Spatio-temporal hyper-relationship graph convolutional network for traffic flow forecasting

doi:10.11772/j.issn.1001-9081.2021060956

Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (12): 3578-3584.DOI: 10.11772/j.issn.1001-9081.2021060956

Special Issue: 第十八届中国机器学习会议(CCML 2021)

• The 18th China Conference on Machine Learning • Previous Articles Next Articles

Spatio-temporal hyper-relationship graph convolutional network for traffic flow forecasting

Yongkai ZHANG¹^,², Zhihao WU¹^,²^,³, Youfang LIN¹^,²^,³, Yiji ZHAO¹^,²()

^1.School of Computer and Information Technology，Beijing Jiaotong University，Beijing 100044，China
^2.Beijing Key Lab of Traffic Data Analysis and Mining （Beijing Jiaotong University），Beijing 100044，China
^3.Key Laboratory of Intelligent Application Technology for Civil Aviation Passenger Services，Civil Aviation Administration of China，Beijing 100105，China

Received:2021-05-12 Revised:2021-06-15 Accepted:2021-06-29 Online:2021-12-28 Published:2021-12-10
Contact: Yiji ZHAO
About author:ZHANG Yongkai， born in 1997， M. S. candidate. His research interests include traffic data mining， machine learning.
WU Zhihao， born in 1984， Ph. D.， associate professor. His research interests include social network analysis， data mining， machine learning.
LIN Youfang， born in 1971， Ph. D.， professor. His research interests include intelligent system， complex network， traffic data mining.
Supported by:
the Fundamental Research Funds for the Central Universities(2019JBM023)

面向交通流量预测的时空超关系图卷积网络

张永凯¹^,², 武志昊¹^,²^,³, 林友芳¹^,²^,³, 赵苡积¹^,²()

^1.北京交通大学计算机与信息技术学院，北京 100044
^2.交通数据分析与挖掘北京市重点实验室（北京交通大学），北京 100044
^3.中国民用航空局民航旅客服务智能化应用技术重点实验室，北京 100105

通讯作者: 赵苡积
作者简介:张永凯（1997—），男，河南信阳人，硕士研究生，主要研究方向：交通数据挖掘、机器学习
武志昊（1984—），男，山西大同人，副教授，博士，主要研究方向：社交网络分析、数据挖掘、机器学习
林友芳（1971—），男，福建武平人，教授，博士，主要研究方向：智能系统、复杂网络、交通数据挖掘；
基金资助:
中央高校基本科研业务费专项资金资助项目(2019JBM023)

Abstract

Abstract:

Traffic flow forecasting is an important research topic for the intelligent transportation system， however， this research is very challenging because of the complex local spatio-temporal relationships among traffic objects such as stations and sensors. Although some previous studies have made great progress by transforming the traffic flow forecasting problem into a spatio-temporal graph forecasting problem， in which the direct correlations across spatio-temporal dimensions among traffic objects are ignored. At present， there is still lack of a comprehensive modeling approach for the local spatio-temporal relationships. A novel spatio-temporal hypergraph modeling scheme was first proposed to address this problem by constructing a kind of spatio-temporal hyper-relationships to comprehensively model the complex local spatio-temporal relationships. Then， a Spatio-Temporal Hyper-Relationship Graph Convolutional Network （STHGCN） forecasting model was proposed to capture these relationships for traffic flow forecasting. Extensive comparative experiments were conducted on four public traffic datasets. Experimental results show that compared with the spatio-temporal forecasting models such as Attention based Spatial-Temporal Graph Convolutional Network （ASTGCN） and Spatial-Temporal Synchronous Graph Convolutional Network （STSGCN）， STHGCN achieves better results in Root Mean Square Error （RMSE）， Mean Absolute Error （MAE） and Mean Absolute Percentage Error （MAPE）； and the comparison of the running time of different models also shows that STHGCN has higher inference speed.

