Marine transportation network link prediction method based on graph convolutional neural network

Abstract

The invention provides a marine transportation network link prediction method based on a graph convolutional neural network, and the method comprises the steps: firstly decomposing and extracting trend features and seasonal features between marine transportation network nodes based on historical monthly OD connection number data, and extracting multi-scale periodic features through Fourier transform; then, inputting the trend feature, the seasonal feature and the multi-scale periodic feature of each node in the previous quarter into a mixed model of a graph convolutional neural network (GCN) and a long short-term memory network (LSTM) by combining the node topological features of the marine transportation network topological structure; a marine transportation network link prediction space-time fusion model is constructed through the spatial dependency relationship and the time evolution law, and model training is carried out; and finally, predicting the link existence probability of each node pair in the current month by using the marine transportation network link prediction space-time fusion model. The method aims at providing a scientific basis for dynamic management and optimization of the marine transportation network.

Description

Technical Field

[0001] The present invention relates to the field of intelligent prediction of geographic information, and in particular to a method for predicting shipping network links based on a graph convolutional neural network. Background Art

[0002] In the process of global shipping network operation and management, historical shipping data is often used for the analysis and prediction of international shipping links. However, the data sparsity and dynamic evolution problems in actual business scenarios make it difficult for traditional methods to accurately capture the characteristics of complex network relationships. For example, in the 2020-2022 global shipping network analysis (January 2020-December 2022), port node pairs with complete biweekly granularity shipping records only account for 38% of the total potential links. When real-time shipping data is missing, existing methods often rely on single-dimensional indicators (such as trade volume, port throughput, route density, etc.) to infer links. However, international trade activities have the characteristics of multi-factor coupling, and it is difficult to effectively characterize the potential correlation characteristics of shipping network nodes by relying solely on individual economic indicators. How to construct a dynamic spatiotemporal coupling model to achieve the transportation intensity prediction of shipping links between national nodes in the coordinated optimization of historical shipping data time series feature mining and network structure modeling has become a key technical bottleneck for improving the reliability of global shipping network planning. Summary of the invention

[0003] The purpose of the present invention is to fill the gap in the existing technology and provide a method for predicting shipping network links based on graph convolutional neural networks. The basic idea of ​​the method of the present invention is: based on the historical monthly OD (Origin-Destination) connection quantity data, the trend characteristics, seasonal characteristics, multi-scale periodic characteristics and topological characteristics of the shipping links are mined; when link prediction is required, the graph convolutional network and the long short-term memory network are used to fuse the above four types of features, predict the shipping network links and generate the future link distribution map, which provides a scientific basis for the dynamic management and optimization of the shipping network.

[0004] Based on the above basic ideas, the technical solution provided by the present invention to achieve the purpose of the invention is a method for predicting shipping network links based on graph convolutional neural networks: first, based on the historical monthly OD connection quantity data, the trend characteristics and seasonal characteristics between shipping network nodes are decomposed and extracted, and their multi-scale periodic characteristics are extracted through Fourier transform; then, the trend characteristics, seasonal characteristics and multi-scale periodic characteristics of each node in the previous quarter are combined with the node topology characteristics of the shipping network topological structure, and input into a hybrid model of graph convolutional neural network (GCN) and long short-term memory network (LSTM), and a spatiotemporal fusion model for shipping network link prediction is constructed through spatial dependency and time evolution law, and the model is trained; finally, the spatiotemporal fusion model for shipping network link prediction is used to predict the link existence probability of each node pair in the current month.

