A sparse-aware traffic scene blind area information interpolation estimation method

Abstract

The application relates to the technical field of intelligent traffic systems, and discloses a sparse perception traffic scene blind area information interpolation estimation method. Traffic data collected by sensors at traffic network nodes is acquired, and a plurality of characteristic information is adaptively fused; dynamic time characteristic extraction is carried out according to the multi-modal fusion characteristics; the extraction result of the dynamic time characteristics is added to the multi-modal fusion characteristics and then input into a space attention module and a bidirectional time attention module to obtain a new adjacency matrix and a dynamic transfer matrix; the new adjacency matrix and the dynamic transfer matrix are input into an S-fusion layer module to obtain a road network adjacency matrix with forward and backward long and short term space-time dependence; the road network adjacency matrix and the multi-modal fusion characteristics are input into a graph attention gate recurrent module and a decoding output module to obtain interpolation estimation of nodes with missing values. The application can accurately capture the complex dynamic space-time correlation characteristics between scene nodes, and guarantee the accuracy and robustness of scene space-time data completion.

Description

Technical Field

[0001] This invention relates to the field of intelligent transportation system technology, specifically to a method for interpolating and estimating blind spot information in sparse perception traffic scenarios. Background Technology

[0002] With the rapid development of intelligent transportation systems, an increasing number of data-driven methods using deep neural networks have been proposed and applied in the field of transportation. These deep learning methods heavily rely on sufficient, high-quality historical spatiotemporal traffic data. However, in most practical large-scale traffic monitoring systems, the spatial resolution of deployed sensors is always sparse and limited (with perception blind spots). Furthermore, even with fixed sensors, practical problems such as detector malfunctions, communication failures, power outages, and storage anomalies can occur, causing the collected traffic information to frequently contain missing data. If not properly processed, this can degrade the model performance of downstream tasks. Therefore, missing scene spatial data is an unavoidable problem. These prevalent perception blind spot data deficiencies severely restrict the real-time monitoring performance of scene monitoring systems and fundamentally limit various downstream applications based on big data intelligent understanding. Therefore, how to estimate and complete missing data has become a key issue in widespread large-scale scene monitoring systems.

[0003] Existing research does not adequately consider the complex dynamic spatiotemporal relationships between spatial nodes in a scene, resulting in inefficient and non-robust imputation of missing scene spatiotemporal data. Although recent research on spatiotemporal data imputation methods based on graph neural networks has demonstrated the effectiveness of deep learning in this field, existing research does not delve deeply enough into the dynamic relationships between spatiotemporal data. They typically assume that spatial dependencies are determined solely by the distance between spatial nodes; however, spatial dependencies are actually influenced by various complex physical factors beyond distance, such as road class in traffic scenes, weather, and unforeseen events. These factors make the dynamic relationships between spatiotemporal data extremely complex. Therefore, how to extract patterns from scene spatiotemporal data using appropriate algorithms to estimate missing values ​​and characterize complex, dynamically changing spatiotemporal dependencies is one of the most important tasks in spatiotemporal data analysis. Summary of the Invention

[0004] To address the aforementioned problems, the present invention aims to provide a method for interpolating and estimating blind spot information in sparse sensing traffic scenarios. This method enhances the accurate capture of complex dynamic spatiotemporal correlations between scene nodes, ensuring improved accuracy and robustness of spatiotemporal data completion. The technical solution is as follows:

[0005] A method for interpolating and estimating blind spot information in sparse perception traffic scenes includes the following steps:

[0006] Step 1: Acquire traffic data collected by sensors at traffic network nodes;

[0007] Step 2: Construct a multimodal auxiliary information fusion module to adaptively fuse multiple feature information from traffic data to obtain multimodal fusion feature E. out ;

[0008] Step 3: Construct a dynamic temporal feature extraction module. Input the multimodal fusion features into the dynamic temporal feature extraction module to obtain global and local information and high-order temporal dependency interaction information of the time series data in the time dimension, i.e., the dynamic temporal feature extraction result X′. t ;

[0009] Step 4: Extract the dynamic temporal features X′ t With multimodal fusion features E out The summation is then fed into the spatial attention module and the bidirectional temporal attention module to obtain a new adjacency matrix A with dynamic temporal dependencies. att and the dynamic transition matrix derived from dynamic real-time time series information. and

[0010] Step 5: Construct the S-fusion layer module, and generate the new adjacency matrix A. att and dynamic transition matrix and The input is fed into the S-fusion layer module to obtain the road network adjacency matrix A with forward long-short-term spatiotemporal dependencies. f，st And the road network adjacency matrix A with backward long and short-term spatiotemporal dependencies b，st ;

[0011] Step 6: Configure the road network adjacency matrix A b，st and A f，st and the multimodal fusion feature E obtained in step 2 out The input is fed into the graph attention gating loop module and the decoding output module to obtain the imputation estimate of the nodes with missing values.