Key words: traffic flow forecasting, local spatio-temporal relationship, spatio-temporal graph forecasting, hypergraph, spatio-temporal hyper-relationship

摘要：

交通流量预测是智能交通系统中的重要研究课题，然而，交通对象（如站点、传感器）之间存在的复杂局部时空关系使得这项研究颇具挑战。尽管以往的一些研究将流量预测问题转化为一个时空图预测问题从而取得了较大的进展，但是它们忽略了交通对象们跨时空维度的直接关联性。目前仍缺乏一种全面建模局部时空关系的方法。针对这一问题，首先提出一种新颖的时空超图建模方案，通过构造一种时空超关系来全面地建模复杂的局部时空关系；然后提出一种时空超关系图卷积网络（STHGCN）预测模型来捕获这些关系用于交通流量预测。在四个公开交通数据集上进行了大量对比实验，结果表明，相比ASTGCN、时空同步图卷积网络（STSGCN）等时空预测模型，STHGCN在均方根误差（RMSE）、平均绝对误差（MAE）、平均绝对百分比误差（MAPE）这三个评价指标上均取得了更优的结果，不同模型运行时间的对比结果也表明，STHGCN有着更高的推理速度。

关键词: 交通流量预测, 局部时空关系, 时空图预测, 超图, 时空超关系

CLC Number:

TP302.1

Yongkai ZHANG, Zhihao WU, Youfang LIN, Yiji ZHAO. Spatio-temporal hyper-relationship graph convolutional network for traffic flow forecasting[J]. Journal of Computer Applications, 2021, 41(12): 3578-3584.

张永凯, 武志昊, 林友芳, 赵苡积. 面向交通流量预测的时空超关系图卷积网络[J]. 《计算机应用》唯一官方网站, 2021, 41(12): 3578-3584.

