Website traffic prediction method and system based on smoothing and sharpening fusion

Abstract

The present invention provides a website traffic prediction method and system based on the fusion of smoothing and sharpening. The method obtains the historical traffic data of the website and converts it into website traffic graph data. The node of the website traffic graph data represents a web page in the website, and the edge represents the link relationship between the web pages. The node attribute information and graph topology information are obtained from the website traffic graph data. Then, a website traffic prediction model is constructed based on a graph convolutional neural network. The node attribute information and graph topology information are used as the input of the model. The output of the model is compressed by a multi-layer perceptron to obtain a one-dimensional column vector formed by vertically stacking the prediction labels of each node, that is, the traffic prediction result of each web page. The model is composed of a plurality of graph convolutional layers stacked together. The sharpening operation is introduced in the graph convolutional layer, and the smoothing operation and the sharpening operation are combined, so that the model can fully extract the similar parts between the attribute information of the node and the neighboring nodes in the website traffic graph data, and can also extract the difference parts, thereby improving the prediction accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of website traffic prediction, and in particular relates to a website traffic prediction method and system based on the fusion of smoothing and sharpening. Background Art

[0002] With the booming development of the internet, more and more users are accessing and gathering information online. Website traffic, reflecting the number of page views over a period of time, is a key metric in online marketing research and plays a crucial role for both users and website administrators. As a new type of data in the internet era, website traffic data can be abstracted into a graph consisting of nodes and edges. Web pages on a website correspond to nodes in the graph, with node attributes consisting of the corresponding keywords and traffic volume. Links between web pages correspond to edges in the graph; that is, if there is a link between web pages, there is an edge connecting the two nodes. By inputting this graph data, abstracted from website traffic data, into a graph neural network, website traffic forecasting can be performed. Website traffic forecasting helps businesses obtain timely information on website growth, user retention, and marketing effectiveness, enabling faster strategic adjustments. It also helps businesses manage risks, promptly identify and troubleshoot anomalies, and avoid unnecessary losses. Therefore, website traffic forecasting can help businesses cope with increasingly fierce industry competition, and its accuracy is directly related to the efficiency and performance of enterprise management.

[0003] Classic graph neural networks (GNNs) are widely used in tasks such as traffic prediction, point cloud data processing, sentiment analysis, and spelling correction. The graph convolution operation of a classic GNN is equivalent to low-pass filtering and smoothing. It can extract low-frequency information from graph data, i.e., the similarities between the attribute information of a node and its neighbors, but has difficulty extracting high-frequency information from the graph data, i.e., the differences between the attribute information of a node and its neighbors. For website traffic data, both low-frequency and high-frequency information in the graph play an important role. Therefore, classic GNNs based on smoothing operations cannot achieve the desired results in website traffic prediction. Furthermore, classic GNNs are prone to oversmoothing when stacking multiple layers, causing node representations to converge after multiple graph convolution operations, resulting in the loss of original node attribute information and reduced prediction accuracy. Summary of the Invention

[0004] In view of the deficiencies in the prior art, the present invention aims to solve the technical problem of proposing a website traffic prediction method and system based on the fusion of smoothing and sharpening.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] In one aspect, the present invention provides a website traffic prediction method based on the fusion of smoothing and sharpening, comprising the following steps:

[0007] Step 1: Obtain the website's historical traffic data and convert it into website traffic graph data. The nodes in the website traffic graph data represent a web page on the website, and the edges represent the links between web pages. Obtain node attribute information and graph topology information from the website traffic graph data. The node attribute information includes the keywords and traffic corresponding to the web page.

[0008] Step 2: Build a website traffic prediction model based on a graph convolutional neural network. Node attribute information and graph topology information are used as input to the model. The model's output is compressed using a multi-layer perceptron into a one-dimensional column vector consisting of a vertical stack of predicted labels for each node, representing the traffic prediction results for each web page.