[0012] Furthermore, step 2 specifically includes:

[0013] A multimodal auxiliary information input fusion module is designed using multimodal data, including travel time and speed information for corresponding road segments from public travel navigation data; firstly, the multimodal data I... a I b I c ... are projected onto a high-dimensional space through embedding layers to obtain multimodal features E. a E b E c ..., and then the features are adaptively fused:

[0014]

[0015] Among them, E out For multimodal fusion features; E m For the multimodal features of the m-th multimodal data, W m These are multimodal features E m The weight.

[0016] Furthermore, step 3 specifically includes:

[0017] Step 3.1: By employing self-attention operations in the time dimension to establish long-range dependencies in the input sequence, global understanding and high-order temporal dependency interactions of the time-series data are extracted; the core expression of the dynamic temporal feature extraction module is as follows:

[0018]

[0019] X t =Self-Attention(Q,K,V)=Softmax(A t V

[0020]

[0021] Where X is the input of the dynamic temporal feature extraction module, W Q W K W V These are learnable parameters to obtain the query matrix Q, the key matrix K, and the value matrix V; X t To consider the temporal feature extraction results that take into account long-term and short-term time dependencies; T is the transpose symbol; A t The attention mechanism, i.e., the attention score obtained from the formula on the right side of the equation; d h The dimension of the defined hidden layer;

[0022] Step 3.2: Extract the time feature information X t The data is fused and enhanced with the original temporal data X in the T-fusion layer to enhance and supplement the details lost after the attention operation, as shown in the following expression:

[0023]

[0024] Where 'a' is the weight score, representing the proportion of each component during fusion; W1, W2, and β represent the proportions of each component during fusion, and X′... t The results are the extraction results of dynamic time features.

[0025] Furthermore, step 4 specifically includes:

[0026] Step 4.1: Establish a spatial attention module and use an attention mechanism to update the adjacency graph matrix in real time to add dynamic spatial dependencies to it;

[0027] Let the time feature extraction result be M. t And M t =X′ t +E out The attention matrix U is then obtained by the following formula:

[0028]

[0029] Among them, W att is the attention weight matrix, used to project the input features into the new space; P is the feature value after projecting the input features into the new space; N is the result of the inner product of P, Λ is the diagonal matrix of N; σ(·) is the sigmoid activation function, and diag(·) is the function to extract diagonal elements;

[0030] Step 4.2: Assign attention weight matrix W att Normalization is performed so that all diagonal elements of the attention matrix U are 1; then A is used. att =A sample U, as the new adjacency matrix, contains the dynamic spatial dependencies learned from the current sequence data, and A sample The matrix is ​​the adjacency matrix after masking, and ⊙ represents the Hadamard product;

[0031] Step 4.3: In the temporal attention module, two fully connected feedforward networks, one for forward and the other for backward, are used to compute the dynamic transition matrix for each time slot. and

[0032]

[0033] in, and It is a learnable parameter matrix. and It is a bias parameter;

[0034] The input to the feedforward network is a set of node features output from the temporal Transformer layer, i.e., the temporal feature extraction result M. t Each feedforward network consists of two linear transformations with a ReLU activation in between.

[0035] Furthermore, step 5 is as follows:

[0036] Through the spatial attention module and bidirectional temporal attention module in step 4, two transition matrices are obtained in each time slot: A obtained by updating the scene network through dynamic spatial correlation.f，s and A b，s and dynamic transition matrix from dynamic real-time time series information and Where A f，s =A att / rowsum(A att ) and A b，s =A T att / rowsum(A T att ) are the forward and backward space transition matrices, respectively; rowsum(·) calculates the sum of the values ​​in each row;

[0037] For the learned bidirectional time dynamic transition matrix, i.e., the dynamic transition matrix and And the bidirectional spatial transition matrix, that is, the forward transition matrix A. f，s and the backward transition matrix A b，s A gated fusion method is employed to obtain a dynamic bidirectional spatiotemporal dependency matrix in the forward direction:

[0038]

[0039] Among them, g f，t To obtain the weight parameters in one step for the gating mechanism, and For learnable weight parameters, β g For offset item; A f，st It is a road network adjacency matrix with forward long and short-term spatiotemporal dependencies;

[0040] Similarly, we obtain the road network adjacency matrix A with backward long-short-term spatiotemporal dependencies. b，st .