Figures/Tables 7

References 24

1	ZHANG J P， WANG F Y， WANG K F， et al. Data-driven intelligent transportation systems： a survey［J］. IEEE Transactions on Intelligent Transportation Systems， 2011， 12（4）： 1624-1639. 10.1109/tits.2011.2158001
2	吕明琪，洪照雄，陈铁明. 一种融合时空关联与社会事件的交通流预测方法［J］. 计算机科学， 2021， 48（2）： 264-270. 10.11896/jsjkx.200300098
	LYU M Q， HONG Z X， CENG T M. Traffic flow forecasting method combining spatio-temporal correlations and social events［J］. Computer Science， 2021， 48（2）： 264-270. 10.11896/jsjkx.200300098
3	YU B， YIN H T， ZHU Z X. Spatio-temporal graph convolutional networks： a deep learning framework for traffic forecasting［C］// Proceedings of the 27th International Joint Conference on Artificial Intelligence. ［S.l.］： IJCAI Organization， 2018： 3634-3640. 10.24963/ijcai.2018/505
4	LI Y G， YU R， SHAHABI C， et al. Diffusion convolutional recurrent neural network： data-driven traffic forecasting［EB/OL］. （2018-02-22）［2021-03-10］.. 10.1109/ictai50040.2020.00063
5	KIPF T N， WELLING M. Semi-supervised classification with graph convolutional networks［EB/OL］. （201702-22）［2021-03-10］..
6	HOCHREITER S， SCHMIDHUBER J. Long short-term memory［J］. Neural Computation， 1997， 9（8）： 1735-1780. 10.1162/neco.1997.9.8.1735
7	CHUNG J， GULCEHRE C， CHO K， et al. Empirical evaluation of gated recurrent neural networks on sequence modeling［EB/OL］. （2014-12-11）［2021-03-10］.. 10.1007/978-3-662-44848-9_34
8	LeCUN Y， BOTTOU L， BENGIO Y， et al. Gradient-based learning applied to document recognition［J］. Proceedings of the IEEE， 1998， 86（11）： 2278-2324. 10.1109/5.726791
9	SONG C， LIN Y F， GUO S N， et al. Spatial-temporal synchronous graph convolutional networks： a new framework for spatial-temporal network data forecasting［C］// Proceedings of the 34th AAAI Conference on Artificial Intelligence. Palo Alto， CA： AAAI Press， 2020： 914-921. 10.1609/aaai.v34i01.5438
10	FENG Y F， YOU H X， ZHANG Z Z， et al. Hypergraph neural networks［C］// Proceedings of the 33rd AAAI Conference on Artificial Intelligence. Palo Alto： CA： AAAI Press， 2019： 3558-3565. 10.1609/aaai.v33i01.33013558
11	KAMARIANAKIS Y， PRASTACOS P. Forecasting traffic flow conditions in an urban network： comparison of multivariate and univariate approaches［J］. Transportation Research Record， 2003， 1857（1）： 74-84. 10.3141/1857-09
12	VOORT M VAN DER， DOUGHERTY M， WATSON S. Combining Kohonen maps with ARIMA time series models to forecast traffic flow［J］. Transportation Research Part C： Emerging Technologies， 1996， 4（5）： 307-318. 10.1016/s0968-090x(97)82903-8
13	翁钢民，李凌雁. 旅游客流量预测：基于季节调整的PSO-SVR模型研究［J］. 计算机应用研究， 2014， 31（3）： 692-695.
