employ external node citation of similar terms, the GCN, the GAT, and the early stop algorithm fusion model for the semi-supervised classification of nodes. This experiment employs a small number of samples as the training set for the model in order to conclude the training and highlight the distinctive benefits of graph neural networks for small sample node classification. Several iterations are used to update the node representation layer-by-layer in order to predict unlabeled node labels, and the experimental results demonstrate that the model produces excellent classification results on some datasets. Figure 1 depicts the classification model for ENode-GAT.

3.1.1. Input Layer

After employing external node references in the graph convolution layer, the input layer consists of the process of inputting the multi-source heterogeneous graph structure. The graph structure information, which consists of node data and connections between nodes, is converted into an adjacency matrix and fed to the convolution layer for the initial convolution operation. Figure 2 depicts the operation diagram of external node reference.

In the structure depicted in Figure 2, nodes are converted into graph structures by establishing virtual edge connections between the central nodes based on their keywords. However, this graph structure is not stable, and there may be isolated nodes, which can reduce the classification accuracy of the model. To address this issue, we suggest introducing similar feature word nodes to reconstruct the structure of the graph and strengthen the association between the nodes. The experimental results indicate that this method can significantly enhance the precision of the classification.

3.1.2. Feature Extraction Layer

In this study, the feature extraction layer primarily employs the TF-IDF [33] formula to determine the association between each feature word. Equation (1) demonstrates the IDF formula.

$$IDF\left(x\right)=log\frac{N+1}{N_{\left(x\right)}+1}+1$$

(1)

In the equation above, $N$ represents the total number of documents in the corpus, and $N_{\left(\mathrm{x}\right)}$ represents the number of documents containing the corresponding computed words. Adding 1 to the numerator denominator prevents the numerator denominator from becoming 0 and influencing the calculation.

After calculating the word frequency and IDF value of each word, the TF-IDF value between each word is calculated using Equation (2). This allows the node text in the original graph structure to be converted into a sparse matrix of TF-IDF, which is subsequently used to represent the feature information of the nodes.

$$TF-IDF\left(x\right)=TF\left(x\right)\times IDF\left(x\right)$$

(2)

In the equation above, $TF$ represents the frequency of words and $IDF$ represents the inverse document frequency.

3.1.3. Graph Convolution Layer

The primary function of the graph convolution layer is to input the heterogeneous graph structure from the input layer and the feature matrix from the feature extraction layer into the graph convolution model for semi-supervised classification model training, and to output the corresponding convolution results at the end of the convolution layer.

The graph structure of the input layer can be understood as a combination of m nodes $V=\left\{v_1,v_2,v_3,\dots ,v_m\right\}$ and n edges $E=\left\{e_1,e_2,e_3,\dots ,e_n\right\}$ that have connections between nodes. In order to implement node classification using the graph convolutional neural network model, it is necessary to calculate the adjacency matrix, the degree matrix, and the Laplace matrix of the graph structure, as shown in Equations (3)–(5).

$$A=\left(a_{ij}\right)$$

(3)

$$D=diag\left({\displaystyle \sum }_{i\ne j}{a}_{ij}\right)$$

(4)

$$L=I_N-D^{-\frac{1}{2}}A{D}^{-\frac{1}{2}}$$

(5)

In the equation above, $A$ represents the adjacency matrix, $D$ represents the degree matrix, $L$ represents the Laplacian matrix, and $I_n$ is a unitary array of order $n$.

For model training, the computed data are fed into two convolutional layers of the GCN model and GAT model. Figure 3 depicts the schematic diagram of the GCN+GAT model.

