A OD passenger flow prediction method based on dynamic hypergraph convolutional neural network

Abstract

A method for predicting OD passenger flow based on a dynamic hypergraph convolutional neural network involves deep learning and other fields, especially OD passenger flow prediction tasks for hypergraph representation and graph convolutional networks. This method introduces a hypergraph convolutional neural network based on the high-order representation of traffic topology using a hypergraph, and uses the historical OD matrix to mine the spatial correlation of OD passenger flow at the starting point (original) and the destination (destination) to construct dynamic hyperedges, thereby achieving dynamic modeling of the complex spatial correlation of OD traffic. Compared with traditional mathematical models and machine learning methods, this method is more in-depth and accurate in modeling OD traffic characteristics, and improves the prediction accuracy.

Description

Technical Field

[0001] The present invention relates to fields such as graph theory and deep learning, and particularly to OD passenger flow prediction. Background Art

[0002] OD (Original Destination) volume refers to the travel volume between the starting point and the destination, which reflects the travel demand of passengers and can provide important reference for the allocation of passenger resources, alleviating passenger congestion, improving operational efficiency and passenger travel efficiency. Therefore, accurate prediction of passenger flow OD is of great significance.

[0003] Most of the current research focuses on the short-term prediction of inbound and outbound traffic, and relatively few studies focus on the short-term OD passenger flow prediction. However, accurate passenger flow OD prediction has guiding significance for passenger resource allocation and passenger congestion relief, so the prediction of passenger flow OD has important research significance.

[0004] Early OD demand forecasting methods were mainly based on statistical models or machine learning methods. The main statistical models include the least squares (GLS), maximum likelihood (ML) estimation, Bayesian method, etc. These methods rely on the assumption that the data is stationary, but this assumption is often not true in reality. The most representative methods in machine learning models include K nearest neighbor (KNN) and support vector regression (SVR). The prediction performance of these methods depends largely on feature samples and has high computational time complexity. At the same time, these models have difficulty modeling the dynamic and nonlinear characteristics in OD prediction.

[0005] In recent years, deep learning has made breakthroughs in many challenging learning tasks. Inspired by these works, more and more researchers have applied deep learning to OD passenger flow prediction. Qian et al. applied recursive multilayer perceptron to OD matrix prediction of road traffic. Toque et al. applied long short-term recursive neural network (LSTM) to OD passenger flow prediction of subway. However, these methods ignore the spatial correlation in the prediction problem, so the prediction accuracy is not high.

[0006] Liu et al. combined convolutional neural network (CNN) and long short-term recurrent neural network (LSTM). CNN models spatial correlation, but CNN is suitable for modeling Euclidean data, but traffic data, a non-Euclidean data, is not suitable for CNN modeling. Wang et al. combined graph convolutional neural network (GCN) and long short-term recurrent neural network (LSTM). The model simultaneously models spatial correlation and temporal correlation. Although graph-based methods have achieved remarkable results, ordinary graphs are difficult to represent complex spatial correlations. At the same time, these methods ignore the two aspects of correlation in OD passenger flow prediction, namely the correlation of the starting point and the correlation of the destination. Moreover, these methods are based on pre-defined graphs and cannot dynamically characterize spatial correlation. Summary of the invention

[0007] The present invention proposes an OD passenger flow prediction method based on a dynamic hypergraph convolutional neural network, which involves fields such as deep learning, and in particular, OD passenger flow prediction tasks for hypergraph representation and graph convolutional networks. This method introduces a hypergraph convolutional neural network based on the high-order representation of traffic topology structure using a hypergraph, and constructs dynamic hyperedges by mining the spatial correlation of OD passenger flow at the starting point (original) and the destination (destination) through the historical OD matrix, thereby realizing dynamic modeling of the complex spatial correlation of OD traffic. Compared with traditional mathematical models and machine learning methods, this method is more in-depth and accurate in modeling OD traffic characteristics, and improves the prediction accuracy.

[0008] A method for predicting OD passenger flow based on a dynamic hypergraph convolutional neural network, characterized by comprising the following steps:

[0009] (1) The road network is modeled using a hypergraph, where the hypergraph node V is the road network node and the hyperedge E is the road network line. The hypergraph representation is the same as the connection method of the road network nodes in the road network. Multiple nodes are connected by hyperedges in the hypergraph representation. From then on, the static hyperedge G is constructed using the road network topology structure. s .

