Traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution
By using high-order principal component decomposition and multi-scale spatiotemporal graph convolutional networks, the problems of memory consumption and computational complexity of high-dimensional traffic data are solved, achieving more accurate traffic speed prediction, suppressing noise interference, and improving the stability and prediction accuracy of the model.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- NANJING UNIV OF SCI & TECH
- Filing Date
- 2022-06-24
- Publication Date
- 2026-05-12
AI Technical Summary
Existing traffic speed prediction models suffer from high memory consumption and computational complexity when processing high-dimensional traffic data. Meanwhile, deep learning models are susceptible to noise interference and have difficulty effectively capturing the spatiotemporal correlation features in traffic networks.
A spatiotemporal graph convolution method based on high-order principal component decomposition is adopted. By constructing a spatiotemporal graph feature tensor, and utilizing high-order tensor decomposition and multi-scale spatiotemporal graph convolutional network, combined with spatial and temporal correlation matrices, a unified spatiotemporal correlation model is established for traffic speed prediction.
This reduces data dimensionality, computational complexity, and noise interference, thereby improving the accuracy and efficiency of traffic speed prediction.
Smart Images
Figure CN115271172B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of artificial intelligence and the interdisciplinary fields of transportation planning and management, specifically to a traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution. Background Technology
[0002] Traffic speed prediction is a crucial piece of data in intelligent transportation systems (ITS). Its primary purpose is to predict the average speed of vehicles traveling at various transportation hubs (routes). The predicted future speed information reflects the traffic conditions at transportation hubs and can be used for travel time prediction and route planning in navigation systems. Traffic lights can also be intelligently controlled based on this information, making it a vital data source for ITS systems.
[0003] Early researchers used statistical prediction models (ARIMA, Autoregressive Integrated Moving Average) and traditional machine learning methods (SVR, Support Vector Product Regression) to predict speed. However, these methods only considered temporal correlations and could only extract linear, shallow data correlation features. Later, deep learning models demonstrated powerful capabilities in mining deep correlation features in the field of artificial intelligence. A series of deep learning models were applied to traffic speed prediction models, mainly including Recurrent Neural Networks (RNNs) and their extended models, Long Short-Term Memory Networks (LSTM) and Gated Recurrent Units (GRUs). However, RNNs can only be used to model temporal correlation features. In traffic networks, congestion at one station gradually leads to congestion at surrounding stations; this is called spatial correlation. Because the distribution of stations within a traffic network is irregular, convolutional networks cannot effectively model this spatial correlation feature. Subsequently, the proposal of Graph Convolutional Neural Networks (GCNs) provided a new solution for modeling this irregular spatial correlation feature within traffic networks. Therefore, some people proposed STGCN to capture spatial correlation features through GCN and temporal correlation features through one-dimensional convolution; later, some people proposed the T-GCN model, which combines GRU and GCN to capture temporal correlation features and spatial correlation features in traffic data respectively.
[0004] However, the two-stage approach described above considers spatiotemporal correlations separately, which presents challenges due to the significant memory consumption and computational complexity of modeling high-dimensional data. Furthermore, traffic data collected by sensors is susceptible to noise from external factors, causing severe noise interference during model training and affecting model stability. Therefore, we propose an improvement: a traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution. Summary of the Invention
[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution:
[0006] This invention relates to a traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution, comprising the following steps:
[0007] Step 1: Obtain the speed data of vehicles passing through each station on the map at multiple times. Each time point corresponds to a graph structure data. Based on the temporal evolution characteristics of the traffic network, splice the data to obtain the spatiotemporal graph feature tensor. Define each station as a node. Data is collected every S minutes. This interval is called a time slice.
[0008] Step 2: Obtain the location information of all stations on the traffic map, and construct their spatial relationship adjacency matrix based on the spatial relationship between different locations on the map;
[0009] Step 3: Based on the dynamic sequence of the traffic map in the time dimension, connect each node with itself in the past T time slices to construct a dynamic temporal adjacency matrix of the spatiotemporal graph.
