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基于图正则化和Schatten-p范数最小化的交通数据恢复

陈小波 梁书荣 柯佳 陈玲 胡煜

陈小波, 梁书荣, 柯佳, 陈玲, 胡煜. 基于图正则化和Schatten-p范数最小化的交通数据恢复[J]. 西南交通大学学报, 2022, 57(6): 1326-1333. doi: 10.3969/j.issn.0258-2724.20210295
引用本文: 陈小波, 梁书荣, 柯佳, 陈玲, 胡煜. 基于图正则化和Schatten-p范数最小化的交通数据恢复[J]. 西南交通大学学报, 2022, 57(6): 1326-1333. doi: 10.3969/j.issn.0258-2724.20210295
CHEN Xiaobo, LIANG Shurong, KE Jia, CHEN Ling, HU Yu. Traffic Data Imputation Based on Graph Regularization and Schatten-p Norm Minimization[J]. Journal of Southwest Jiaotong University, 2022, 57(6): 1326-1333. doi: 10.3969/j.issn.0258-2724.20210295
Citation: CHEN Xiaobo, LIANG Shurong, KE Jia, CHEN Ling, HU Yu. Traffic Data Imputation Based on Graph Regularization and Schatten-p Norm Minimization[J]. Journal of Southwest Jiaotong University, 2022, 57(6): 1326-1333. doi: 10.3969/j.issn.0258-2724.20210295

基于图正则化和Schatten-p范数最小化的交通数据恢复

doi: 10.3969/j.issn.0258-2724.20210295
基金项目: 国家自然科学基金(61773184);国家重点研发计划(2018YFB0105000);江苏省六大人才高峰高层次人才项目(JXQC-007)
详细信息
    作者简介:

    陈小波(1982—),男,研究员,博士,研究方向为智能交通,E-mail:1000003032@ujs.edu.cn

  • 中图分类号: U495;TP311.1

Traffic Data Imputation Based on Graph Regularization and Schatten-p Norm Minimization

  • 摘要:

    为充分利用交通数据低秩特性与局部近邻关系,准确恢复交通数据采集系统中的缺失数据,首先,应用基于核范数的低秩矩阵补全模型对交通数据矩阵进行预插补,以获得缺失值的初始估计,基于此,构建表征数据局部近邻结构的图模型;然后,提出融合图正则化和Schatten-p范数最小化的交通数据缺失值恢复模型;进一步,提出基于交替方向乘子框架的优化算法,求解缺失值恢复的最优化问题,得到最终的数据恢复结果;最后,用实际的高速公路交通流量和速度数据比较多种方法的恢复误差,同时给出所提方法的参数敏感性分析. 实验结果表明:在完全随机缺失、随机缺失和混合缺失模式下,缺失率为10% ~ 50%时,相比于局部最小二乘、概率主成分分析和低秩矩阵补全等方法,基于图正则化和Schatten-p范数最小化的算法恢复误差降低了3.02% ~ 28.49%.

     

  • 图 1  交通数据恢复算法框架

    Figure 1.  Diagram of traffic data imputation algorithm

    图 2  ADMM流程

    Figure 2.  Flow chart of ADMM

    图 3  同一天中不同传感器交通流和交通速度的变化情况

    Figure 3.  Changes in traffic flow and speed from different sensors over the same day

    图 4  数据缺失模式模拟示例

    Figure 4.  Simulation examples of data missing modes

    图 5  SPGR模型在交通流量数据上的RMSE随参数$ p $$ K $$ \lambda $的变化

    Figure 5.  RMSEs of SPGR model on traffic flow data varied with the parameters of$ p、K、\lambda $

    表  1  MCAR模式下不同算法的恢复误差

    Table  1.   Imputation error of different algorithms in MCAR mode

    算法δ交通流量交通速度
    RMSE/(辆·
    (15 min)−1
    MAPE/%RMSE/
    (km·h−1
    MAPE/%
    LRMC 0.1 80.63 13.29 2.53 5.76
    0.2 83.80 13.75 2.64 6.07
    0.3 86.58 14.29 2.65 6.40
    0.4 90.94 14.86 2.79 6.83
    0.5 95.91 15.74 2.99 7.37
    PPCA 0.1 79.06 13.00 2.41 5.82
    0.2 82.98 13.80 2.53 6.08
    0.3 85.47 14.67 2.72 6.27
    0.4 89.69 15.55 2.81 6.85
    0.5 95.83 17.11 2.98 6.95
    LLS 0.1 76.62 13.26 3.15 7.40
    0.2 82.26 14.21 3.28 7.74
    0.3 89.94 15.81 3.43 8.13
    0.4 99.01 17.61 3.67 8.82
    0.5 113.01 19.92 4.06 9.76
    SP 0.1 75.77 12.73 2.39 5.65
    0.2 78.36 13.18 2.50 5.95
    0.3 82.43 13.73 2.63 6.31
    0.4 88.06 14.51 2.78 6.74
    0.5 93.66 15.56 2.98 7.29
    SPGR 0.1 74.56 12.67 2.38 5.64
    0.2 76.96 13.17 2.50 5.95
    0.3 80.93 13.59 2.63 6.30
    0.4 86.24 14.38 2.76 6.70
    0.5 92.40 15.44 2.95 7.19
    下载: 导出CSV