The convolution of the two-layer graph convolution network is calculated as in Equations (6) and (7).

$$H^{\left(1\right)}=ReLU\left(\widehat{A}X{W}^{\left(1\right)}\right)$$

(6)

$$H^{\left(2\right)}=\hat{A}{H}^{\left(1\right)}{W}^{\left(2\right)}$$

(7)

In the above equation, $H^{\left(1\right)}$ denotes the output of the first layer and the input of the second layer; $H^{\left(2\right)}$ denotes the output of the second layer; $ReLU$ denotes the activation function; $X$ denotes the input of the first layer neural network; $W$ denotes the weight of the graph neural network; $W^{\left(1\right)}$ denotes the weight of the first layer neural network; $W^{\left(2\right)}$ denotes the weight of the second layer neural network. $\widehat{A}$ is a single-layer convolution operation, which can be interpreted as a convolution kernel, as shown in Equation (8).

$$\widehat{A}=\tilde{D}{ }^{-\frac{1}{2}} \tilde{A}\tilde{D}{ }^{-\frac{1}{2}}$$

(8)

The GAT module begins by calculating the attention factor using the obtained calculation data. We calculate the similarity coefficients of vertex $i$ is neighbors and itself, one by one, as illustrated by Equation (9).

$$e_{ij}=a(\left[W{h}_i\left|\right|W{h}_j]\right),j\in N_i$$

(9)

In the equation above, $h$ can be expressed as a series of vectors embedded within vectors. $W$ represents the dimensioning of the vertices’ features; $\left|\right|$ represents the stitching of the transformed features for vertices $i,j$; and $a()$ represents the mapping of the stitched high-dimensional features to a real number. The original attention factor is $e_{ij}$.

As shown in Equation (10), the initial attention coefficients are then subjected to a normalization operation to acquire the final attention coefficients $a_{ij}$.

$$a_{ij}=\frac{\exp \left(LeakyReLU\left(e_{ij}\right)\right)}{{{\displaystyle \sum }}_{k\in N_i}\exp \left(LeakyReLU\left(e_{ik}\right)\right)}$$

(10)

In the equation above, $LeakyReLU$ denotes the activation function; $a_{ij}$ denotes the final attention coefficient calculated.

Finally, the features are weighted and summed according to the calculated attention coefficients, as shown in Equation (11).

$$h_i^{l+1}=\sigma \left({\displaystyle \sum }_{j\in N_i}{a}_{ij}W{h}_j\right)$$

(11)

In the equation above, $W$ is the weight matrix of feature multiplication; $a_{ij}$ denotes the final attention coefficient calculated previously; $\sigma$ denotes the nonlinear activation function; $j\in N_i$ denotes traversing all nodes adjacent to $i$.

The early stop algorithm can effectively prevent the overfitting phenomenon that occurs during small sample training. The algorithm can be viewed as a process for terminating training by keeping track of the cycles in which cross-validation drops occur. In order to obtain the lowest generalization error with good cost performance and to demonstrate that there is no overfitting of the model during the process of small sample classification, the stop rounds are recorded. The specific steps of the algorithm are as follows.

Consider $E_{opt}\left(t\right)$ to be the optimal validation set error at iteration number $t$. The formula is represented by Equation (12).

$$E_{opt}\left(t\right)≔mi{n}_{t^{\prime }\le t}{E}_{va}\left(t^{\prime }\right)$$

(12)

Generalization loss is a written variable that describes the growth rate of the normalization error relative to its lowest value in the present iteration cycle, as shown in Equation (13).

$$GL\left(t\right)=100 · \left(\frac{E_{va}\left(t\right)}{E_{opt}\left(t\right)}-1\right)$$

(13)

A greater generalization loss represents the occurrence of overfitting phenomena, so it is a candidate criterion for terminating training. In other words, training ceases when the generalization loss exceeds a predetermined threshold.

The feature matrix is then convolved by two layers of GCN and GAT combined model convolution operations, and the final convolution result is output to the output layer in the form of a vector matrix.

3.1.4. Output Layer

This module applies the softmax function to normalize the results of the convolutional layer operation, resulting in the corresponding category labels of the m nodes. The final result module of this study model consists of the corresponding category labels for the nodes. The softmax function is represented by Equation (14).

$$Z=softmax\left(H^{\left(2\right)}\right)$$

(14)

where $H^{\left(2\right)}$ is the input to the output layer and $Z$ is the classification result of the model.