[0010] Step 4: Based on the two types of association matrices constructed in Step 2 and Step 3, the spatiotemporal graph feature tensor constructed in Step 1 is used to establish a multi-scale spatiotemporal graph convolutional network model from the perspective that the spatial association within each time slice is a graph structure and the temporal association of each node at different times is a graph structure.
[0011] Step 5: Apply the principal component decomposition algorithm of higher-order tensors to the spatiotemporal graph feature tensor constructed in Step 1 to decompose and calculate the core tensor and the factor matrix corresponding to each dimension.
[0012] Step 6: Use the multi-scale spatiotemporal graph convolutional network model established in Step 4 to perform convolution operations on the core tensor and the factor matrices corresponding to each dimension obtained in Step 5.
[0013] Step 7: Perform linear regression on the node embeddings learned in Step 6 to obtain the predicted velocity values.
[0014] As a preferred embodiment of the present invention, step 4 includes the following steps.
[0015] Step 4.1: Introduce the spatial adjacency matrix constructed in Step 2. The spatiotemporal graph feature tensor constructed in step 1 Perform spatial association information transfer, for the feature matrix of the spatial map of the m-th time slice. Its spatial correlation filter expression is,
[0016]
[0017] Step 4.2: Introduce the dynamic temporal adjacency matrix constructed in Step 3. The spatiotemporal graph feature tensor constructed in step 1 Execute the time-series correlation information transfer, for the feature matrix of the time-series graph of the k-th node. Its expression in time-series correlation filtering is:
[0018] Step 4.3: Introduce two operations for multidimensional tensors.
[0019] definition The tensor matrix n-mode product is defined as follows:
[0020]
[0021]
[0022] definition Three-dimensional tensor batch multiplication is defined as follows:
[0023]
[0024]
[0025] The multi-scale spatiotemporal graph convolutional network is defined as follows:
[0026]
[0027] In a graph network, the k-th order neighbors of node i represent the nodes that node i can reach in k steps. The k-th order neighbors of the adjacency matrix are... S and k T The exponentiation includes the power over k. S and k T The fusion of neighbor information.
[0028] As a preferred embodiment of the present invention, the higher-order principal component decomposition algorithm in step 5 is as follows:
[0029]
[0030] in, This represents the decomposed feature core tensor. Know This represents the factor matrix after decomposition in three dimensions: space, features, and time, where n < N, d < D, and t < T.
[0031] As a preferred embodiment of the present invention, the specific operation of step six is to approximate the multi-scale spatiotemporal graph convolutional network defined in step four as follows:
[0032]
[0033] Since the tensor matrix n-mode product satisfies the commutative and associative laws, the above equation is equal to:
[0034]
[0035] In the above equation, spatial correlation filtering, temporal correlation filtering, and feature space mapping can be exchanged for filtering operations on the corresponding dimension factor matrices after decomposition, denoted as ,
[0036]
[0037]
[0038]
[0039] Then we can further derive the expression form of the spatiotemporal graph convolutional network based on high-order principal component decomposition as follows:
[0040]
[0041] Finally, for a specific node k, the expression for spatiotemporal information aggregation in its spatiotemporal graph convolution model is:
[0042]
[0043] The above formula intuitively expresses that the node characteristics of node k come from the aggregation of information of spatially similar nodes on the map and the aggregation of information of the node in the past.
[0044] The beneficial effects of this invention are:
[0045] This traffic speed prediction method based on high-order principal component decomposition (HPD) spatiotemporal graph convolution decomposes the traffic spatiotemporal graph into a core tensor and factor matrices in various dimensions, thereby inferring the representation of the spatiotemporal graph convolutional network after HPD, and realizing a spatiotemporal graph convolutional network model that unifies spatiotemporal correlation modeling. This invention is the first to apply a higher-order principal component decomposition (HPCD) algorithm to spatiotemporal graph convolutional networks. Starting from the perspective of high-dimensional correlation modeling in tensor space, it proposes a spatiotemporal graph convolutional model based on HPCD truncation, which has advantages such as reduced data dimensionality, parallel computation, and noise suppression, achieving excellent performance in traffic location average driving speed prediction tasks. This invention considers spatiotemporal correlations from the tensor space, unlike hybrid models that model spatiotemporal correlations separately, proposing a unified method for modeling complex spatiotemporal correlations within the spatiotemporal graph. Based on the truncation operation of HPCD, the spatiotemporal convolution filtering operation of the decomposed factor matrix alleviates the high memory consumption and high computational complexity problems of high-dimensional data modeling. By retaining the main components of HPCD and discarding unimportant noise components, it suppresses noise interference within traffic data, achieving more accurate traffic speed prediction. Attached Figure Description
[0046] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:
[0047] Figure 1 This is a flowchart illustrating the traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution of the present invention.