[0005] Based on the historical monthly OD connection quantity data, the trend characteristics and seasonal characteristics between the shipping network nodes are decomposed and extracted, and the multi-scale periodic characteristics are extracted through Fourier transform. The steps are as follows:

[0006] Step 1: Data input and hyperparameter initialization

[0007] Input historical continuous monthly OD connection sequence data Y o→d (t), where t is the time series subscript, the time series length is N, o is the departure country, and d is the destination country; the number of nodes in the input OD connection sequence data is Num; the hyperparameters of the present invention are initialized as shown in Table 1;

[0008] Table 1 Hyperparameters involved in the present invention

[0009]

[0010] Step 2: Extracting shipping links and shipping nodes features

[0011] Step 2.1 Extraction of trend features of shipping links

[0012] In order to extract the trend characteristics of the maritime OD link and reflect the changes in the general trend of maritime trade, this step adopts the local weighted regression method; o→d For any OD pair time column in (t), perform the following steps:

[0013] According to formula (1), the weights of the neighborhood points in the sequence are calculated; based on the weighted least squares method, according to formula (2), the local linear model is fitted; according to formula (3), the local coefficient β is solved by minimizing the weighted residual sum of squares 0 With β 1 ; According to formula (4), calculate the trend characteristics;

[0014]

[0015] y i =β 0 +β 1 t i +ε i (2)

[0016]

[0017] T o→d (t) = β 0 +β 1 t (4)

[0018] In formulas (1)-(4), t represents the month for which the trend characteristics are to be calculated; t i indicates other months in the time series; h T is the bandwidth of the trend term; ω(t,t i ) indicates that when trend characteristics are calculated, t i The weight at target t; β 0 With β 1 is the local coefficient to be fitted; ε i represents the residual; y i Represents Y o→d (t) t in the sequence i The corresponding value; T o→d (t) represents the trend characteristics of month t;

[0019] Step 2.2 Link seasonality feature extraction

[0020] In order to extract the seasonal characteristics of the maritime OD link and reflect the seasonal changes of maritime trade, Y o→d For any OD pair time column in (t), perform the following steps:

[0021] According to formula (5), the trend characteristics are removed from the original time series to obtain the detrended time series Y′ o→d (t); Divide the detrended sequence into subsequences D according to K-month periods k (t); for each subsequence D k (t), according to formula (6), calculate the weights of the neighborhood points in the sequence; based on the weighted least squares method, according to formula (7), fit the local linear model; according to formula (8), solve the local coefficient β by minimizing the weighted residual sum of squares 0 ′ and β 1 ′; According to formula (9), calculate its seasonal characteristics; According to formula (10), perform centralization to ensure that its mean is 0;

[0022] Y′ o→d (t) = Y o→d (t)-T o→d (t) (5)

[0023]

[0024] D k (t i )=β 0 ′+β 1 't i +ε i ′ (7)

[0025]

[0026] S(t)=β 0 ′+β 1 ′t (9)

[0027]

[0028] In formulas (5)-(10), t represents the month for which the seasonal characteristics are to be calculated; t i indicates other months in the time series; h T is the seasonal bandwidth; ω(t,t i ) indicates that when calculating seasonal characteristics, t i The weight at target t; β 0 ′ and β 1 ′ is the local coefficient to be fitted; ε i ′ represents the residual; D k (t i ) means D k (t) t in the sequence i The corresponding value; S(t) represents the seasonal characteristics of month t; S o→d (t) represents the seasonal characteristics after decentralization, hereinafter referred to as seasonal characteristics; K is the number of cycles;

[0029] Step 2.3 Multi-scale periodic feature extraction of shipping links

[0030] In order to extract the multi-scale periodic characteristics of maritime OD links and reflect the seasonal changes of maritime trade, Y o→d For any OD pair time column in (t), perform the following steps:

[0031] According to formula (11), the monthly OD connection time series data Y o→d (t) Perform discrete Fourier transform to convert it from time domain to frequency domain to obtain Y o→d (f); each Y o→d (f) contains amplitude and phase information, and selects the first m frequency components Y with the largest amplitude o→d (f 1 ),Y o→d (f 2 ),…,Yo→d (f M ), and their corresponding amplitudes are |Y o→d (f 1 )|,|Y o→d (f 2 )|,…,|Y o→d (f M )|, and their corresponding phases are φ(f 1 ),φ(f 2 ),…,φ(f M ) ; Reconstruct the time series signal through inverse Fourier transform to obtain the simulation signal Select Simulation Signal As a multi-scale periodic feature of the link;

[0032]

[0033] In formulas (11)-(12), N represents the total length of the time series; M represents the total number of selected frequency components; t represents the time point; f represents the frequency; e represents the natural logarithm; π represents the circumference of a circle; i represents the imaginary unit, and i satisfies 2 =-1.