Labelling the samples allows the graph convolution model to evaluate the corresponding cross-entropy loss function for semi-supervised node classification as a whole. The main equation representation is shown by Equation (15).

$$L_{ENode-GAT}=-{\displaystyle \sum }_{l\in H_L}{\displaystyle \sum }_{f=1}^F{Y}_{lf}ln{Z}_{lf}$$

(15)

where $H_L$ is the index set with labelled nodes and the Adam [34] optimizer is used to train the neural network weights $W^{\left(1\right)}$ and $W^{\left(2\right)}$ by gradient descent. After a fixed number of model iterations, the softmax [35] normalization function is used to classify the convolutional results computed by the convolutional layer in order to derive the final labels of the nodes to be classified.

In this study, semi-supervised node classification is achieved through the properties of graph convolutional neural networks and the proposed model.

4. Data Preparation

4.1. Dataset Selection

This experiment selected the publicly available Cora [36] citation network dataset and the stock dataset constructed by crawling the stock prospectus of China Eastern Wealth Network’s STB by itself for the experimental dataset selection.

Cora dataset: At this time, the Cora dataset is one of the most popular and convincing datasets for graph neural networks in node classification problems. The Cora dataset was selected as the dataset to be compared with other models for the analysis experiments in order to incorporate the robust application capability and high classification accuracy of the proposed model. The Cora dataset is a citation network made up of papers on machine learning. Each paper was initially categorized into one of seven classes: case-based, genetic algorithms, neural networks, probabilistic methods, reinforcement learning, rule-based learning, and theory.

Table 1. Information about the Cora dataset.

Number of nodes	2708
Number of sides	5429
Initial feature dimension	1433
Classifying categories	7
Category	Case-based, genetic algorithms, neural networks, probabilistic methods reinforcement learning, rule-based learning, theoretical
Is there a class imbalance	No

displays the categorization and associated explanatory remarks for the dataset.

Stock dataset: The reason for selecting another dataset in this paper is to crawl the stock data from Oriental Wealth to create the stock dataset by itself, in order to demonstrate the broad application scope, strong applicability, and good future application value of the model proposed in this paper. This example also demonstrates that the same model-based strategy can be applied to comparable classification tasks. Document classification, government tendering document classification, news classification, government announcement classification at each prefecture level, etc., are all examples. The stock dataset used in this study comprises several Eastern Wealth Network Kotex stock prospectuses. For the category division, a total of eight categories were designed, including pharmaceutical manufacturing, computer technology, equipment manufacturing, material manufacturing, metal manufacturing, electrical machinery, environmental protection, and rubber-plastic manufacturing.

4.2. Dataset Processing

In the Cora dataset, each node represents a machine learning paper, each keyword in the paper represents a feature dimension, and the papers are connected through cross-references. However, there is a possibility that the citation relationship between papers will influence the classification results of the experiment. For instance, papers that belong to the same category but lack cross-references will not constitute a virtual connection between them, which will influence the experiment. Second, some papers may incorporate knowledge from other disciplines in order to expand and innovate the field. The inevitable citation linkage between papers from distinct categories can also influence the experiment. Consequently, this research employs the following method to bring about change. This paper introduces external nodes on fixed nodes to strengthen the connection between papers in the same category, i.e., to increase the number of edges between papers, since the number of nodes cannot be altered. Compared to the stock dataset used prior to this study [37], this study expands the original stock dataset by increasing the number of edges between firms through external referencing due to the increase in the number of stock firms in STB in recent years, which provides superior material to expand the dataset and can demonstrate the utility of the model to a significant degree.

Table 2. Information about the stock dataset prior to this study.