    表  2  MAR模式下不同算法的恢复误差

    Table  2.   Imputation error of different algorithms in MAR mode

    算法δ交通流量交通速度
    RMSE/(辆·
    (15 min)−1
    MAPE/%RMSE/
    (km·h−1
    MAPE/%
    LRMC 0.1 98.31 14.62 3.38 8.42
    0.2 100.92 15.14 3.45 8.68
    0.3 103.11 15.72 3.48 8.77
    0.4 106.22 16.30 3.55 8.98
    0.5 109.81 17.03 3.63 9.15
    PPCA 0.1 90.14 13.71 3.60 8.48
    0.2 95.13 14.70 3.75 8.83
    0.3 97.45 15.49 3.77 8.87
    0.4 101.55 18.49 3.80 8.93
    0.5 105.51 17.72 3.85 9.02
    LLS 0.1 84.31 13.40 3.75 8.89
    0.2 91.89 14.70 3.86 9.30
    0.3 100.10 16.38 3.91 9.40
    0.4 112.55 16.44 4.11 10.02
    0.5 130.83 21.11 4.51 10.69
    SP 0.1 88.08 13.64 3.26 8.17
    0.2 90.99 14.09 3.37 8.42
    0.3 94.50 14.96 3.43 8.60
    0.4 99.86 15.83 3.53 8.86
    0.5 105.22 16.77 3.60 9.00
    SPGR 0.1 86.31 13.51 3.22 7.97
    0.2 89.01 13.93 3.31 8.23
    0.3 92.76 14.79 3.36 8.35
    0.4 97.51 15.63 3.48 8.64
    0.5 101.82 16.62 3.56 8.81
    下载: 导出CSV

    表  3  MIXED模式下不同算法的恢复误差

    Table  3.   Imputation error of different algorithms in MIXED mode

    算法δ交通流量交通速度
    RMSE/(辆·
    (15 min)−1
    MAPE/%RMSE/
    (km·h−1
    MAPE/%
    LRMC 0.1 89.57 13.56 2.97 7.10
    0.2 92.73 14.31 2.99 7.28
    0.3 95.18 14.70 3.10 7.59
    0.4 99.00 15.61 3.19 7.86
    0.5 103.12 16.24 2.99 8.24
    PPCA 0.1 84.40 12.95 3.13 7.24
    0.2 89.37 14.08 3.10 7.33
    0.3 91.37 14.76 3.18 7.57
    0.4 95.26 16.10 3.24 7.73
    0.5 100.80 17.33 2.98 7.91
    LLS 0.1 79.48 13.11 3.65 8.05
    0.2 86.60 14.34 3.54 8.39
    0.3 93.75 15.77 3.66 8.74
    0.4 104.31 17.83 3.82 9.20
    0.5 118.90 20.15 4.06 10.09
    SP 0.1 82.10 12.85 2.92 6.95
    0.2 85.54 13.62 3.02 7.10
    0.3 88.72 14.34 3.10 7.49
    0.4 94.10 15.35 3.18 7.79
    0.5 99.60 16.18 3.31 8.15
    SPGR 0.1 80.51 12.74 2.86 6.81
    0.2 83.82 13.49 2.89 7.03
    0.3 86.62 14.18 3.02 7.36
    0.4 92.01 15.21 3.10 7.62
    0.5 97.81 16.04 3.24 7.98
    下载: 导出CSV

    表  4  在交通流量数据上不同初始化方法对SPGR恢复误差的影响

    Table  4.   Effect of different initialization methods on SPGR imputation error on traffic flow data 辆/15 min

    数据模式KNNLLSLRMC
    MCAR81.2180.9980.93
    MAR93.6893.1492.76
    MIXED87.7487.4886.62
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-13
  • 修回日期:  2021-09-10
  • 网络出版日期:  2022-09-01
  • 刊出日期:  2021-09-13

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