[0009] The website traffic prediction model is composed of multiple stacked graph convolutional layers. The node attribute information is used as the input matrix of the first graph convolutional layer. The graph topology information is multiplied by the input matrix of the first graph convolutional layer to obtain the output matrix of the first graph convolutional layer. The expression of the first graph convolutional layer is:

[0010] Z 1 =X (1)

[0011] H 1 =AZ 1 =AX (2)

[0012] Where Z 1 represents the input matrix of the first graph convolutional layer, X represents node attribute information, A represents graph topology information, and H 1 Represents the output matrix of the first graph convolutional layer;

[0013] Subtract the input matrix and output matrix of the first graph convolution layer, and use the learnable parameters of the first graph convolution layer to obtain the input matrix of the second graph convolution layer according to formula (3); then multiply the graph topology information with the input matrix of the second graph convolution layer to obtain the output matrix of the second graph convolution layer;

[0014] Z 2 =γ 1 (Z 1 -H 1 )=γ 1 (x-AX)=γ 1 (IA)X (3)

[0015] H 2 =AZ 2 =γ 1 (IA)AX (4)

[0016] Where, γ 1 represents the learnable parameters of the first graph convolutional layer, Z 2 represents the input matrix of the second graph convolutional layer, I represents the identity matrix, and H 2 represents the output matrix of the second graph convolutional layer;

[0017] Subtract the input matrix and output matrix of the i-1th graph convolution layer and use the learnable parameter γ of the i-1th graph convolution layer i-1 , according to formula (5), the input matrix of the i-th graph convolution layer is obtained; then the graph topology information is multiplied by the input matrix of the i-th graph convolution layer to obtain the output matrix of the i-th graph convolution layer;

[0018] Z i =γ i-1 (Z i-1 -H i-1 ) (5)

[0019] H i =AZ i (6)

[0020] Where Z i-1 , Z i Represents the input matrix of the i-1th and i-th graph convolutional layers, H i-1 、H i Represent the output matrices of the i-1th and i-th graph convolutional layers respectively;

[0021] Repeat the above operation until the learnable parameters converge to zero; then, according to formula (7), accumulate the output matrices of all graph convolutional layers to obtain the output P of the website traffic prediction model;

[0022]

[0023] Where Q represents the number of graph convolutional layers;

[0024] Finally, the output of the website traffic prediction model is compressed into a one-dimensional column vector formed by vertically stacking the prediction labels of each node through a multi-layer perceptron, which is the traffic prediction result of each web page.

[0025] Step 3: Use the website traffic graph data to train the website traffic prediction model to obtain a trained website traffic prediction model; then convert the historical traffic data of the website to be predicted into website traffic graph data, and input the node attribute information and topology information of the website traffic graph data into the trained website traffic prediction model to predict the website's traffic data.

[0026] On the other hand, the present invention also provides a website traffic prediction system, including a processor, a memory and a computer program; the processor is connected to the memory, and the computer program is stored in the memory. When the system is running, the processor executes the computer program in the memory, so that the system performs the above method.

[0027] The present invention also provides a computer-readable storage medium for storing computer instructions, which complete the above method when executed by a processor.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. The present invention targets a new type of data, website traffic data, by converting it into graph data and performing website traffic prediction through a graph neural network, which helps companies obtain important information such as user retention and marketing promotion effects. However, the graph convolution operation of the classic graph neural network is essentially equivalent to low-pass filtering and smoothing operations, making it difficult to capture the differences between the attribute information of nodes and neighboring nodes in the graph data. Therefore, the present invention improves the classic graph neural network by introducing a sharpening operation corresponding to the smoothing operation in the graph convolution layer, and combining the smoothing operation and the sharpening operation to form a graph convolution operation. This allows the website traffic prediction model to fully extract both the similarities and differences between the attribute information of nodes and neighboring nodes in the website traffic graph data, thereby more fully extracting information from the website traffic graph data and avoiding the loss of node attribute information. At the same time, it also alleviates the over-smoothing phenomenon that occurs in the classic graph neural network due to multi-layer stacking, thereby improving prediction accuracy.