	WENG G M， LI L Y. Study on tourism flow forecast： based on seasonal adjustment’ PSO-SVR model［J］. Application Research of Computers， 2014， 31（3）： 692-695.
14	林培群，周楠楠. 基于多特征GBDT模型的收费站短时交通流量预测［J］. 广西大学学报（自然科学版）， 2018， 43（3）： 340-347.
	LIN P Q， ZHOU N N. Short-term traffic flow prediction at toll stations based on multi-feature GBDT model［J］. Journal of Guangxi University （Natural Science Edition）， 2018， 43（3）： 340-347.
15	ZHANG J B， ZHENG Y， QI D K. Deep spatio-temporal residual networks for citywide crowd flows prediction［C］// Proceedings of the 31st AAAI Conference on Artificial Intelligence. Palo Alto， CA： AAAI Press， 2017： 1655-1661. 10.1016/j.artint.2018.03.002
16	GUO S N， LIN Y F， LI S J， et al. Deep spatial-temporal 3D convolutional neural networks for traffic data forecasting［J］. IEEE Transactions on Intelligent Transportation Systems， 2019， 20（10）： 3913-3926. 10.1109/tits.2019.2906365
17	SHI X J， CHEN Z R， WANG H， et al. Convolutional LSTM network： a machine learning approach for precipitation nowcasting［C］// Proceedings of the 28th International Conference on Neural Information Processing Systems. Cambridge： MIT Press， 2015： 802-810.
18	冯宁，郭晟楠，宋超，等. 面向交通流量预测的多组件时空图卷积网络［J］. 软件学报， 2019， 30（3）： 759-769. 10.13328/j.cnki.jos.005697
	FENG N， GUO S N， SONG C， et al. Multi-component spatial-temporal graph convolution networks for traffic flow forecasting［J］. Journal of Software， 2019， 30（3）： 759-769. 10.13328/j.cnki.jos.005697
19	GUO S N， LIN Y F， FENG N， et al. Attention based spatial-temporal graph convolutional networks for traffic flow forecasting［C］// Proceedings of the 33rd AAAI Conference on Artificial Intelligence. Palo Alto， CA： AAAI Press， 2019： 922-929. 10.1609/aaai.v33i01.3301922
20	WU Z H， PAN S R， LONG G D， et al. Graph WaveNet for deep spatial-temporal graph modeling［C］// Proceedings of the 28th International Joint Conference on Artificial Intelligence. ［S.l.］： IJCAI Organization， 2019： 1907-1913. 10.24963/ijcai.2019/264
21	WU Z H， PAN S R， LONG G D， et al. Connecting the dots： multivariate time series forecasting with graph neural networks［C］// Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York： ACM， 2020： 753-763. 10.1145/3394486.3403118
22	ZHANG Q， CHANG J L， MENG G F， et al. Spatio-temporal graph structure learning for traffic forecasting［C］// Proceedings of the 34th AAAI Conference on Artificial Intelligence. Palo Alto， CA： AAAI Press， 2020： 1177-1185. 10.1609/aaai.v34i01.5470
23	LI M Z， ZHU Z X. Spatial-temporal fusion graph neural networks for traffic flow forecasting［EB/OL］. （2021-03-06）［2021-03-10］.. 10.1109/ijcnn52387.2021.9534420
24	DONG Y， SAWIN W， BENGIO Y. HNHN： hypergraph networks with hyperedge neurons［EB/OL］. （2020-06-22）［2021-03-10］..