[0034] The steps of extracting the node topology features of the shipping network topology structure are:

[0035] In order to extract the topological characteristics of the shipping network nodes and reflect important information such as node importance and connectivity, according to formula (13), the OD connection data at time t is expressed as the adjacency matrix A o→d (t); For each node v, calculate its out-degree, in-degree and degree according to formulas (14), (15) and (16);

[0036]

[0037] In formulas (13)-(16), Num is the total number of nodes, v and j both represent the node subscripts, and t is the month subscript.

[0038] The steps of constructing a spatiotemporal fusion model for shipping network link prediction through spatial dependency and time evolution law are as follows:

[0039] Step 3.1 Input feature definition

[0040] For any month t, the feature vector x of each node v v =[outdeg(v,t),indeg(v,t),deg(v,t)]; the time series Y of each link o→d The eigenvector of (t) is According to formula (17), the edge attribute is mapped to the weight value w through a linear transformationi,j ;

[0041] w i,j =σ(W a a o→d ) (17)

[0042] In formula (17), is a learnable weight matrix, σ is a sigmoid activation function used to map weight values ​​to the (0,1) interval, i is the subscript of node o, and j is the subscript of node d;

[0043] Step 3.2 Graph Convolutional Network Construction

[0044] In order to effectively extract the graph data characteristics of the shipping network, a graph convolutional network is used in this step. According to formula (18), L graph convolution operations are performed to update the node features to obtain the node feature matrix H L ; Node feature matrix after graph convolution layer processing It can well reflect the position and connection relationship of nodes in the graph structure;

[0045]

[0046] In formula (18), is the set of neighboring nodes of node i, is the learnable weight matrix of layer l, d g is the hidden layer dimension, is the node feature vector of the lth layer;

[0047] Step 3.3 Long short-term memory neural network construction

[0048] The node feature sequence H of the first three months t-1 ,H t-2 ,H t-3 As input, according to formula (19), the LSTM network is used to model the time series of node features; the final output of LSTM is the feature representation of each node in the fourth month Can reflect the dynamic changes of nodes in the time dimension;

[0049]

[0050] in, is the hidden state at time t; is the cell state; d l is the hidden layer dimension in LSTM; the specific update formula of LSTM is shown in equations (20)-(25);

[0051]

[0052] Formula (19)-(25), W i , W f , W g , W o and U i , U f , U g , U o is the learnable weight matrix of LSTM, b i , b f , b g , b o is the bias term, σ is the Sigmoid activation function, tanh is the hyperbolic tangent activation function, and ⊙ represents element-by-element multiplication;

[0053] Step 3.4 Prediction of shipping network links

[0054] In order to convert the LSTM prediction results into actual link prediction results, the features of each node are expanded into a matrix according to formula (26) and formula (27) to calculate the interactions between all node pairs; according to formula (28), the interaction score S in each pair of nodes is calculated using a bilinear layer; according to formula (29), the interaction score is normalized into a probability value, which indicates the possibility of a link between node pairs.

[0055]

[0056] in, represents the tensor product, is the weight matrix of the bilinear layer, Indicates H 2 The transpose of d v is the node feature dimension.