[0030] 2. The website traffic prediction model of the present invention achieves adaptive training of model depth by introducing learnable parameters in the input matrix of each graph convolutional layer, and can therefore be applied to website traffic prediction of different scales. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0032] Specific embodiments of the present invention are given below in conjunction with the accompanying drawings. The specific embodiments are only used to further illustrate the present invention in detail and do not limit the scope of protection claimed in this patent application.

[0033] The present invention is a website traffic prediction method based on smoothing and sharpening fusion (hereinafter referred to as method, see Figure 1 ), including the following steps:

[0034] Step 1: Obtain the website's historical traffic data and convert it into website traffic graph data. A node in the website traffic graph data represents a web page on the website, and an edge represents a link between web pages. Obtain node attribute information X and graph topology information A from the website traffic graph data. The node attribute information includes the keywords and traffic corresponding to the web page.

[0035] The historical traffic data of a website refers to the traffic within a certain period of time. Assume that the website traffic graph data is G = (V, E), where V represents the node set and E represents the edge set. The node attribute information is recorded as X∈R N×F The graph topology information is represented by the adjacency matrix A∈R N×N Indicates, R represents the matrix space, N represents the number of nodes, and F represents the attribute dimension of the node;

[0036] Step 2: Build a website traffic prediction model based on a graph convolutional neural network. The node attribute information X and graph topology information A are used as inputs to the website traffic prediction model. The output of the website traffic prediction model is the representation of each node. The representation of each node is then compressed into a one-dimensional column vector using a multi-layer perceptron to obtain the traffic prediction results for each web page, i.e., the website traffic prediction results.

[0037] The website traffic prediction model is composed of multiple graph convolutional layers stacked together, with the node attribute information X as the input matrix Z of the first graph convolutional layer. 1 , Z 1 ∈R N×F , the graph topology information A is combined with the input matrix Z of the first graph convolutional layer 1 Multiply them together to get the output matrix H of the first graph convolution layer 1 ∈R N×F ; The expression of the first graph convolution layer is:

[0038] Z 1 =X (1)

[0039] H 1 =AZ 1 =AX (2)

[0040] Subtract the input matrix from the output matrix of the first graph convolution layer and use the learnable parameters γ of the first graph convolution layer 1 , according to formula (3), we get the input matrix Z of the second graph convolution layer 2 ; Then combine the graph topology information A with the input matrix Z of the second graph convolution layer 2 Multiply them together to get the output matrix H of the second graph convolution layer 2 ∈R N×F ;

[0041] Z 2 =γ 1 (Z1 -H 1 )=γ 1 (x-AX)=γ 1 (IA)X (3)

[0042] H 2 =AZ 2 =γ 1 (IA)AX (4)

[0043] Subtract the input matrix and output matrix of the i-1th graph convolution layer and use the learnable parameter γ of the i-1th graph convolution layer i-1 , according to formula (5), the input matrix of the i-th graph convolution layer is obtained, the purpose of which is to allow the next graph convolution layer to fully process the information that has not been processed by the previous graph convolution layer; then the graph topology information A is multiplied by the input matrix of the i-th graph convolution layer to obtain the output matrix of the i-th graph convolution layer i ;

[0044] Z i =γ i-1 (Z i-1 -H i-1 ) (5)

[0045] H i =AZ i (6)

[0046] Repeat the above operation until the learnable parameters converge to zero; then accumulate the output matrices of all graph convolutional layers according to formula (7) to obtain the output P∈R of the website traffic prediction model. N×F ;

[0047]

[0048] Where Q represents the number of graph convolutional layers;

[0049] Finally, the output P of the website traffic prediction model is compressed into The one-dimensional column vector formed by vertically stacking the predicted labels of each node, that is, the traffic prediction results of each web page;

[0050] In classic graph neural networks, the operation AX in formula (2) has been proven from the spectral domain to be equivalent to a low-pass filtering operation on the node attribute information X, that is, a smoothing operation, which is equivalent to an aggregation operation in the spatial domain, thereby aggregating the same attribute information for each node as its neighboring nodes; while (IA)X in formula (3) is equivalent to a sharpening operation on the node attribute information X, so the role of (IA)X is opposite to that of AX, which is equivalent to a high-pass filtering operation on the node attribute information X, with the purpose of retaining attribute information for each node that is different from its neighboring nodes, that is, capturing high-frequency information in the website traffic graph data;