[0041] Furthermore, step 6 is as follows:

[0042] Step 6.1: Learn the weights of neighbors through a graph attention mechanism to achieve weighted aggregation of neighbors. The formula is as follows:

[0043]

[0044] Among them, h i and h j W represents the feature information of node i and its neighbor node j, where W is a projection matrix and α is the feature information of node i and its neighbor node j. ij These are the attention weight parameters; 'a' is the weight parameter, used for dimension mapping. Let h be the set of neighboring nodes of node i, and → indicates the vector representation; ii represents the result obtained after weighted aggregation; LeakyReLU(·) is an activation function;

[0045] The attention weight parameter α ij The vector representations of neighboring nodes are weighted and summed, and then passed through a sigmoid activation function to obtain the final output, which is the new node information that integrates neighborhood information.

[0046] A graph attention mechanism is injected into the gated recurrent unit to capture both the spatial dependencies represented by the input graph topology and the temporal dependencies represented in a sequential manner; the formula is as follows:

[0047] u t =sigmoid([X t H t-1 ]★g+b u )

[0048] r t =sigmoid([X t H t-1 ]★g+b r )

[0049] C t =tanh([X t ,(r t ⊙H t-1 )]★g+b C )

[0050] H t =u t ⊙H t-1 +(1-u t )⊙C t

[0051] Among them, the time feature extraction result X, which considers long-term and short-term time dependencies, is used. t As input to the graph attention operation; b is a learnable bias parameter; subscripts u, r, and C represent the update gate, reset gate, and candidate state in the recurrent unit, respectively; u t r t and C t These are the update gate, reset gate, and candidate gate in the gating mechanism; H t This is the output obtained by the gating mechanism at each time step; ★g represents the graph attention operation;

[0052] For the decoder, a common two-layer fully connected layer is used, with a ReLU activation function in between:

[0053] X sample =W 2 ReLU(W 1 M out+β 1 )+β 2

[0054] Among them, M out for Output features after ST Encoder; W 1 and W 2 Let β be a learnable parameter matrix. 1 and β 2 X is the bias parameter; sample This represents the final output of the model. This represents the model input after the masking operation;

[0055] Finally, the output is the imputation estimate for nodes with missing values.

[0056] The beneficial effects of this invention are:

[0057] This invention establishes long-range dependencies in the input sequence by employing self-attention operations in the time dimension, extracting global understanding and high-order temporal dependency interactions from time-series data; and learns the spatial transfer mechanism between scene nodes through graph attention-gated recurrent units, thereby enabling the imputation of missing value nodes based on recorded nodes, improving the accuracy of capturing complex dynamic spatiotemporal correlation characteristics between scene nodes, and ensuring the accuracy and robustness of scene spatiotemporal data completion. Attached Figure Description

[0058] Figure 1 This is a diagram illustrating the overall framework of the sparse sensing traffic scene blind spot information interpolation estimation method of the present invention.

[0059] Figure 2 A schematic diagram of the multimodal auxiliary information input fusion module.

[0060] Figure 3 This is a schematic diagram of the dynamic time feature extraction module. Detailed Implementation

[0061] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0062] This invention is a sparse sensing traffic scene blind spot information interpolation and estimation method that considers graph attention and dynamic spatiotemporal dependence. The overall framework diagram is as follows: Figure 1 As shown, the main steps are as follows:

[0063] Step 1: Acquire traffic data (graphical signals) collected by sensors at traffic network nodes.

[0064] Specifically, sensors at traffic network nodes report data at regular intervals, such as capacity, speed, delay, vehicle mileage, and vehicle travel hours. This embodiment uses the PEMS04 public transportation traffic data dataset collected by California Transit Corporation on California highways. The PEMS04 dataset contains traffic data from 307 sensors collected over 59 consecutive days starting January 1, 2018, collected every 5 minutes. It has three dimensions of features: flow, occupy, and speed.

[0065] Step 2: Construct a multimodal auxiliary information fusion module to adaptively fuse various feature information in traffic data.

[0066] Adaptive fusion of multiple features in traffic data is performed; if no auxiliary information is available, the input multimodal becomes unimodal.