[0057] The steps of training the spatial-temporal fusion model for predicting shipping network links are as follows:

[0058] Step 4.1 Generation of training and validation datasets

[0059] For any month t, the node feature sequence H of the first three months t-1 ,H t-2 ,H t-3 As input, the link matrix A of the current month o→d (t) is used as the label value to form an input label pair data set; 80% is selected as the training set and the remaining 20% ​​is used as the test set;

[0060] Step 4.2 Link prediction model training

[0061] The model parameters are randomly initialized, and the training data set is input into the spatiotemporal fusion model for shipping network link prediction in step 3 for forward propagation calculation. According to formula (30), the binary focal entropy loss function is used. To measure the difference between the model's predictions and the true labels; backpropagate by calculating the gradient of the loss function, and use the stochastic gradient descent (SGD) optimizer to update the model parameters, where the learning rate is set to lr to minimize the loss value. After each training round, switch the model to evaluation mode, input the validation set data for forward propagation, calculate the loss on the validation set, and monitor its changes. Repeat the above process of forward propagation, loss calculation, backpropagation, and validation set evaluation until the validation set loss no longer decreases significantly (or starts to increase) within several consecutive rounds, or stop training when the preset number of training rounds is reached;

[0062]

[0063] In formula (30), γ is the focus parameter, α is the category weight parameter; y is the actual value, is the predicted value.

[0064] The spatiotemporal fusion model of shipping network link prediction is used to predict the link existence probability of each node pair in the current month. The steps are:

[0065] After the model training is completed, the data to be predicted is input into the model for forward propagation to obtain the predicted probability value. If the OD pair prediction probability exceeds 0.5, it is considered that there will be a link in that month; otherwise, it is considered that there will be no link in that month.

[0066] The present invention aims to provide a shipping network link prediction method based on graph convolutional neural network, which fully mines the spatiotemporal characteristics of the shipping network presented in the historical OD connection output by extracting the characteristics of shipping links and shipping nodes and constructing a spatiotemporal fusion model for shipping network link prediction, so as to effectively predict future shipping network links. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Attached Figure 1 is a flow chart of the present invention;

[0068] Attached Figure 2 It is the actual input data diagram of the present invention;

[0069] Attached Figure 3 The link prediction result diagram and the actual result diagram of the present invention; DETAILED DESCRIPTION

[0070] This example uses the monthly coal shipping network connection data from January 2013 to June 2024 as an example to predict shipping network links. Figure 2An embodiment of the present invention is given for data input and hyperparameter optimization, shipping link and shipping node feature extraction, spatiotemporal fusion model construction for shipping network link prediction, and link prediction model training and application.

[0071] (I) Data input and hyperparameter optimization

[0072] Input the continuous monthly OD connection sequence data Y from January 2014 to December 2016 o→d (t), time series length N = 36, number of nodes Num = 115; initialize hyperparameter h T =6,h s =3, K=12, lr=0.01, α=0.75, γ=2, m=5, L=2, d g =64,d l =128,d v =32;

[0073] 2. ...

[0074] Step 21: For each OD pair, o→d (t), using the local weighted regression method to calculate the trend characteristic T o→d (t); For example, for June 2015, i.e., t = 18, according to formula (1), calculate its neighborhood point t i =12 to t i =24 weight ω(t,t i ), and according to formulas (2)-(4), the local linear model is fitted to obtain the trend characteristic T o→d (18) = 0.85;

[0075] Step 22: According to formula (5), obtain the detrended time series Y′ o→d (t); divide the subsequence according to the period K = 12; for example, for June 2015, that is, t = 18, calculate its seasonal characteristic S according to formulas (6)-(10): o→d (18) = 0.42;

[0076] Step 23: According to formula (11), o→d (t) Perform discrete Fourier transform, select the first m = 5 frequency components with the largest amplitude, and reconstruct the simulation signal according to formula (12) For time point t=18, we get the multi-scale periodic features

[0077]

[0078] Step 24: Calculate the out-degree, in-degree and degree of each node; for example, the out-degree of node v=1 at time point t=18 is outdeg(1,18)=15, the in-degree is indeg(1,18)=12, and the degree is deg(1,18)=27;