[0051] With the stacking of graph convolutional layers, Equation (6) can be expanded as:

[0052]

[0053] Where, γ k represents the learnable parameters of the k-th graph convolutional layer, 1≤k≤i-1, represents the cumulative multiplication of the learnable parameters of the first i-1 graph convolutional layers;

[0054] Substituting formula (8) into formula (7), the output of the website traffic prediction model is:

[0055]

[0056] From formula (8), we can see that for the output matrix H of the i-th graph convolution layer i In general, the website traffic prediction model performs both smoothing and sharpening operations on the node attribute information X to avoid over-smoothing.

[0057] In addition, the website traffic prediction model can also be explained from the perspective of numerical optimization, which can be equivalent to the objective function of formula (10);

[0058]

[0059] In the formula, ||·|| F represents the Frobenius norm, δ represents the balance factor, tr(·) represents the trace of the matrix, and T represents the matrix transpose; is a feature fitting term, which is used to constrain the distance between the output P of the website traffic prediction model and the node attribute information X, so that the output P of the website traffic prediction model and the low-frequency information in the node attribute information X can maintain a similar relationship as much as possible; δtr(P T AP) is a graph regularization term used to constrain the distance between nodes and their neighboring nodes, so that each node representation maintains a dissimilarity relationship with its neighboring nodes as much as possible, in order to fully extract high-frequency information from the website traffic graph data;

[0060] The smoothing and sharpening operations of the website traffic prediction model correspond to the feature fitting term and graph regularization term in the objective function, respectively. Compared with the classic graph neural network, the website traffic prediction model of the present invention can better capture the low-frequency and high-frequency information in the website traffic graph data, and solves the problems of the classic graph neural network's inability to capture high-frequency information in the graph and the tendency to over-smoothing.

[0061] Step 3: Use the website traffic graph data in step 1 to train the website traffic prediction model to obtain a trained website traffic prediction model; then convert the historical traffic data of the website to be predicted into website traffic graph data, and input the node attribute information and topology information of the website traffic graph data into the trained website traffic prediction model to predict the website traffic data;

[0062] The website traffic prediction model is trained using a semi-supervised learning method. Some nodes or edges of the website traffic graph data in step 1 are randomly selected for training. 60% of the nodes corresponding to each label are used as the training set, 20% of the nodes are used as the validation set, and 20% of the nodes are used as the test set. During the training process, the training loss is calculated using the loss function of formula (10).

[0063]

[0064] Among them, c represents the interval corresponding to web page traffic, such as 10-20 times / month, and K represents the maximum traffic interval. represents the probability of predicting the traffic of web page j to be c; y jc represents the real label of web page j, that is, its real traffic data.

[0065] The multi-layer perceptron is composed of multiple hidden layers and is used to compress the output P of the website traffic prediction model into a one-dimensional column vector.

[0066] The present invention also provides a website traffic prediction system comprising a processor, a memory, and a computer program. The processor is connected to the memory, and the computer program is stored in the memory. When the system is running, the processor executes the computer program in the memory, causing the system to perform the above-mentioned method. The processor can be a central processing unit (CPU), or other general-purpose processor, a digital signal processor (DSP), a field-programmable gate array (FPGA), etc. The memory can be a read-only memory (ROM) or a random access memory (RAM), and provides instructions and data to the processor. During implementation, each step of the above-mentioned method can be completed by hardware integrated logic circuits in the processor or by software instructions.

[0067] The present invention also provides a computer-readable storage medium for storing computer instructions, which complete the above method when executed by a processor.

[0068] Simulation test:

[0069] Website traffic prediction is essentially a node classification task, and its prediction result is the interval corresponding to the web page traffic. In order to verify the effectiveness of the website traffic prediction model of the present invention, the node classification task is performed on six real data sets using the website traffic prediction model and the graph neural network model commonly used in the prior art. The parameter settings of the model on each real data set are shown in Table 1.