[0067] In transportation networks, besides the time-series data collected by node sensors, there is also various heterogeneous auxiliary information, such as public travel navigation data which may contain travel time and speed information for a particular road segment. The data flow and aggregation patterns contained in this information also help to fill in the gaps in missing sensor data. Therefore, we fully utilize this information to design systems such as... Figure 2 The multimodal auxiliary information input fusion module is shown. First, we input the multimodal data I... a I b I c ...and so on, projecting the multimodal features E onto a high-dimensional space through the embedding layer. a E b E c ...then we will adaptively fuse the features:

[0068]

[0069] Among them, E out For multimodal fusion features; E m For the multimodal features of the m-th multimodal data, W m These are multimodal features E m The weight.

[0070] Step 3: Input the fused features into the dynamic temporal feature extraction module to obtain global and local information and high-order temporal dependency interaction information of the time-series data extracted in the time dimension. The overall architecture of the dynamic temporal feature extraction module is as follows: Figure 3 As shown.

[0071] This embodiment establishes long-range dependencies in the input sequence using self-attention operations in the time dimension, extracting a global understanding and high-order temporal dependency interactions from the time-series data. The core expression of this module is as follows:

[0072]

[0073] Where X is the input of this module, W Q W K W V These are learnable parameters to obtain Q, K, V. X t The time feature extraction results take into account both long and short-term time dependencies.

[0074] Then the obtained information X t The data is fused and enhanced with the original time-series data X in the T-fusion layer. This aims to supplement and enhance some of the detailed information lost after the self-attention operation. The expression is as follows:

[0075]

[0076] X′ t =X t a+(1-a)X

[0077] Step 4: Extract the above dynamic time features X′ t With multimodal fusion features E out The summation is then fed into the Spatial Attention (SA) module and the Bidirectional Temporal Attention (TA) module to obtain the adjacency matrix and the dynamic transition matrix, which have dynamic temporal dependencies.

[0078] In this embodiment of the invention, the spatial dependency between road network nodes depends not only on their simple Euclidean distance dependency, but also on other factors such as road slope, weather, and pedestrian mobility. Furthermore, the spatial dependency of road network nodes is dynamically changing. Inaccurate spatial correlations can degrade the performance of spatiotemporal missing value imputation. Therefore, to extract more accurate spatial correlations, the spatial attention module (SA) designed in this invention employs an attention mechanism to update the adjacency graph matrix in real time, thereby adding dynamic spatial dependencies. Let the temporal feature extraction result be M. t (M t =X′ t +E out Then the attention matrix U can be obtained by the following formula:

[0079]

[0080] Among them, W attU is the weight matrix of the attention mechanism. It projects the input features into a new space. Then, the attention weight matrix is ​​determined by the inner product of the features in this new space. We normalize the attention weight matrix so that all diagonal elements of U are 1. Thus, we can obtain an attention matrix U using the above method, and then use A... att =A sample ⊙U, as the new adjacency matrix, contains the dynamic spatial dependencies learned from the current sequence data. A sample Let be the adjacency matrix after masking, and ⊙ denote the Hadamard product.

[0081] In the TA module, we use two fully connected feedforward networks (FFNs), one for forward and one for backward, to compute the dynamic transition matrix for each time slot. and

[0082]

[0083] in, It is a learnable parameter matrix. and These are the bias parameters. The input to the feedforward network is a set of node features M output from the temporal Transformer layer. t Each feedforward network consists of two linear transformations with a ReLU activation in between. In this way, our proposed network structure can utilize information from both the past and the future.

[0084] Step 5: Input the new adjacency matrix and dynamic transition matrix obtained above into the S-fusion layer module to obtain the road network adjacency matrix.

[0085] In this embodiment of the invention, through SA and TA, we obtain two transition matrices in each time slot, namely A obtained by updating the scene network through dynamic spatial correlation. f，s and A b，s and dynamic transition matrix from dynamic real-time time series information and Where A f，s =A att / rowsum(A att ) and A b，s =A T att / rowsum(A T att These are the forward transition matrix and the backward transition matrix, respectively.

[0086] For the learned bidirectional temporal dependency matrix and bidirectional spatial transition matrix, we propose an effective gating fusion method to obtain the dynamic bidirectional spatiotemporal dependency matrix, taking the forward direction as an example:

[0087]

[0088] in, For learnable weight parameters, β g This is the offset term. At this point, the module's output A... f，st Let A be the road network adjacency matrix with forward long short-term spatiotemporal dependencies. Similarly, we can obtain the road network adjacency matrix A with backward long short-term spatiotemporal dependencies. b，st .