[0079] 3. Construction of spatiotemporal fusion model for shipping network link prediction

[0080] Step 31: For time point t=18, feature vector x of node v=1 1 =[15,12,27]; link feature vector a o→d =[0.67, 0.42, 0.85]; Calculate the edge weight w according to formula (17) i,j , for example 1,2 =0.73;

[0081] Step 32: According to formula (18), perform L = 2 graph convolution operations to update the node feature matrix H L , for example, the feature vector of node v=1 is updated to

[0082] Step 33: Taking time point t=18 as an example, the node feature sequence H of the first three months 17 ,H 16 ,H 15 Input the LSTM network and predict the feature representation of t=18. For example, the feature representation of node v=1 is

[0083] Step 34: Calculate the interaction score S between the node pairs and normalize it to a probability value using the Sigmoid function Taking nodes v=1 and v=2 as examples, their link prediction probabilities are

[0084] (IV) Link prediction model training and application

[0085] Step 41: Use 36 months of shipping OD connection data to form an input-label pair dataset, select 80% as the training set, and the remaining 20% ​​as the test set;

[0086] Step 42: Randomly initialize the model parameters, input the training data set into the spatiotemporal fusion model for shipping network link prediction in step 3 for forward propagation calculation, and use the binary focal entropy loss function according to formula (30): For training, the optimizer uses the stochastic gradient descent (SGD) method with a learning rate of lr = 0.001. During the training process, the training is stopped when the validation set loss decreases significantly within 10 consecutive rounds;

[0087] Step 43: Input the data to be predicted and obtain the link prediction result. For example, predict the probability that nodes v=1 and v=2 have a link in the 37th month. If it is greater than 0.5, it is considered that a link exists;

[0088] Test analysis: Compare the extracted shipping network link prediction results with the actual observation data (such as Figure 3 As shown), it can be seen that the two have a high consistency, which shows the effectiveness of the method; in the actual emergency prediction process, the prediction accuracy, false alarm rate and missed alarm rate of the present invention are 0.9231±0.0456, 0.0769±0.0345 and 0.0812±0.0287 respectively, which proves that the method can effectively assist the dynamic prediction and emergency decision-making when the shipping network link is missing, and has high practicality and reliability.

Claims

1. A method for predicting shipping network links based on graph convolutional neural network, characterized by: Firstly, based on the historical monthly OD connection quantity data, the trend characteristics and seasonal characteristics between the shipping network nodes are decomposed and extracted, and the multi-scale periodic characteristics are extracted through Fourier transform. Then, the trend characteristics, seasonal characteristics and multi-scale periodic characteristics of each node in the previous quarter are combined with the node topology characteristics of the shipping network topology structure and input into the hybrid model of graph convolutional neural network (GCN) and long short-term memory network (LSTM). Through the spatial dependency relationship and time evolution law, a spatiotemporal fusion model for shipping network link prediction is constructed and the model is trained. Finally, the spatiotemporal fusion model for shipping network link prediction is used to predict the link existence probability of each node pair in the current month.