[0048] Figure 2 This is a schematic diagram of the spatiotemporal correlation of the traffic network constructed by the present invention based on the high-order principal component decomposition spatiotemporal graph convolution traffic speed prediction method. Detailed Implementation
[0049] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.
[0050] Example: Figure 1 As shown, this invention is a traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution. Its main framework is a spatiotemporal graph convolutional network derived from the factor matrices after tensor Tucker decomposition. After learning the feature representations of nodes through spatiotemporal graph convolution, the nodes integrate spatial and temporal correlation features. Finally, a linear regression model can be used to obtain the average speed value of each node on the map at future times. The implementation of this invention includes two stages: network training and test sample inference. In the network training stage, training data is input into the network for forward propagation to obtain the predicted average speed of each traffic station in the traffic map over the next T time slices. Then, the loss is calculated based on the mean squared error of the regression prediction, and finally, the model parameters are updated in reverse using the Adam optimizer. After the model training is completed, it can be used to predict the average speed of each station in the traffic network over the next T time slices, mainly including the following steps:
[0051] Step 1: Obtain speed data of vehicles passing through each station on the map at multiple times. Each time point corresponds to a graph structure data. Based on the temporal evolution characteristics of the traffic network, splice the data to obtain the spatiotemporal graph feature tensor. Define each station as a node. Data is collected every S minutes. This interval is called a time slice.
[0052] Includes the following sub-steps,
[0053] Step 1.1: At time t, the transportation network stations construct graph G based on their spatial distances. (t) ={V, X (t)}, where V represents the set of nodes, and the total number of nodes is N. The matrix represents the features of all nodes in the graph. In this invention, the node features are initialized by encoding the velocity values of the node over the past K time steps using a shallow encoder (two-layer neural network).
[0054] Step 1.2: Spatiotemporal graph data is usually collected at fixed time intervals of S minutes. Therefore, the data from T time slices actually records a time length of T×S, which is denoted as a graph sequence.
[0055] Step 2: Obtain the location information of all stations on the traffic map, and construct a spatial adjacency matrix based on the spatial relationships between different locations on the map. In this invention, the spatial correlation matrix is constructed by setting a threshold S. If the distance between two stations l and j is less than the threshold, then A i，j =1 indicates that there is a connecting edge between them, otherwise A i，j =0 indicates that there are no connecting edges between them. For transportation networks, the spatial graph structure does not change over time.
[0056] Step 3: Based on the dynamic sequence of the traffic map over time, such as... Figure 2 As shown, each node is connected to itself in the past T time slices to construct a dynamic temporal adjacency matrix of the spatiotemporal graph. This tensor is a dynamically learned tensor parameter, where each node in the graph and its past T time slices form a graph. For node k, its temporal correlation matrix is... In this invention, T = 12.
[0057] Step 4: Based on the two types of association matrices constructed in Step 2 and Step 3, the spatiotemporal graph feature tensor constructed in Step 1 is used to establish a multi-scale spatiotemporal graph convolutional network model from the perspective that the spatial association within each time slice is a graph structure and the temporal association of each node at different times is a graph structure.
[0058] Step 5: Apply the principal component decomposition algorithm of higher-order tensors to the spatiotemporal graph feature tensor constructed in Step 1 to decompose and calculate the core tensor and the factor matrix corresponding to each dimension.
[0059] Step 6: Use the multi-scale spatiotemporal graph convolutional network model established in Step 4 to perform convolution operations on the core tensor and the factor matrices corresponding to each dimension obtained in Step 5.
[0060] Step 4 includes the following steps.