[0010] (2) Collect historical data of passenger flow OD. The sequential time series of passenger flow OD history is {x0, x1, x2, ..., x t}, x t represents the OD value at time t. The historical passenger flow OD tensors are added along the time axis to obtain the passenger flow OD matrix of the period. Based on this, the cosine similarity analysis of the passenger flow OD matrix is ​​performed to construct a dynamic hyperedge G at the starting point (original) level. do and dynamic hyperedges G at the destination level dd .

[0011] The formula for calculating the correlation between the starting points i1 and i2 can be changed to:

[0012] Corr t (O i1 , O i2 )=COS(X[i1,:,t],X[i2,:,t]

[0013] Corr t (O i1 , O i2 ) represents the correlation between the two starting points, COS represents the cosine similarity, t represents the current time period, and X[i1,:,t] represents the i1th row of the OD matrix. It can be concluded that the nodes with strong correlation with themselves form a hyperedge. The correlation of the destination can be calculated in the same way.

[0014] (3) For the dynamic hypergraph, the spatiotemporal convolution module consists of a two-dimensional dynamic hypergraph convolution module (2D-HGCN) and a multi-receptive field dilated causal convolution module. The two-dimensional hypergraph convolution module (2D-HGCN) models the spatial correlation between the starting point (original) level and the destination (destination) level, and the multi-receptive field dilated causal convolution module models the temporal correlation.

[0015] The two-dimensional dynamic hypergraph convolution module is constructed as follows:

[0016] The Laplacian matrix of the hypergraph G is:

[0017]

[0018] in is the degree matrix of the hypergraph nodes, is the degree matrix of the hypergraph hyperedge, H is the incidence matrix of the hypergraph, W is the weight matrix of the hyperedge, Δ is a semi-positive definite matrix with only real eigenvalues. By eigendecomposing the hypergraph Laplace matrix and taking the eigenvector as the basis of Fourier transform, the hypergraph convolution expression can be obtained:

[0019] (x*g) HG =Φ((Φ T g)⊙(Φ T x))=Φ(g θ (Λ)⊙(Φ T x))

[0020] Among them, ⊙ is the Hadamard product, Φ T g is a trainable convolution kernel, denoted as g θ (Λ) is the function of Laplace eigenvalue, x is the characteristic data of the node on the hypergraph, Λ=diag(λ1,...,λ n ), is the non-negative eigenvalue matrix obtained by eigendecomposing the hypergraph Laplacian matrix, Φ=diag(Φ1,...,Φ n) is the orthogonal eigenvector obtained after the eigendecomposition of the hypergraph Laplacian matrix. Since the time complexity of calculating the eigendecomposition is too high in practical applications, the computational complexity can be reduced by using Chebyshev polynomials, namely:

[0021]

[0022] (x*g) HG Indicates the hypergraph convolution operation on the signal on the hypergraph. is the scaled and normalized Laplacian matrix, λ max is the maximum eigenvalue of Δ, θ k (k=0, 1, ...k) is the coefficient of the Kth term of the heptaphin polynomial, The k-th order Chebyshev polynomial is recursively defined as: Because hypergraphs can represent high-order relationships between nodes, further setting K to 1, the hypergraph convolution can be further simplified as:

[0023] θ0 and θ1 are learnable parameters in model training. In order to prevent overfitting problems, a single parameter θ is used to replace θ0 and θ1:

[0024]

[0025] Hypergraph convolution can be simplified as follows:

[0026]

[0027] Θ is the convolution kernel applied to extract features on the hypergraph nodes.

[0028] On the basis of the hypergraph convolution, a two-dimensional hypergraph convolution (2D-HGCN) operation is performed on the input features of the nodes, and the spatial correlation of the OD passenger flow at the origin (original) level and the destination (destination) level is integrated, which can be expressed as:

[0029]

[0030] L1 represents the hypergraph Laplacian matrix at the original level, L2 represents the hypergraph Laplacian matrix at the destination level, σ(·) is the activation function, T i (·), T j (·) is the Chebyshev polynomial, W l represents the learnable convolution kernel of layer 1, H( l ) is the output of the l-1 layer 2D hypergraph convolution, H (l+1)It is the output of the 2D-HGCN operation in the first layer.

[0031] Temporal Convolution Module:

[0032] The expansion of causal convolution captures the hidden correlation in the temporal layer, and the receptive field can be increased exponentially by stacking layers. The expansion of causal convolution operation can be expressed as:

[0033]

[0034] Among them, X is the input one-dimensional time series signal, f is the convolution kernel, M is the size of the convolution kernel, d represents the size of the dilation rate, s represents the position in the convolution kernel, t represents the time t, td×s represents the position moved in the time dimension, and the dilated causal convolution is performed in the time dimension. The parameters of the convolution kernel are shared for each pair of OD pairs.