[0070] Table 1 Parameter settings of the model on various real datasets

[0071]

[0072] Table 2 shows the accuracy statistics of various models for node classification tasks on six real-world datasets. The co-fitness of each dataset is calculated as the ratio of connected nodes with the same label to all nodes. A higher co-fitness indicates greater importance of low-frequency information in the graph data, while a lower co-fitness (i.e., higher hetero-fitness) indicates greater importance of high-frequency information in the graph data. Cora, Pubmed, and Citeseer are three commonly used citation network datasets. Nodes represent papers, node attributes represent keywords corresponding to the papers, and edges between nodes represent citation relationships between papers. Nodes tend to connect to nodes with the same or similar attributes. These datasets describe citation relationships between papers of the same or similar categories and exhibit high co-fitness. Both the Chameleon and Squirrel datasets describe the relationships between entries in Wikipedia. Nodes represent entries, and node attributes are the corresponding keywords and average monthly pageviews. The data distribution shows high heterogeneity, meaning that entries with different attributes are more likely to be linked. The Actor dataset describes the relationships between movie actors. Nodes represent actors, and node attributes are their characteristics. Edges between nodes represent two actors appearing in the same Wikipedia article. The Chameleon, Squirrel, and Actor datasets all exhibit heterogeneous graph data, where high-frequency information is more important.

[0073] Table 2 Accuracy statistics of each model for node classification tasks on real datasets

[0074]

[0075] As shown in Table 2, all models achieved high accuracy on the Cora, Pubmed, and Citeseer datasets, but their accuracy varied significantly on the Chameleon, Squirrel, and Actor datasets. Specifically, GCN is a classic graph neural network used to process graph data. The graph convolution operations in each GCN layer are equivalent to smoothing operations. When multiple GCN layers are stacked, severe oversmoothing occurs. Furthermore, while GCN can fully extract low-frequency information from the original graph structure data, it cannot extract dissimilar attribute information. Therefore, GCN is difficult to use for processing highly heterogeneous graph data. GAT improves model accuracy by modifying propagation weights based on GCN, but oversmoothing still occurs. GCNII and APPNP introduce an initial residual mechanism based on GCN to effectively mitigate oversmoothing. JKNet accumulates the results of each layer in the model as the final output, aggregating node information from different neighborhoods to mitigate oversmoothing. However, the five models, GCN, GAT, GCNII, APPNP and JKNet, essentially follow the homogametic assumption and have high accuracy for homogametic graph data, but are difficult to apply to graph data with high heterogameticity.

[0076] Geom-GCN, GPR-GNN, FAGCN, and H2GCN are all models designed for graph data with high heterogeneity, and can effectively capture high-frequency information in the original graph data. Geom-GCN uses three different network embedding strategies to obtain high-frequency information in the graph; GPR-GNN obtains high-frequency information in the graph by assigning learnable weights to different neighborhoods, and stipulating that learnable weights can be negative; FAGCN allows negative values ​​in the adjacency matrix to represent the dissimilarity of the attributes between node pairs, thereby capturing high-frequency information in the graph; H2GCN assumes that in a highly heterogeneous network, second-order neighbors are more likely to maintain similarity with the central node's attributes than first-order neighbors. Therefore, H2GCN proposes to splice second-order information with central node information to improve model performance.

[0077] The website traffic prediction model of the present invention has achieved a high accuracy rate on the data sets Chameleon, Squirrel and Actor, especially the accuracy rate on the data sets Chameleon and Squirrel has been greatly improved. The reason is that in heterogeneous graph data, nodes usually tend to be connected to nodes with different attribute information, and the difference between the node attribute information is more important, that is, the high-frequency information in the graph data is more important. The website traffic prediction model of the present invention integrates the two operations of smoothing and sharpening, so that the output of the model can capture the similarities between the node attribute information in the graph data through the smoothing operation, and can capture the differences between the node attribute information in the graph data through the sharpening operation, thereby being able to more fully extract the information in the graph data. In addition, the website traffic prediction model of the present method solves the technical problem that the classical graph neural network is prone to over-smoothing by introducing the sharpening operation.