[0089] Step 6: Input the road network adjacency matrix and the fused features into the graph attention gating loop module and the decoding output module to obtain the interpolation estimate of the nodes with missing values.

[0090] Graph Attention (GAT) learns the weights of its neighbors to achieve weighted aggregation of neighbors. Therefore, GAT is not only robust to noisy neighbors, but the attention mechanism also lends the model a degree of interpretability. Its formula is:

[0091]

[0092] Among them, h i and h j W represents the feature information of node i and its neighbor node j, where W is a projection matrix and α is the feature information of node i and its neighbor node j. ij This is the attention weight parameter. Let α... ij The vector representations of neighboring nodes are weighted, summed, and then passed through a sigmoid activation function to obtain the final output, which is the new node information that incorporates neighborhood information. 'a' is the weight parameter, used for dimension mapping. Let h be the set of neighboring nodes of node i, and → indicates the vector representation; i ′ represents the result obtained after weighted aggregation; LeakyReLU(·) is an activation function.

[0093] In this embodiment of the invention, we inject a graph attention mechanism (GAT) into the gated recurrent unit, which allows us to simultaneously capture both the spatial dependencies represented by the input graph topology and the temporal dependencies represented in a sequential manner. The formula is as follows:

[0094] u t =sigmoid([X t H t-1 ]★g+b u )

[0095] r t=sigmoid([X t H t-1 ]★g+b r )

[0096] C t =tanh([X t ,(r t ⊙H t-1 )]★g+b C )

[0097] H t =u t ⊙H t-1 +(1-u t )⊙C t

[0098] X t The input to the graph attention operation (★g) is represented by b, which is a learnable bias parameter. The subscripts u, r, and C represent the update gate, reset gate, and candidate state in the recurrent unit, respectively.

[0099] For the decoder, we use a general two-layer fully connected layer, with a ReLU activation function in between:

[0100] X sample =W 2 ReLU(W 1 M out +β 1 )+β 2

[0101] Among them, M out for After passing through the output features of the ST Encoder, W 1 W 2 Let β be a learnable parameter matrix. 1 ,β 2 This is the bias parameter. At this point, the output is the imputation estimate for nodes with missing values.

[0102] ST Encoder is a spatiotemporal encoder, that is... Figure 1 The entire encoder module is enclosed in a dashed box.

Claims

1. A method for interpolating and estimating blind spot information in sparse sensing traffic scenes, characterized in that, Includes the following steps: Step 1: Acquire traffic data collected by sensors at traffic network nodes; Step 2: Construct a multimodal auxiliary information fusion module to adaptively fuse various feature information in traffic data to obtain multimodal fusion features. ; Step 3: Construct a dynamic temporal feature extraction module. Input the multimodal fusion features into the dynamic temporal feature extraction module to obtain global and local information and high-order temporal dependency interaction information of the time series data in the time dimension, i.e., the extraction result of dynamic temporal features. ; Step 4: Extract the results of the dynamic temporal features Features with multimodal fusion The summation is then fed into the spatial attention module and the bidirectional temporal attention module to obtain a new adjacency matrix with dynamic temporal dependencies. and the dynamic transition matrix derived from dynamic real-time time series information. and ; Step 5: Construct the S-fusion layer module and generate the new adjacency matrix. and dynamic transition matrix and The input is fed into the S-fusion layer module to obtain the road network adjacency matrix with forward long-short-term spatiotemporal dependencies. and the road network adjacency matrix with backward long and short-term spatiotemporal dependencies ; Step 6: Configure the road network adjacency matrix and and the multimodal fusion features obtained in step 2 The input is fed into the graph attention gating loop module and the decoding output module to obtain the imputation estimate of the nodes with missing values; Step 4 specifically involves: Step 4.1: Establish a spatial attention module and use an attention mechanism to update the adjacency graph matrix in real time to add dynamic spatial dependencies to it; Let the time feature extraction result be ,and Then the attention matrix We obtain it from the following formula: ； in, is the attention weight matrix, used to project the input features into a new space; P is the feature value after projecting the input features into the new space; The result after taking the inner product of P. for a diagonal matrix; It is the sigmoid activation function. A function to extract diagonal elements; Step 4.2: Calculate the attention weight matrix. Normalization makes the attention matrix The diagonal elements are all 1; then use As a new adjacency matrix, it contains the dynamic spatial dependencies learned from the current sequence data. This is the adjacency matrix after masking. It represents the Hadamardi (or Hadama) stack; Step 4.3: In the temporal attention module, two fully connected feedforward networks, one for forward and the other for backward, are used to compute the dynamic transition matrix for each time slot. and : ； in, , It is a learnable parameter matrix. It is a bias parameter; The input to the feedforward network is a set of node features output from the temporal Transformer layer, i.e., the temporal feature extraction result. Each feedforward network consists of two linear transformations, with one in between. activation; Step 5 is as follows: Through the spatial attention module and bidirectional temporal attention module in step 4, two transition matrices are obtained in each time slot, namely, those obtained by updating the scene network through dynamic spatial correlation. and and dynamic transition matrix from dynamic real-time time series information and ;in and These are the forward space transition matrix and the backward space transition matrix, respectively; This indicates that the sum of the values ​​in each row is calculated; For the learned bidirectional time dynamic transition matrix, i.e., the dynamic transition matrix and And the bidirectional spatial transition matrix, also known as the forward transition matrix. and backward transition matrix A gated fusion method is employed to obtain a dynamic bidirectional spatiotemporal dependency matrix in the forward direction: ； in, To obtain the weight parameters in one step for the gating mechanism, These are learnable weight parameters. For offset items; It is a road network adjacency matrix with forward long and short-term spatiotemporal dependencies; Similarly, the road network adjacency matrix with backward long-short-term spatiotemporal dependencies is obtained. .