[0035] Gating mechanisms are widely used in recurrent neural networks and are important for passing information through the temporal convolution layer. The gated temporal convolution is expressed as:

[0036] h=g(Θ1*X+b)⊙σ(Θ2*X+c)

[0037] Θ1, Θ2 represent dilated convolution operations, the two convolution operations are the same, b, c represent bias terms, which are learnable parameters, h represents the result of temporal convolution, ⊙ represents the Hadamard product, and g represents the hyperbolic tangent activation function, which is defined as follows:

[0038] σ represents the sigmoid activation function, which is defined as follows:

[0039]

[0040] After the convolution operation, the sigmoid function is used to activate the input layer, and the Hadamard product is performed with the result of the hyperbolic tangent function activation to obtain the characteristics of the input layer.

[0041] The framework of the dynamic hypergraph convolutional model is as follows Figure 1 As shown in the figure, it consists of 4 groups of spatiotemporal convolution modules. The input is first transformed by a linear layer and then passed to a gated temporal convolution module (Gated TCN) to model the temporal correlation of each OD pair. Secondly, a two-dimensional hypergraph convolution (2D-HGCN) is used to model the spatial correlation at the origin and destination levels. Each spatiotemporal convolution module has a residual connection and jump connection to the output layer. The output layer consists of two ReLu layers and two linear layers, and is normalized to the prediction dimension by the last linear layer.

[0042] ReLu stands for rectified linear unit, which is a commonly used activation function in artificial neural networks and is defined as follows: BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Dynamic Hypergraph Convolutional Model

[0044] Figure 2 Atrous Causal Convolution DETAILED DESCRIPTION

[0045] In one embodiment of the present invention, OD data covering 5 million people in 47 regions of Japan are used to select 425 days of data from 2020 / 1 / 1 / to 2021 / 2 / 28 to predict the OD traffic in 47 regions. First, the basic hypergraph and dynamic hypergraph are obtained according to steps 1)-2). Secondly, the above data and OD data are input into Figure 1 In the OD prediction model shown, the prediction results are obtained; finally, the prediction results are compared with the traditional methods. represents the predicted value of the OD matrix at time t, X t Represents the true value of the OD matrix at time t, and then calculates the mean absolute error MAE and root mean square error RMSE, which are two performance indicators. The two performance indicators are defined as follows:

[0046] Mean absolute error:

[0047]

[0048] Root Mean Square Error:

[0049]

[0050] Among them, z represents the total number of moments, represents the predicted value of the OD matrix at time t, X t Represents the true value of the OD matrix at time t.

[0051] We use 7 days of historical data to predict the OD traffic data for the next 7 days and compare it with 7 models: STResNet, PCRN, STGCN, DCRNN, Graph WaveNet, MPGCN, and ODCRN.

[0052] The comparison results are shown in the following table:

[0053] Model MAE RMSE STResNet 0.2822 0.4060 PCRN 0.2864 0.4044 STGCN 0.2910 0.4070 DCRNN 0.2954 0.4102 Graph WaveNet 0.2887 0.4040 MPGCN 0.2859 0.4011 ODCRN 0.2802 0.3947 The present invention 0.2731 0.3854

[0054] (1) High prediction accuracy. Compared with all baseline methods, under different evaluation indicators, the present invention can always achieve the smallest prediction error, indicating that the model can fit the data well and capture the changing patterns of the data.

[0055] (2) Spatiotemporal prediction capability: The prediction effect of the method of the present invention is higher than the prediction accuracy based on ordinary graphs, which shows that the present invention better models the spatial correlation and temporal correlation in OD prediction.