数据	节点数	时间范围
PEMS03	358	2018-09-01—2018-11-30
PEMS04	307	2018-01-01—2018-02-28
PEMS07	883	2017-05-01—2017-08-31
PEMS08	170	2016-07-01—2016-08-31

数据	节点数	时间范围
PEMS03	358	2018-09-01—2018-11-30
PEMS04	307	2018-01-01—2018-02-28
PEMS07	883	2017-05-01—2017-08-31
PEMS08	170	2016-07-01—2016-08-31

数据	指标	VAR	SVR	GRU	DCRNN	STGCN	ASTGCN	STSGCN	STHGCN
PEMS03-5	MAE	21.18	21.75	19.96±0.03	17.43±0.03	17.93±0.03	18.29±0.24	17.43±0.08	16.80±0.04
	MAPE	21.97	21.00	19.83±0.42	16.78±0.16	18.54±0.20	18.30±0.53	16.48±0.12	17.35±0.27
	RMSE	35.04	34.70	32.90±0.28	30.18±0.42	29.92±0.36	30.40±0.40	28.98±0.49	28.56±0.30
PEMS03-10	MAE	51.43	55.57	48.85±0.11	38.20±0.11	40.21±0.08	38.83±0.82	37.09±0.35	34.38±0.25
	MAPE	27.93	28.74	27.97±1.22	19.12±0.19	23.40±0.61	21.41±1.02	18.11±0.20	16.81±0.37
	RMSE	84.65	91.80	81.68±0.21	66.89±0.78	67.77±0.41	65.13±1.29	63.16±0.89	60.13±0.30
PEMS03-15	MAE	95.67	105.26	87.87±0.30	66.60±0.19	70.74±0.35	63.34±2.62	62.59±0.45	55.05±0.46
	MAPE	38.01	39.54	38.29±0.98	23.33±0.12	27.67±0.73	23.59±1.89	20.44±0.20	18.70±0.52
	RMSE	154.01	172.03	145.61±0.29	118.40±0.88	119.05±0.63	105.54±4.10	107.49±0.69	96.29±1.08
PEMS04-5	MAE	24.00	28.11	25.68±0.01	23.58±0.05	23.10±0.03	22.60±0.39	21.10±0.04	20.50±0.05
	MAPE	18.06	19.29	17.83±0.18	15.64±0.02	15.89±0.14	16.72±0.29	13.74±0.04	13.58±0.13
	RMSE	37.01	43.54	39.81±0.03	37.04±0.15	35.47±0.06	34.22±0.50	33.98±0.05	32.35±0.07
PEMS04-10	MAE	50.33	69.01	61.66±0.11	52.23±0.15	51.24±0.49	45.06±0.67	43.42±0.37	39.23±0.30
	MAPE	22.10	27.28	25.70±0.65	18.91±0.07	20.50±0.52	18.90±0.62	14.56±0.18	13.36±0.14
	RMSE	76.54	108.63	95.43±0.14	83.55±0.33	77.78±0.54	68.35±0.91	69.05±0.69	62.20±0.50
PEMS04-15	MAE	85.17	126.54	112.97±0.28	90.63±0.75	95.54±2.57	72.26±1.46	71.89±0.50	59.38±0.80
	MAPE	28.65	40.35	41.45±1.02	26.96±0.19	32.57±1.37	23.27±1.48	17.81±0.19	14.72±0.13
	RMSE	127.54	199.02	173.21±0.27	148.14±1.45	145.63±3.62	108.15±1.78	114.93±0.85	94.92±1.43
PEMS07-5	MAE	35.91	31.68	27.45±0.03	24.12±0.23	26.53±0.07	26.73±0.74	24.19±0.06	23.94±0.08
	MAPE	16.41	13.84	12.30±0.10	10.68±0.50	12.14±0.08	13.07±0.60	10.15±0.01	10.12±0.08
	RMSE	55.48	48.95	42.74±0.05	37.72±0.25	40.77±0.06	40.29±1.30	39.35±0.24	37.53±0.14
PEMS07-10	MAE	105.04	82.05	68.06±0.16	53.24±0.05	65.06±0.32	58.39±1.52	53.94±0.65	52.08±0.47
	MAPE	24.90	18.68	16.60±0.27	11.92±0.02	15.82±0.31	14.95±2.78	11.44±0.16	11.08±0.04
	RMSE	153.68	127.63	106.91±0.26	84.53±0.11	99.58±0.26	90.36±1.95	87.52±0.57	83.91±0.76
PEMS07-15	MAE	245.48	157.24	122.98±0.20	99.86±1.55	119.18±0.85	95.03±2.71	97.66±1.62	86.03±1.01
	MAPE	37.42	25.27	23.09±0.69	15.71±0.29	20.36±0.59	15.20±0.58	14.10±0.26	12.32±0.16
	RMSE	350.04	239.94	195.08±0.23	156.98±2.31	183.63±0.98	147.77±4.54	161.53±2.45	143.00±1.68
PEMS08-5	MAE	23.31	22.74	20.03±0.03	18.20±0.06	17.92±0.03	19.76±0.50	17.11±0.19	16.53±0.04
	MAPE	15.02	14.16	13.11±0.22	11.64±0.01	12.16±0.07	13.35±0.83	10.91±0.13	10.41±0.09
	RMSE	34.79	35.39	31.55±0.04	28.21±0.10	27.67±0.08	29.16±0.48	26.81±0.33	25.57±0.06
PEMS08-10	MAE	52.73	56.38	47.78±0.15	41.15±0.20	39.74±0.16	42.61±0.57	35.14±0.21	32.97±0.50
	MAPE	17.21	17.86	17.94±0.63	13.18±0.05	14.95±0.06	15.21±0.88	11.31±0.08	10.27±0.22
	RMSE	77.65	89.64	76.24±0.07	65.42±0.27	61.64±0.17	63.12±0.59	55.86±0.41	52.40±0.61
PEMS08-15	MAE	92.20	105.04	85.43±0.08	71.61±0.31	74.06±1.42	70.21±3.31	57.23±0.83	50.80±0.57
	MAPE	21.08	23.88	26.31±1.36	16.51±0.12	20.40±0.50	18.96±0.96	12.84±0.17	10.73±0.16
	RMSE	134.35	164.96	136.05±0.23	116.18±0.54	112.93±1.59	103.84±4.74	90.69±1.21	81.06±0.75