2. The sparse sensing traffic scene blind spot information interpolation estimation method according to claim 1, characterized in that, Step 2 specifically involves: A multimodal auxiliary information input fusion module is designed using multimodal data, including travel time and speed information for corresponding road segments from public travel navigation data; firstly, the multimodal data... Multimodal features are obtained by projecting them into a high-dimensional space through the embedding layer. Then, the features are adaptively fused: ； in, This is a multimodal fusion feature; For the first Multimodal features of multimodal data, Multimodal features The weight.

3. The sparse sensing traffic scene blind spot information interpolation estimation method according to claim 1, characterized in that, Step 3 specifically involves: Step 3.1: By employing self-attention operations in the time dimension to establish long-range dependencies in the input sequence, global understanding and high-order temporal dependency interactions of the time-series data are extracted; the core expression of the dynamic temporal feature extraction module is as follows: ； ； ； in, This serves as the input for the dynamic temporal feature extraction module. These are learnable parameters to obtain ; This is to consider the time feature extraction results that take into account long-term and short-term time dependencies; T is the transpose symbol; The attention mechanism is the attention score obtained from the formula on the right side of the equation. The dimension of the defined hidden layer; Step 3.2: Extract the time feature information Compared with the initial time series data information Fusion enhancement is performed in the T-fusion layer to enhance and supplement the details lost after the attention operation, as shown in the following expression: ； in, The weighted score represents the proportion of each part during fusion. , and To indicate the proportion of each part during fusion, The results are the extraction results of dynamic time features.

4. The sparse sensing traffic scene blind spot information interpolation estimation method according to claim 1, characterized in that, Step 6 is as follows: Step 6.1: Learn the weights of neighbors through a graph attention mechanism to achieve weighted aggregation of neighbors. The formula is as follows: ； ； in, and This represents the feature information of node i and its neighbor node j. It is a projection matrix. These are attention weight parameters; For the weight parameters, perform dimension mapping. Let i be the set of neighboring nodes of node i. The way to represent vectors; This is the result obtained after weighted aggregation; It is an activation function; Attention weight parameters The vector representations of neighboring nodes are weighted and summed, and then passed through a sigmoid activation function to obtain the final output, which is the new node information that integrates neighborhood information. A graph attention mechanism is injected into the gated recurrent unit to capture both the spatial dependencies represented by the input graph topology and the temporal dependencies represented in a sequential manner; the formula is as follows: ； Among them, the time feature extraction results considering long-term and short-term time dependencies As input to the graph attention operation; b is a learnable bias parameter; subscripts u, r, and C represent the update gate, reset gate, and candidate state in the recurrent unit, respectively; , and These are the update gate, reset gate, and candidate gate in the gating mechanism; It is the output obtained by the gating mechanism at each time step; For graph attention operations; For the decoder, a common two-layer fully connected layer is used, with one intermediate connection layer. Activation function: ； in, for Output characteristics after passing through the spatiotemporal encoder; For learnable parameter matrix, These are bias parameters; This represents the final output of the model. This represents the model input after the masking operation; Finally, the output is the imputation estimate for nodes with missing values.

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