Number of nodes	273
Number of sides	1452
Initial feature dimension	368
Classifying categories	8
Category	Pharmaceutical manufacturing, computer technology, equipment manufacturing, material manufacturing, metal manufacturing, electrical machinery, environmental protection, rubber-plastic manufacturing.
Is there a class imbalance	No

displays the information from the stock dataset prior to this investigation. As shown in

Table 3. Information on the changes in the expanded Stock dataset.

Basic Information	Original Dataset after Expansion	ENode-GAT Model after the Introduction of External Nodes
Number of nodes	380	380
Number of sides	2152	4329
Initial feature dimension	368	368
Classifying categories	8	8
Category	Pharmaceutical manufacturing, computer technology, equipment manufacturing, material manufacturing, metal manufacturing, electrical machinery, environmental protection, rubber-plastic manufacturing.
Is there a class imbalance	No	No

, the stock nodes are added using external node references before and after the modification of the dataset information.

Using the natural language processing jieba word separation technique, the dataset’s initial keywords are extracted from the prospectus, and the initial feature dimensions of the stock dataset are determined through data cleansing. Following this, logic and operations are utilized to calculate the connections between nodes and establish the initial edge relationships. Lastly, the technique of utilizing external node references to strengthen the connection between nodes and expand the number of edges. Reconstructing the graph structure for classification input to the graph neural network.

5. Experiment and Result Analysis

5.1. Experimental Dataset Partitioning

In this study, in order to highlight the unique benefits of a graph neural network for small sample learning, the training set samples and test set samples of the experimental dataset are appropriately reduced, while the number of test samples is increased, so as to highlight the characteristic that a graph neural network can achieve good classification results when performing small sample learning.

Table 4. The division of the required dataset for the experiment.

Experimental Dataset	Training Set	Validation Set	Test Set
Cora dataset	200	300	1000
Stock dataset	40	40	300

displays the results of the division of the dataset.

5.2. Model Parameter Setting

To assure a detailed comparison test under the same conditions as the prior study, the following model parameters were set for both datasets.

In the experiments with the Cora dataset, the model parameters are set to 300 iterations, a learning rate of 0.005, a weight degradation of 5 × 10⁻⁴, and a packet capture rate of 0.5.

In the Stock dataset experiments, the model parameters are set to 300 iterations, 0.010 learning rate, 5 × 10⁻⁴ weight decay, and 0.5 packets per capture.

5.3. Analysis of the Over-Fitting Phenomenon

When classifying small samples with graph neural networks, overfitting is likely to occur due to the comparatively small number of samples in the training set. The principal manifestation is that the training set has a very high accuracy rate in the classification results, while the validation set has a very low validation result. This will impact the final accuracy of the experiment, so the Dropout layer and the early stop algorithm are added to the graph convolutional model in the experimental phase of this paper to immediately stop the graph neural network classification experiment when there is a clear overfitting phenomenon, and the result of the last iteration is used to complete the node classification.

Table 5. Classification accuracy under different scaling conditions.

	Split Ratio	1:2:5	2:3:3	1:4:3	6:1:1
ENode-GAT-Cora	Training Accuracy	0.8500	0.8350	0.8500	0.8258
	Validation Accuracy	0.8233	0.8600	0.8375	0.8800
	Test Accuracy	0.8510	0.8460	0.8480	0.8800
	Rounds	270	298	299	295
ENode-GAT-Stock	Split ratio	1:1:8	6:1:3	2:6:2	5:2:3
	Training Accuracy	0.9000	0.9045	0.8625	0.9000
	Validation Accuracy	0.8750	0.8750	0.8250	0.9000
	Test Accuracy	0.8533	0.8767	0.8682	0.8912
	Rounds	287	296	290	292

displays the classification results derived by the ENode-GAT model by dividing the dataset using various scales.