数据	指标	VAR	SVR	GRU	DCRNN	STGCN	ASTGCN	STSGCN	STHGCN
PEMS03-5	MAE	21.18	21.75	19.96±0.03	17.43±0.03	17.93±0.03	18.29±0.24	17.43±0.08	16.80±0.04
	MAPE	21.97	21.00	19.83±0.42	16.78±0.16	18.54±0.20	18.30±0.53	16.48±0.12	17.35±0.27
	RMSE	35.04	34.70	32.90±0.28	30.18±0.42	29.92±0.36	30.40±0.40	28.98±0.49	28.56±0.30
PEMS03-10	MAE	51.43	55.57	48.85±0.11	38.20±0.11	40.21±0.08	38.83±0.82	37.09±0.35	34.38±0.25
	MAPE	27.93	28.74	27.97±1.22	19.12±0.19	23.40±0.61	21.41±1.02	18.11±0.20	16.81±0.37
	RMSE	84.65	91.80	81.68±0.21	66.89±0.78	67.77±0.41	65.13±1.29	63.16±0.89	60.13±0.30
PEMS03-15	MAE	95.67	105.26	87.87±0.30	66.60±0.19	70.74±0.35	63.34±2.62	62.59±0.45	55.05±0.46
	MAPE	38.01	39.54	38.29±0.98	23.33±0.12	27.67±0.73	23.59±1.89	20.44±0.20	18.70±0.52
	RMSE	154.01	172.03	145.61±0.29	118.40±0.88	119.05±0.63	105.54±4.10	107.49±0.69	96.29±1.08
PEMS04-5	MAE	24.00	28.11	25.68±0.01	23.58±0.05	23.10±0.03	22.60±0.39	21.10±0.04	20.50±0.05
	MAPE	18.06	19.29	17.83±0.18	15.64±0.02	15.89±0.14	16.72±0.29	13.74±0.04	13.58±0.13
	RMSE	37.01	43.54	39.81±0.03	37.04±0.15	35.47±0.06	34.22±0.50	33.98±0.05	32.35±0.07
PEMS04-10	MAE	50.33	69.01	61.66±0.11	52.23±0.15	51.24±0.49	45.06±0.67	43.42±0.37	39.23±0.30
	MAPE	22.10	27.28	25.70±0.65	18.91±0.07	20.50±0.52	18.90±0.62	14.56±0.18	13.36±0.14
	RMSE	76.54	108.63	95.43±0.14	83.55±0.33	77.78±0.54	68.35±0.91	69.05±0.69	62.20±0.50
PEMS04-15	MAE	85.17	126.54	112.97±0.28	90.63±0.75	95.54±2.57	72.26±1.46	71.89±0.50	59.38±0.80
	MAPE	28.65	40.35	41.45±1.02	26.96±0.19	32.57±1.37	23.27±1.48	17.81±0.19	14.72±0.13
	RMSE	127.54	199.02	173.21±0.27	148.14±1.45	145.63±3.62	108.15±1.78	114.93±0.85	94.92±1.43
PEMS07-5	MAE	35.91	31.68	27.45±0.03	24.12±0.23	26.53±0.07	26.73±0.74	24.19±0.06	23.94±0.08
	MAPE	16.41	13.84	12.30±0.10	10.68±0.50	12.14±0.08	13.07±0.60	10.15±0.01	10.12±0.08
	RMSE	55.48	48.95	42.74±0.05	37.72±0.25	40.77±0.06	40.29±1.30	39.35±0.24	37.53±0.14
PEMS07-10	MAE	105.04	82.05	68.06±0.16	53.24±0.05	65.06±0.32	58.39±1.52	53.94±0.65	52.08±0.47
	MAPE	24.90	18.68	16.60±0.27	11.92±0.02	15.82±0.31	14.95±2.78	11.44±0.16	11.08±0.04
	RMSE	153.68	127.63	106.91±0.26	84.53±0.11	99.58±0.26	90.36±1.95	87.52±0.57	83.91±0.76
PEMS07-15	MAE	245.48	157.24	122.98±0.20	99.86±1.55	119.18±0.85	95.03±2.71	97.66±1.62	86.03±1.01
	MAPE	37.42	25.27	23.09±0.69	15.71±0.29	20.36±0.59	15.20±0.58	14.10±0.26	12.32±0.16
	RMSE	350.04	239.94	195.08±0.23	156.98±2.31	183.63±0.98	147.77±4.54	161.53±2.45	143.00±1.68
PEMS08-5	MAE	23.31	22.74	20.03±0.03	18.20±0.06	17.92±0.03	19.76±0.50	17.11±0.19	16.53±0.04
	MAPE	15.02	14.16	13.11±0.22	11.64±0.01	12.16±0.07	13.35±0.83	10.91±0.13	10.41±0.09
	RMSE	34.79	35.39	31.55±0.04	28.21±0.10	27.67±0.08	29.16±0.48	26.81±0.33	25.57±0.06
PEMS08-10	MAE	52.73	56.38	47.78±0.15	41.15±0.20	39.74±0.16	42.61±0.57	35.14±0.21	32.97±0.50
	MAPE	17.21	17.86	17.94±0.63	13.18±0.05	14.95±0.06	15.21±0.88	11.31±0.08	10.27±0.22
	RMSE	77.65	89.64	76.24±0.07	65.42±0.27	61.64±0.17	63.12±0.59	55.86±0.41	52.40±0.61
PEMS08-15	MAE	92.20	105.04	85.43±0.08	71.61±0.31	74.06±1.42	70.21±3.31	57.23±0.83	50.80±0.57
	MAPE	21.08	23.88	26.31±1.36	16.51±0.12	20.40±0.50	18.96±0.96	12.84±0.17	10.73±0.16
	RMSE	134.35	164.96	136.05±0.23	116.18±0.54	112.93±1.59	103.84±4.74	90.69±1.21	81.06±0.75

模型	PEMS03-5		PEMS04-5		PEMS08-5
模型	训练	推理	训练	推理	训练	推理
DCRNN	144.8	22.2	77.7	12.8	45.5	8.3
STGCN	47.9	7.1	32.3	4.5	36.6	4.7
ASTGCN	38.9	7.2	22.5	4.1	23.2	4.2
STSGCN	91.2	11.0	52.5	6.4	27.8	3.1
STHGCN	18.9	2.8	7.9	1.5	9.9	1.3

Spatio-temporal hyper-relationship graph convolutional network for traffic flow forecasting

面向交通流量预测的时空超关系图卷积网络

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