[0078] To further verify the prediction effect of the website traffic prediction model of the present invention, under the same experimental conditions, the website traffic prediction model of the present invention and two existing classic graph neural network models were used to perform node classification tasks on a synthetic dataset. The classification performance of each model was tested, and the statistical results shown in Table 3 were obtained.

[0079] Table 3 Accuracy of the model in node classification task in synthetic dataset

[0080] Φ -1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1 <![CDATA[GPR-GNN [8] ]]> 96.25 95.50 93.75 86.50 81.25 86.25 92.25 96.75 97.00 <![CDATA[GCNII [4] ]]> 50.50 64.00 57.50 73.50 77.00 91.00 91.00 97.25 96.75 This method 98.50 97.25 96.50 91.50 88.50 91.50 96.00 97.00 97.00

[0081] Here, Φ represents the assortativity of the synthetic dataset. Φ = -1 means that the synthetic dataset has a high degree of heteroassortativity; Φ = 1 means that the synthetic dataset has a high degree of assortativity.

[0082] As shown in Table 3, compared to the GCNII model, which was designed to mitigate oversmoothing in graph neural networks, the website traffic prediction model of the present invention achieves higher accuracy on datasets with high heterogeneity. Compared to the GPR-GNN model, which was designed for heterogeneous graph data, the website traffic prediction model of the present invention has significantly improved accuracy. In summary, the website traffic prediction model of the present invention has high accuracy for heterogeneous graph data, effectively extracting high-frequency information from website traffic graph data and ensuring the accuracy of prediction results.

[0083] The sources of various common classic graph neural network models in the existing technology are:

[0084] [1]Thomas N.Kipf and Max Welling.Semi-supervised classification withgraph convolutional networks.In ICLR,2017.

[0085] [2]PetarVelickovic,GuillemCucurull,ArantxaCasanova,AdrianaRomero,Pietro Liò,and Yoshua Bengio.Graph attention networks.In ICLR,2018.

[0086] [3]William L.Hamilton,Zhitao Ying,and Jure Leskovec.Inductiverepresentation learning on large graphs.In NIPS,pages 1024–1034,2017.

[0087] [4]Ming Chen,Zhewei Wei,Zengfeng Huang,Bolin Ding,and YaliangLi.Simple and deep graph convolutional networks.In ICML,pages 1725–1735,2020.

[0088] [5]Johannes Klicpera,Aleksandar Bojchevski,and Stephan Günnemann.Predict then propagate:Graph neural networks meetpersonalizedpagerank.In ICLR,2019.

[0089] [6]Keyulu Xu,Chengtao Li,Yonglong Tian,Tomohiro Sonobe,Ken-ichiKawarabayashi,and Stefanie Jegelka.Representation learning on graphs withjumping knowledge networks.In ICML,pages 5449–5458,2018.

[0090] [7]Hongbin Pei, Bingzhe Wei, Kevin Chen-Chuan Chang, Yu Lei, and BoYang. Geom-gcn: Geometric graph convolutional networks. In ICLR, 2020.

[0091] [8] Eli Chien, Jianhao Peng, Pan Li, and Olgica Milenkovic. Adaptiveuniversal generalized pagerank graph neural network. In ICLR, 2021.

[0092] [9] Deyu Bo, Xiao Wang, Chuan Shi, and Huawei Shen. Beyond low-frequency information in graph convolutional networks. pages 3950–3957, 2021.

[0093] Any matters not described in the present invention are applicable to the prior art.