[0061] Step 4.1: Introduce the spatial adjacency matrix constructed in Step 2. The spatiotemporal graph feature tensor constructed in step 1 Perform spatial association information transfer, for the feature matrix of the spatial map of the m-th time slice. Its spatial correlation filter expression is,
[0062]
[0063] Step 4.2: Introduce the dynamic temporal adjacency matrix constructed in Step 3. The spatiotemporal graph feature tensor constructed in step 1 Execute the time-series correlation information transfer, for the feature matrix of the time-series graph of the k-th node. Its expression in time-series correlation filtering is:
[0064] Step 4.3: Introduce two operations for multidimensional tensors.
[0065] definition The tensor matrix n-mode product is defined as follows:
[0066]
[0067]
[0068] definition Three-dimensional tensor batch multiplication is defined as follows:
[0069]
[0070]
[0071] From the graph convolution of the defined spatial and temporal relational graphs, it can be deduced that spatiotemporal graph convolution achieves spatial relational graph convolution operations on the graph nodes of each time slice. Furthermore, the spatial relational relationships of the traffic network are identical for any time slice. Spatiotemporal graph convolution establishes dynamic temporal relational relationships between each node and itself in different time slices. Combining this with the introduction of two tensor operations, the multi-scale spatiotemporal graph convolutional network is defined as follows:
[0072]
[0073] In a graph network, the k-th order neighbors of node i represent the nodes that node i can reach in k steps. The k-th order neighbors of the adjacency matrix are... S and k T The exponentiation includes the power over k. S and k T By fusing neighbor information, a multi-scale convolutional spatiotemporal graph convolutional network is realized.
[0074] The higher-order principal component decomposition algorithm in step 5 is as follows:
[0075]
[0076] in, This represents the decomposed feature core tensor. Know This represents the factor matrix after decomposition in three dimensions: space, features, and time. Here, n < N, d < D, and t < T indicate the truncated decomposition form. Truncated decomposition can represent tensors with a smaller amount of data than the original large amount of data.
[0077] For the sake of brevity in derivation and description, this derivation only considers the scale k of the spatiotemporal graph convolution. S =1,k T In the case where = 1, the results of the following derivation can be directly generalized to the multi-scale case. The specific operation of step six is to approximate the multi-scale spatiotemporal graph convolutional network defined in step four as follows:
[0078]
[0079] Since the tensor matrix n-mode product satisfies the commutative and associative laws, the above equation is equal to:
[0080]
[0081] In the above equation, it can be seen that spatial correlation filtering, temporal correlation filtering, and feature space mapping can be exchanged for filtering operations on the corresponding dimension factor matrices after decomposition, denoted as ,
[0082]
[0083]
[0084]
[0085] Then we can further derive the expression form of the spatiotemporal graph convolutional network based on high-order principal component decomposition as follows:
[0086]
[0087] Finally, for a specific node k, the expression for spatiotemporal information aggregation in its spatiotemporal graph convolution model is:
[0088]
[0089] The above formula intuitively expresses that the node characteristics of node k come from the aggregation of information of spatially close nodes on the map and the aggregation of information of the node in the past. By constructing a temporal adjacency tensor, it is realized that each node follows a different temporal evolution pattern, thereby achieving a precise grasp of spatiotemporal correlation information and ensuring the accuracy of velocity prediction.
[0090] Step 7: Perform linear regression on the node embeddings learned in Step 6 to obtain the predicted velocity value, including the following sub-steps:
[0091] Step 7.1: For the learned node feature tensor Expanding its modulus-1 matrix is
[0092] Step 7.2, the expression for predicting the velocity information of the next T′ time slices based on the linear regression model is:
[0093]
[0094] in, Know If the time slice is 15 minutes and T′=4, it means that traffic speed information for the next hour is predicted.
[0095] Step 8: Calculate the mean squared error between the predicted and actual values, and minimize this error using the gradient optimizer Adam.