2. The method for predicting shipping network links based on graph convolutional neural network according to claim 1 is characterized in that: Based on the historical monthly OD connection quantity data, the trend characteristics and seasonal characteristics between the shipping network nodes are decomposed and extracted, and the multi-scale periodic characteristics are extracted through Fourier transform. The steps are as follows: Step 1: Data input and hyperparameter initialization Input historical continuous monthly OD connection sequence data Y o→d (t), where t is the time series subscript, the time series length is N, o is the departure country, and d is the destination country; the number of nodes in the input OD connection sequence data is Num; initialize the hyperparameters; The hyper parameters are shown in the following table Step 2: Extracting shipping links and shipping nodes features Step 2.1 Extraction of trend features of shipping links In order to extract the trend characteristics of the maritime OD link and reflect the changes in the general trend of maritime trade, this step adopts the local weighted regression method; o→d For any OD pair time column in (t), perform the following steps: According to formula (1), the weights of the neighborhood points in the sequence are calculated; based on the weighted least squares method, according to formula (2), the local linear model is fitted; according to formula (3), the local coefficients β0 and β1 are solved by minimizing the weighted residual sum of squares; according to formula (4), the trend characteristics are calculated; y i =β0+β1t i +e i (2) T o→d (t)=β0+β1t (4) In formulas (1)-(4), t represents the month for which the trend characteristics are to be calculated; t i indicates other months in the time series; h T is the bandwidth of the trend term; ω(t,t i ) indicates that when trend characteristics are calculated, t i The weight at target t; β0 and β1 are the local coefficients to be fitted; ε i represents the residual; y i Represents Y o→d (t) t in the sequence i The corresponding value; T o→d (t) represents the trend characteristics of month t; Step 2.2 Link seasonality feature extraction In order to extract the seasonal characteristics of the maritime OD link and reflect the seasonal changes of maritime trade, Y o→d For any OD pair time column in (t), perform the following steps: According to formula (5), the trend characteristics are removed from the original time series to obtain the detrended time series Y ′ o→d (t); Divide the detrended sequence into subsequences D according to K-month periods k (t); for each subsequence D k (t), according to formula (6), calculate the weights of the neighborhood points in the sequence; based on the weighted least squares method, according to formula (7), fit the local linear model; according to formula (8), solve the local coefficient β0 by minimizing the weighted residual sum of squares ′ With β1 ′ ; According to formula (9), calculate its seasonal characteristics; According to formula (10), perform centralization to ensure that its mean is 0; Y ′ o→d (t)=Y o→d (t)-T o→d (t) (5) D k (t i )=β0 ′ +β1 ′ t i +e i ′ (7) S(t)=β0 ′ +β1 ′ t (9) In formulas (5)-(10), t represents the month for which the seasonal characteristics are to be calculated; t i indicates other months in the time series; h T is the seasonal bandwidth; ω(t,t i ) indicates that when calculating seasonal characteristics, t i The weight at target t; β0 ′ With β1 ′ is the local coefficient to be fitted; ε i ′ Residual error; D k (t i ) means D k (t) t in the sequence i The corresponding value; S(t) represents the seasonal characteristics of month t; S o→d (t) represents the seasonal characteristics after decentralization, hereinafter referred to as seasonal characteristics; K is the number of cycles; Step 2.3 Multi-scale periodic feature extraction of shipping links In order to extract the multi-scale periodic characteristics of maritime OD links and reflect the seasonal changes of maritime trade, Y o→d For any OD pair time column in (t), perform the following steps: According to formula (11), the monthly OD connection time series data Y o→d (t) Perform discrete Fourier transform to convert it from time domain to frequency domain to obtain Y o→d (f); each Y o→d (f) contains amplitude and phase information, and selects the first m frequency components Y with the largest amplitude o→d (f1),Y o→d (f2),…,Y o→d (f M ), and their corresponding amplitudes are |Y o→d (f1)|,|Y o→d (f2)|,…,|Y o→d (f M )|, and their corresponding phases are φ(f1), φ(f2),…, φ(f M ) ; Reconstruct the timing signal through inverse Fourier transform to obtain the simulation signal Select Simulation Signal As a multi-scale periodic feature of the link; In formulas (11)-(12), N represents the total length of the time series; M represents the total number of selected frequency components; t represents the time point; f represents the frequency; e represents the natural logarithm; π represents the circumference of a circle; i represents the imaginary unit, and i satisfies 2 =-1.

3. The method for predicting shipping network links based on graph convolutional neural network according to claim 1 is characterized by: The node topology features of the shipping network topology structure are extracted in the following steps: According to formula (13), the OD connection data at time t is expressed as the adjacency matrix A o→d (t); For each node v, calculate its out-degree, in-degree and degree according to formulas (14), (15) and (16); In formulas (13)-(16), Num is the total number of nodes, v and j both represent the node subscripts, and t is the month subscript.