Claims

1. A method for predicting OD passenger flow based on a dynamic hypergraph convolutional neural network, characterized in that The following steps are involved: (1) The road network is modeled using a hypergraph, where the hypergraph node V is the road network node and the hyperedge E is the road network line. The hypergraph representation is the same as the connection method of the road network nodes in the road network. Multiple nodes are connected by hyperedges in the hypergraph representation. From then on, the static hyperedge G is constructed using the road network topology structure. s ; (2) Collect the historical data of passenger flow OD. The sequential time series of passenger flow OD history is {x0,x1,x2,...,x t }, x t represents the OD value at time t. The historical passenger flow OD tensors are added along the time axis to obtain the passenger flow OD matrix of the period. Based on this, the cosine similarity analysis of the passenger flow OD matrix is ​​performed to construct a dynamic hyperedge G at the starting point level. do and dynamic hyperedge G at the destination level dd ; (3) For the dynamic hypergraph, the spatiotemporal convolution module consists of a two-dimensional dynamic hypergraph convolution module (2D-HGCN) and a multi-receptive field dilated causal convolution module. The two-dimensional hypergraph convolution module models the spatial correlation between the starting point level and the destination level, and the multi-receptive field dilated causal convolution module models the temporal correlation. The two-dimensional dynamic hypergraph convolution module is constructed as follows: The Laplacian matrix of the hypergraph G is: in is the degree matrix of the hypergraph nodes, is the degree matrix of the hypergraph hyperedge, H is the incidence matrix of the hypergraph, W is the weight matrix of the hyperedge, Δ is a semi-positive definite matrix with only real eigenvalues. By eigendecomposing the hypergraph Laplace matrix and taking the eigenvector as the basis of Fourier transform, the hypergraph convolution expression can be obtained: (x*g) HG =Φ((Φ T g)⊙(Φ T x))=Φ(g θ (L)⊙(F T x)) Where ⊙ is the Hadamard product, Φ T g is a trainable convolution kernel, denoted as g θ (Λ) is the function of Laplace eigenvalue, x is the characteristic data of the node on the hypergraph, Λ=diag(λ1,...,λ n ), is the non-negative eigenvalue matrix obtained by eigendecomposing the hypergraph Laplacian matrix, Φ=diag(Φ1,...,Φ n ) are the orthogonal eigenvectors obtained by eigendecomposition of the hypergraph Laplacian matrix; Since the time complexity of calculating eigendecomposition is too high in practical applications, the computational complexity is reduced by using Chebyshev polynomials, namely: (x*g) HG Indicates the hypergraph convolution operation on the signal on the hypergraph. is the scaled and normalized Laplacian matrix, λ max is the maximum eigenvalue of Δ, θ k (k=0,1,...k) is the coefficient of the kth term of the Chebyshev polynomial, The k-th order Chebyshev polynomial is recursively defined as: Because the hypergraph represents the high-order associations between nodes, k is further set to 1, and the hypergraph convolution is further simplified to: θ0 and θ1 are learnable parameters in model training. In order to prevent overfitting problems, a single parameter θ is used to replace θ0 and θ1: Hypergraph convolution is simplified to the following representation: Θ is the convolution kernel applied to the hypergraph nodes to extract features; where X is the input one-dimensional time series signal; On the basis of the hypergraph convolution, a two-dimensional hypergraph convolution operation is performed on the input features of the nodes, and the spatial correlation of the OD passenger flow at the starting point level and the destination level is integrated, which can be expressed as: L1 represents the hypergraph Laplacian matrix at the origin level, L2 represents the hypergraph Laplacian matrix at the destination level, σ(·) is the activation function, T i (·), T j (·) is the Chebyshev polynomial, W l represents the learnable convolution kernel of layer l, H (l) is the output of the l-1 layer 2D hypergraph convolution, H (l+1) It is the output of the two-dimensional hypergraph convolution operation on the lth layer; Temporal Convolution Module: The hidden correlations in the temporal layer are captured by dilated causal convolution, and the receptive field increases exponentially by stacking layers. The dilated causal convolution operation is expressed as: Among them, X is the input one-dimensional time series signal, f is the convolution kernel, M is the size of the convolution kernel, s represents the position in the convolution kernel, t represents the time t, d represents the size of the dilation rate, td×s represents the position moved in the time dimension, and the dilated causal convolution is performed in the time dimension. The parameters of the convolution kernel for each pair of OD pairs are shared; Gating mechanisms are widely used in recurrent neural networks and are important for passing information through the temporal convolution layer; the gated temporal convolution is expressed as: h=g(Θ1*X+b)⊙σ(Θ2*X+c) Θ1 and Θ2 represent dilated convolution operations. The two convolution operations are the same. b and c represent bias terms, ⊙ represents the Hadamard product, h represents the result of temporal convolution, g represents the hyperbolic tangent activation function, and σ represents the sigmoid function. After the convolution operation, the sigmoid function is used to activate the ratio of the input to the next layer, and the Hadamard product is performed with the result of the hyperbolic tangent function activation to obtain the characteristics of the input to the next layer.

Images