Claims

1. A website traffic prediction method based on the fusion of smoothing and sharpening, characterized in that: The method comprises the following steps: Step 1: Obtain the website's historical traffic data and convert it into website traffic graph data. The nodes in the website traffic graph data represent a web page on the website, and the edges represent the links between web pages. Obtain node attribute information and graph topology information from the website traffic graph data. The node attribute information includes the keywords and traffic corresponding to the web page. Step 2: Build a website traffic prediction model based on a graph convolutional neural network. Node attribute information and graph topology information are used as input to the model. The output of the model is compressed using a multi-layer perceptron to obtain a one-dimensional column vector consisting of vertically stacked predicted labels for each node, i.e., the traffic prediction results for each web page. The website traffic prediction model is composed of multiple stacked graph convolutional layers. The node attribute information is used as the input matrix of the first graph convolutional layer. The graph topology information is multiplied by the input matrix of the first graph convolutional layer to obtain the output matrix of the first graph convolutional layer. The expression of the first graph convolutional layer is: Z 1 =X (1)H 1 =THE 1 =AX (2) Where Z 1 represents the input matrix of the first graph convolutional layer, X represents node attribute information, A represents graph topology information, and H 1 Represents the output matrix of the first graph convolutional layer; Subtract the input matrix and output matrix of the first graph convolution layer, and use the learnable parameters of the first graph convolution layer to obtain the input matrix of the second graph convolution layer according to formula (3); then multiply the graph topology information with the input matrix of the second graph convolution layer to obtain the output matrix of the second graph convolution layer; z 2 =γ 1 (Z 1 -H 1 )=γ 1 (X-AX)=γ 1 (I-A)X (3) H 2 =THE 2 =γ 1 (IA)AX (4) Where, γ 1 represents the learnable parameters of the first graph convolutional layer, Z 2 represents the input matrix of the second graph convolutional layer, I represents the identity matrix, and H 2 Represents the output matrix of the second graph convolutional layer; Subtract the input matrix and output matrix of the i-1th graph convolution layer and use the learnable parameter γ of the i-1th graph convolution layer i-1 , according to formula (5), the input matrix of the i-th graph convolution layer is obtained; then the graph topology information is multiplied by the input matrix of the i-th graph convolution layer to obtain the output matrix of the i-th graph convolution layer; WITH i =γ i-1 (WITH i-1 -H i-1 ) (5) H i =THE i (6) Where Z i-1 、Z i Represents the input matrix of the i-1th and i-th graph convolutional layers, H i-1 、H i Represent the output matrices of the i-1th and i-th graph convolutional layers respectively; Repeat the above operation until the learnable parameters converge to zero; then, according to formula (7), accumulate the output matrices of all graph convolutional layers to obtain the output P of the website traffic prediction model; Where Q represents the number of graph convolutional layers; Finally, the output of the website traffic prediction model is compressed by a multi-layer perceptron to obtain a one-dimensional column vector formed by vertically stacking the prediction labels of each node, which is the traffic prediction result of each web page; Step 3: Use the website traffic graph data to train the website traffic prediction model to obtain a trained website traffic prediction model; then convert the historical traffic data of the website to be predicted into website traffic graph data, and input the node attribute information and topology information of the website traffic graph data into the trained website traffic prediction model to predict the website traffic data; From the perspective of numerical optimization, the website traffic prediction model is equivalent to the objective function of formula (10); In the formula, ||·|| F represents the Frobenius norm, δ represents the balance factor, tr(·) represents the trace of the matrix, and T represents the matrix transpose; is a feature fitting term, which is used to constrain the distance between the output of the website traffic prediction model and the node attribute information, corresponding to the smoothing operation of the website traffic prediction model; δtr(P T AP) is a graph regularization term used to constrain the distance between a node and its neighboring nodes, corresponding to the sharpening operation of the website traffic prediction model.

2. The website traffic prediction method based on smoothing and sharpening fusion according to claim 1 is characterized in that: The multi-layer perceptron is composed of multiple hidden layers and is used to compress the output P of the website traffic prediction model into a one-dimensional column vector.

3. A website traffic prediction system, characterized in that: The system comprises a processor, a memory and a computer program; the processor is connected to the memory, the computer program is stored in the memory, and when the system is running, the processor executes the computer program in the memory, so that the system executes any one of the methods described in claims 1 to 2.

4. A computer-readable storage medium for storing computer instructions; characterized in that: When the computer instructions are executed by a processor, the method according to any one of claims 1 to 2 is completed.

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