4. The method for predicting shipping network links based on graph convolutional neural network according to claim 1 is characterized by: The steps of constructing a spatiotemporal fusion model for shipping network link prediction through spatial dependency and time evolution law are as follows: Step 4.1 Input feature definition For any month t, the feature vector x of each node v v =[outdeg(v,t),indeg(v,t),deg(v,t)]; the time series Y of each link o→d The eigenvector of (t) is According to formula (17), the edge attribute is mapped to the weight value w through a linear transformation i,j ; In formula (17), is a learnable weight matrix, σ is a sigmoid activation function used to map weight values ​​to the (0,1) interval, i is the subscript of node o, and j is the subscript of node d; Step 4.2 Graph Convolutional Network Construction In order to effectively extract the graph data characteristics of the shipping network, a graph convolutional network is used in this step. According to formula (18), L graph convolution operations are performed to update the node features to obtain the node feature matrix H L ; Node feature matrix after graph convolution layer processing It can well reflect the position and connection relationship of nodes in the graph structure; In formula (18), is the set of neighboring nodes of node i, is the learnable weight matrix of layer l, d g is the hidden layer dimension, is the node feature vector of the lth layer; Step 4.3 Long Short-Term Memory Neural Network Construction The node feature sequence H of the first three months t-1 ,H t-2 ,H t-3 As input, according to formula (19), the LSTM network is used to model the time series of node features; the final output of LSTM is the feature representation of each node in the fourth month Can reflect the dynamic changes of nodes in the time dimension; in, is the hidden state at time t; is the cell state; d l is the hidden layer dimension in LSTM; the specific update formula of LSTM is shown in equations (20)-(25); Formula (19)-(25), W i , W f , W g , W o and U i , U f , U g , U o is the learnable weight matrix of LSTM, b i , b f , b g , b o is the bias term, σ is the Sigmoid activation function, tanh is the hyperbolic tangent activation function, and ⊙ represents element-by-element multiplication; Step 4.4 Prediction of shipping network links In order to convert the LSTM prediction results into actual link prediction results, the features of each node are expanded into a matrix according to formula (26) and formula (27) to calculate the interactions between all node pairs; according to formula (28), the interaction score S in each pair of nodes is calculated using a bilinear layer; according to formula (29), the interaction score is normalized into a probability value, which indicates the possibility of a link between node pairs. in, represents the tensor product, is the weight matrix of the bilinear layer, represents the transpose of H2; d v is the node feature dimension.

5. The method for predicting shipping network links based on graph convolutional neural network according to claim 1 is characterized by: The steps of training the spatial-temporal fusion model for predicting shipping network links are as follows: Step 5.1 Generation of training and validation datasets For any month t, the node feature sequence H of the first three months t-1 ,H t-2 ,H t-3 As input, the link matrix A of the current month o→d (t) is used as the label value to form an input label pair data set; 80% is selected as the training set and the remaining 20% ​​is used as the test set; Step 5.2 Link prediction model training The model parameters are randomly initialized, and the training data set is input into the spatiotemporal fusion model for shipping network link prediction in step 3 for forward propagation calculation. According to formula (30), the binary focal entropy loss function is used. To measure the difference between the model's predictions and the true labels; backpropagate by calculating the gradient of the loss function, and use the stochastic gradient descent (SGD) optimizer to update the model parameters, where the learning rate is set to lr to minimize the loss value. After each training round, switch the model to evaluation mode, input the validation set data for forward propagation, calculate the loss on the validation set, and monitor its changes. Repeat the above process of forward propagation, loss calculation, backpropagation, and validation set evaluation until the validation set loss no longer decreases significantly (or starts to increase) within several consecutive rounds, or stop training when the preset number of training rounds is reached; In formula (30), γ is the focus parameter, α is the category weight parameter; y is the actual value, is the predicted value; The final spatiotemporal fusion model for shipping network link prediction is obtained.

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