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Graph convolutional dynamic recurrent network with attention for traffic forecasting

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Abstract

Traffic forecasting is a typical spatio-temporal graph modeling problem, which has become one of the key technical issues in modern intelligent transportation systems. However, existing methods cannot capture the long-range spatial and temporal characteristics very well because of the complexity and heterogeneity of the traffic flows. In this paper, a new deep learning framework called Graph Convolutional Dynamic Recurrent Network with Attention (GCDRNA) is proposed to predict the traffic state in the traffic network. GCDRNA mainly consists of two components, which are Graph Convolutional with Attention (GCA) block and Dynamic GRU with Attention (DGRUA) block. GCA block can capture both global and local spatial correlations of the traffic flows by k-hop GC, similarity GC and spatial attention modules. DGRUA block captures the long-term temporal correlation of the traffic flows by Dynamic GRU (DGRU) and Node Attention Unit (NAU) modules. Experimental results show that GCDRNA achieves the best prediction performance compared with other baseline models on two public real-world traffic datasets.

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Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This research is supported by National Natural Science Foundation of China under Grants Nos. 61872191 and 41571389.

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Authors and Affiliations

  1. School of Computer, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Jiagao Wu, Junxia Fu, Hongyan Ji & Linfeng Liu

  2. Jiangsu Key Laboratory of Big Data Security and Intelligent Processing, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China

    Jiagao Wu, Junxia Fu, Hongyan Ji & Linfeng Liu

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  1. Jiagao Wu
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  2. Junxia Fu
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  3. Hongyan Ji
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  4. Linfeng Liu
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Correspondence to Jiagao Wu.

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Junxia Fu, HongyanJi and Linfeng Liu are contributed equally to this work.

Complexity Analysis of GCDRNA

Complexity Analysis of GCDRNA

As Fig. 2, GCDRNA mainly consists of two blocks, i.e., GCA block and DGRUA block. Furthermore, GCA block consists of k-hop GC, similarity GC and spatial attention modules, and DGRUA block consists of DGRU and NAU modules. We will analyze the complexity of these modules one by one as follows.

Since the time complexities of Eqs. (2) and (3) are \(O(KN^3)\) and \(O(N^2C)\) respectively, the time complexity of the k-hop GC module will be \(O(K(KN^3+N^2C))\). Next, the time complexities of Eqs. (4), (5) and (6) are \(O(N^2C)\), O(KNC) and \(O(K^2NC)\), respectively. Then, the time complexity of the spatial attention module will be \(O(K^2NC+N^2C)\). Similarly, the time complexity of similarity GC is \(O(N^2(D+C))\) according to Eqs. (7) and (8). Now, put the time complexities of these three modules together and consider that \(C, D<< N\) as usual, we can obtain the time complexity of GCA block as \(O(K^2N^3)\). And with the same method, it is easy to obtain the space complexity of GCA as \(O(KN^2)\).

The time complexities of Eqs. (10)-(13), (15) and (17) are all O(NCQ), and the time complexities of Eqs. (14), (16) and (18) are all O(NQ). Then, the time complexity of DGRU module is O(NCQ). Similarly, the time complexity of NAU module is \(O(NQQ^{\prime })\). Since Q and \(Q^{\prime }\) are also no greater than N, the time complexity of DGRUA block can be expressed as \(O(N^3)\). With the same approach, we can obtain the the space complexity of DGRUA as \(O(N^2)\).

Finally, according the above analysis, we can find the time complexity of GCDRNA as \(O(K^2N^3)\), and space complexity as \(O(KN^2)\). When K is small, the time and space complexities of GCDRNA will approximately be \(O(N^3)\) and \(O(N^2)\), respectively, which are similar to most related graph convolution models for traffic prediction. Therefore, the computation cost of the proposed GCDRNA is moderate and acceptable.

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Wu, J., Fu, J., Ji, H. et al. Graph convolutional dynamic recurrent network with attention for traffic forecasting. Appl Intell 53, 22002–22016 (2023). https://doi.org/10.1007/s10489-023-04621-5

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