[0096]
[0097] In practical application, this invention was simulated using the SZ-taxi dataset, based on the PyTorch deep learning framework and collected from Shenzhen taxi trajectories. This dataset collected the average speed of vehicles traveling at 156 stations in Shenzhen, with data collected every 15 minutes (i.e., a 15-minute time slice). The dataset recorded traffic speed data for one month, from January 1st to January 31st, 2015. During the experiment, 80% of the dataset was used for training, and 20% was used for prediction. The experiment showed that the root mean square error (RMSE) between the predicted and actual speed values for the next 15, 30, 45, and 60 minutes, as disclosed in this invention, was 3.1, 3.5, 3.6, and 3.7, respectively.
[0098] Finally, it should be noted that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution, characterized in that: Includes the following steps: Step 1: Obtain speed data of vehicles passing through each station on the map at multiple times. Each time point corresponds to a graph structure data. Based on the temporal evolution characteristics of the traffic network, stitch together the data to obtain a spatiotemporal graph feature tensor. Define each station as a node, and the data is processed every... Data is collected every minute, the aforementioned This is called a time slice; Step 2: Obtain the location information of all stations on the traffic map, and construct their spatial relationship adjacency matrix based on the spatial relationship between different locations on the map; Step 3: Based on the dynamic sequence of the traffic map in the time dimension, link each node with the past... By connecting time slices themselves, a dynamic temporal adjacency matrix is constructed in the spatiotemporal graph; Step 4: Based on the two types of association matrices constructed in Step 2 and Step 3, construct a multi-scale spatiotemporal graph convolutional network model from the spatiotemporal graph feature tensor constructed in Step 1, constructing a graph structure from the spatial association within each time slice and the temporal association of each node at different times. Step 5: Apply the principal component decomposition algorithm of higher-order tensors to the spatiotemporal graph feature tensor constructed in Step 1 to decompose and calculate the core tensor and the factor matrix corresponding to each dimension. Step 6: Use the multi-scale spatiotemporal graph convolutional network model established in Step 4 to perform convolution operations on the core tensor and the factor matrices corresponding to each dimension obtained in Step 5. Step 7: Perform linear regression on the node embeddings learned in Step 6 to obtain the predicted velocity values. Step 4 includes the following steps. Step 4.1: Introduce the spatial adjacency matrix constructed in Step 2. For the spatiotemporal graph feature tensor constructed in step 1 Execute the spatial association information transfer, for the first Feature matrix of the spatial domain map of each time slice The expression for its spatial correlation filtering is: ， Step 4.2: Introduce the dynamic temporal adjacency matrix constructed in Step 3. For the spatiotemporal graph feature tensor constructed in step 1 Execution sequence association information transmission, for the first Feature matrix of a time series graph of each node Its expression in time-series correlation filtering is: Step 4.3: Introduce two operations for multidimensional tensors. Define the first type of computation: tensor ,matrix The tensor matrix n-mode product is defined as follows: ， ； Define the second type of calculation: The three-dimensional tensor batch multiplication is defined as follows: ， ； The multi-scale spatiotemporal graph convolutional network is defined as follows: ， In a graph network, nodes of Rank neighbor represents a node go through Nodes reachable in steps, adjacency matrix and The power contains the power of and The fusion of neighbor information. The higher-order principal component decomposition algorithm in step 5 is as follows: ， in, Represents the decomposed feature core tensor. , and This represents the factor matrix after decomposition in three dimensions: space, features, and time. , as well as .
2. The traffic speed prediction method based on high-order principal component decomposition spatiotemporal graph convolution according to claim 1, characterized in that, The specific operation of step 6 is to approximate the multi-scale spatiotemporal graph convolutional network defined in step 4 as follows: ， Since the tensor matrix n-mode product satisfies the commutative and associative laws, the above equation is equal to: In the above equation, spatial correlation filtering, temporal correlation filtering, and feature space mapping exchange are transformed into filtering operations on the corresponding dimension factor matrices after decomposition, denoted as . ， ， ， This leads to the following further derivation: the expression form of the spatiotemporal graph convolutional network based on high-order principal component decomposition is... ， Finally, for specific nodes The expression for spatiotemporal information aggregation in its spatiotemporal graph convolution model is: ； The above formula intuitively expresses the nodes. The node features are derived from the aggregation of information about spatially similar nodes on the map and the aggregation of information about the node in the past.