Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (5): 1708-1715.doi: 10.13229/j.cnki.jdxbgxb20200535

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Data imputation approach for lane⁃scale traffic flow based on tensor decomposition theory

Wen-qi LU1(),Tian ZHOU2,Yuan-li GU2,Yi-kang RUI1(),Bin RAN1   

  1. 1.School of Transportation，Southeast University，Nanjing 211189，China
    2.Key Laboratory of Transport Industry of Big Data Application Technologies for Comprehensive Transport，Ministry of Transport，Beijing Jiaotong University，Beijing 100044，China
  • Received:2020-07-16 Online:2021-09-01 Published:2021-09-16
  • Contact: Yi-kang RUI E-mail:lplwq93@126.com;101012189@seu.edu.cn

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Abstract:

To reduce the impact of the missing traffic data on traffic flow prediction， advanced driving assistance， traffic state estimation， and other traffic applications， an adaptive rank Tucker decomposition-based imputation approach （ARTDI） is proposed to recover the missing data and improve the data quality. Multi-lane traffic flow data are represented as a tensor to make full use of the spatial-temporal characteristics of traffic flow. The objective function of the imputation approach is determined through Tucker decomposition and solved by the momentum gradient descent method. Three missing types of traffic datasets including the completely random missing， random missing， and mixed missing were constructed based on the lane-scale traffic speed data of the multiple road sections of the expressway in Beijing. The experimental results indicate that the mean absolute percentage errors （MAPE） of the ARTDI approach are 11.67%， 12.03%， and 11.89% respectively under the three missing types. Besides， the results demonstrate that with the increase of the missing rate， the ARTDI approach outperforms the benchmark approaches in terms of recovery accuracy under different missing types and the MAPEs of the ARTDI approach does not increase significantly. Hence， the ARTDI approach is stable and applicable.

Key words: traffic system engineering, data imputation, tensor decomposition theory, Tucker decomposition, lane-scale traffic flow

CLC Number: 

  • U491

Fig.1

Tucker decomposition of a third-order tensor"

Fig.2

Research scope"

Fig.3

Missing types of multi-lane traffic data"

Fig.4

Tensor pattern construction"

Table 1

Parameters summary of compared algorithms"

模型名称模型参数

KNN

SVR

TDI

CP-WOPT

欧氏距离，k=7

径向基函数，gamma=0.1，C=5

R］

R=30

Fig.5

Comparison of recovery results under different thresholds P"

Table 2

Comparison of MAPEs of different data imputation approaches under MCR mode %"

缺失率/%KNNSVRCP-WOPTTDIARTDI
1011.6912.2516.5511.8210.84
2014.0514.2218.0712.6411.22
3016.3116.6118.8113.6311.68
4020.6620.9421.3814.3512.07
5029.0728.6224.7216.5112.52
平均值18.3618.5319.9013.7911.67

Table 3

Comparison of MAPEs of different data imputation approaches under MR mode %"

缺失率/%KNNSVRCP-WOPTTDIARTDI
1012.3311.3116.4214.3711.52
2014.5414.7518.0315.6211.59
3016.1915.9320.3617.6412.02
4020.4021.8222.1019.0512.38
5028.0231.4727.6521.8212.66
平均值18.3019.0520.9117.7012.03

Table 4

Comparison of MAPEs of different data imputation approaches under MCR&MR mode"

缺失率/%KNNSVR

CP-

WOPT

TDIARTDI
1012.2512.4116.6812.8211.19
2014.2214.7717.7215.0411.70
3016.6116.9718.7916.0611.73
4020.9421.8521.0116.9912.26
5028.6232.7724.7119.6812.58
平均值18.5319.7519.7816.1211.89

Fig.6

Recovery results of different lanes"

Table 5

Comparison of MAPE of ARTDI model under different missing modes"

张量模式MRMCRMR&MCR平均值
30×24×319.0317.6718.5018.77
30×168×312.0311.6711.8911.96
30×168×916.9115.9516.7816.85
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