When experimenting with limited samples of graph neural networks, the division of arbitrary dataset proportions does not significantly affect the accuracy of the training set or the validation set, as shown in the table above. The various scaled divisions and respective stop rounds demonstrate that the introduction of the early stop algorithm plays a significant role in terminating the experiment prior to the occurrence of the overfitting phenomenon, thereby ensuring the accuracy of the experimental classification results. In addition, the results in the table above demonstrate that this method can effectively prevent the occurrence of overfitting and that graph neural networks have the unique ability to classify tiny sample nodes.

5.4. Model Comparison Analysis

This paper includes two experimental sections. The first section involves traditional supervised machine learning experiments, semi-supervised classification experiments based on the GCN model framework, semi-supervised classification experiments using recently proposed graph neural network models, and semi-supervised classification experiments using the enhanced model proposed in this paper, all performed on the Cora dataset. The classification results are compared and analyzed, as shown in

Table 6. Comparison of the classification results for the Cora dataset model.

Classification Method	Accuracy
SVM	71.0%
Logistic Regression	71.7%
GraphSAGE	79.5%
GCN	80.1%
PA-GCN [37]	81.2%
ENode-GAT	85.1%

. To provide a visual comparison of the accuracy trends for each model, bar graphs were created for the accuracy of each model, as shown in Figure 4. The second section highlights the application areas of the model proposed in this study for the Stock dataset and compares the ENode-GAT model proposed in this paper to existing models; the results are presented in

Table 7. Comparison of the classification results for the Stock dataset model.

Classification Method	Accuracy
SVM	77.7%
Logistic Regression	78.2%
Random Forest	77.9%
GCN	81.9%
PA-GCN	83.3%
ENode-GAT	85.3%

. As depicted in Figure 5, a visualization of the model’s accuracy was also created. In this comparison experiment, all of the previous experiment’s results were selected for comparison and validation, and the following are the results.

Based on the classification results in Table 6 and the visualization in Figure 4, it is possible to conclude that GCN outperforms conventional machine learning models when solving certain semi-supervised node classification problems. The unique benefits of the graph neural network model for graph structure issues are highlighted. According to the results in the table, it can be seen that the classification accuracy of the model proposed in this paper is 85.1%, which is excellent and indicates that the model proposed in this paper has unique advantages.

The six classification results for the Stock dataset are displayed in Table 7 and Figure 5, and it is evident that the model proposed in this paper has inherent advantages in managing this classification task. It exceeds the 2% classification precision of the previously proposed Stock model. This suggests that this model will be able to conduct similar classification tasks in the future and increase classification efficiency.

6. Conclusions

On the basis of graph neural network node classification, this paper proposes a graph convolutional neural network classification model based on the introduction of external nodes, with full consideration of the potential relationships between nodes and the corresponding graph structure information. Combining graph convolutional neural network, graph attention mechanism, early stop algorithm, and Dropout algorithm, the construction of the model is completed. Using the outcomes of classification on both datasets, this study concludes that this model has a significant classification advantage. In the public Cora dataset, the classification accuracy of the model proposed in this paper is 85.1%. In a limited sample of the Stock dataset, the proposed model produced accurate classification results with an accuracy of 85.3%. This result infers the possibility and potential benefits of applying this model to problems of a comparable nature in the future. Due to the two-sided character of the results, however, the application of the model may present certain difficulties and obstacles. The confidentiality of government and corporate information, for instance, can pose significant obstacles to data access. To circumvent these issues, classification must be accomplished in consultation with the relevant authorities and with their sanction. In accordance with legal and ethical restrictions, the model’s application area must be expanded to the greatest extent feasible. For me, this study is not an endpoint, but a good starting point. To assess the adaptability and practical value of the model across various disciplines, the Stock dataset will be expanded to include over 4000 stocks from the Chinese stock market, and additional enormous datasets will be selected for experiments. The model will be applied in diverse disciplines to demonstrate its validity and utility, as well as to emphasise its wide range of applications. Through this study, valuable insisghts and directions will be provided to researchers. In future work, this paper aims to pursue innovative approaches in emerging fields and fundamental algorithms related to graph neural network algorithms.