Accurate and timely short-term traffic flow forecasting plays a key role in intelligent transportation systems, especially for prospective traffic control. For the past decade, a series of methods have been developed for short-term traffic flow forecasting. However, due to the intrinsic stochastic and evolutionary trend, accurate forecasting remains challenging. In this paper, we propose a noise-immune long short-term memory (NiLSTM) network for short-term traffic flow forecasting, which embeds a noise-immune loss function deduced by maximum correntropy into the long short-term memory (LSTM) network. Different from the conventional LSTM network equipped with the mean square error loss, the maximum correntropy induced loss is a local similar metric, which is immunized to non-Gaussian noises. Extensive experiments on four benchmark datasets demonstrate the superior performance of our NiLSTM network by comparing it with the frequently used models and state-of-the-art models.

1.
Y.
Zhang
,
S.
Wang
,
B.
Chen
,
J.
Cao
, and
Z.
Huang
, “Trafficgan: Network-scale deep traffic prediction with generative adversarial nets,”
IEEE Trans. Intell. Transp. Syst.
1–12
(
2019
).
2.
A.
Fragkou
,
T.
Karakasidis
, and
E.
Nathanail
, “
Detection of traffic incidents using nonlinear time series analysis
,”
Chaos
28
,
063108
(
2018
).
3.
J.
Villalobos
,
V.
Muñoz
,
J.
Rogan
,
R.
Zarama
,
J. F.
Penagos
,
B.
Toledo
, and
J. A.
Valdivia
, “
Modeling a bus through a sequence of traffic lights
,”
Chaos
25
,
073117
(
2015
).
4.
Z.
Zhang
,
Y.
Sheng
,
Z.
Hu
, and
G.
Chen
, “
Optimal and suboptimal networks for efficient navigation measured by mean-first passage time of random walks
,”
Chaos
22
,
043129
(
2012
).
5.
E. I.
Vlahogianni
,
M. G.
Karlaftis
, and
J. C.
Golias
, “
Short-term traffic forecasting: Where we are and where we’re going
,”
Transp. Res. Part C Emerg. Technol.
43
,
3
19
(
2014
).
6.
Y.
Lv
,
Y.
Chen
,
X.
Zhang
,
Y.
Duan
, and
N. L.
Li
, “
Social media based transportation research: The state of the work and the networking
,”
IEEE/CAA J. Autom. Sin.
4
,
19
26
(
2017
).
7.
L.
Li
,
Y.
Lv
, and
F.
Wang
, “
Traffic signal timing via deep reinforcement learning
,”
IEEE/CAA J. Autom. Sin.
3
,
247
254
(
2016
).
8.
U.
Mori
,
A.
Mendiburu
,
M.
Álvarez
, and
J. A.
Lozano
, “
A review of travel time estimation and forecasting for advanced traveller information systems
,”
Transportmetrica A Transport Sci.
11
(
2
),
119
157
(
2015
).
9.
I.
Kaysi
,
M.
Ben-Akiva
, and
H.
Koutsopoulos
, “
Integrated approach to vehicle routing and congestion prediction for real-time driver guidance
,”
Transp. Res. Rec.
1408
,
66
74
(
1993
).
10.
K. Y.
Chan
,
T. S.
Dillon
,
J.
Singh
, and
E.
Chang
, “
Neural-network-based models for short-term traffic flow forecasting using a hybrid exponential smoothing and Levenberg–Marquardt algorithm
,”
IEEE Trans. Intell. Transp. Syst.
13
(
2
),
644
654
(
2012
).
11.
D.
Tikunov
and
T.
Nishimura
, “Traffic prediction for mobile network using Holt-Winter’s exponential smoothing,” in 2007 15th International Conference on Software, Telecommunications and Computer Networks (IEEE, 2007), pp. 1–5.
12.
T.
Zhou
,
D.
Jiang
,
Z.
Lin
,
G.
Han
,
X.
Xu
, and
J.
Qin
, “
Hybrid dual Kalman filtering model for short-term traffic flow forecasting
,”
IET Intell. Transp. Syst.
13
,
1023
1032
(
2019
).
13.
L.
Cai
,
Z.
Zhang
,
J.
Yang
,
Y.
Yu
,
T.
Zhou
, and
J.
Qin
, “
A noise-immune Kalman filter for short-term traffic flow forecasting
,”
Phys. A Stat. Mech. Appl.
536
,
1
9
(
2019
).
14.
S.
Zhang
,
Y.
Song
,
D.
Jiang
,
T.
Zhou
, and
J.
Qin
, “Noise-identified Kalman filter for short-term traffic flow forecasting,” in The 15th International Conference on Mobile Ad-Hoc and Sensor Networks (IEEE, 2019), pp. 1–5.
15.
H.
Zare Moayedi
and
M. A.
Masnadi-Shirazi
, “Arima model for network traffic prediction and anomaly detection,” in 2008 International Symposium on Information Technology (IEEE, 2008), Vol. 4, pp. 1–6.
16.
L. J.
Yu Peng
,
M.
Lei
, and
P.
XiYuan
, “
A novel hybridization of echo state networks and multiplicative seasonal arima model for mobile communication traffic series forecasting
,”
Neural Comput. Appl.
24
,
883
890
(
2014
).
17.
B. M.
Williams
and
L. A.
Hoel
, “
Modeling and forecasting vehicular traffic flow as a seasonal arima process: Theoretical basis and empirical results
,”
J. Transp. Eng.
129
(
6
),
664
672
(
2003
).
18.
Y.
Zhang
,
Y.
Zhang
, and
A.
Haghani
, “
A hybrid short-term traffic flow forecasting method based on spectral analysis and statistical volatility model
,”
Transp. Res. Part C Emerg. Technol.
43
,
65
78
(
2014
).
19.
B.
Ghosh
,
B.
Basu
, and
M.
O’Mahony
, “
Multivariate short-term traffic flow forecasting using time-series analysis
,”
IEEE Trans. Intell. Transp. Syst.
10
(
2
),
246
254
(
2009
).
20.
H.
Liu
,
Z.
Canfang
,
L.
Jiansha
,
L.
Mian
,
Z.
Shusheng
,
J.
Yuyang
, and
Z.
Yufen
, “
Simultaneous measurement of trace monoadenosine and diadenosine monophosphate in biomimicking prebiotic synthesis using high-performance liquid chromatography with ultraviolet detection and electrospray ionization mass spectrometry characterization
,”
Anal. Chim. Acta
566
(
1
),
99
108
(
2006
).
21.
J. Z.
Zhu
,
J. X.
Cao
, and
Y.
Zhu
, “
Traffic volume forecasting based on radial basis function neural network with the consideration of traffic flows at the adjacent intersections
,”
Transp. Res. Part C Emerg. Technol.
47
,
139
154
(
2014
).
22.
W.
Cai
,
J.
Yang
,
Y.
Yu
,
Y.
Song
,
T.
Zhou
, and
J.
Qin
, “
Pso-elm: A hybrid learning model for short-term traffic flow forecasting
,”
IEEE Access
8
,
6505
6514
(
2020
).
23.
L.
Cai
,
Y.
Yu
,
S.
Zhang
,
Y.
Song
,
Z.
Xiong
, and
T.
Zhou
, “A sample-rebalanced outlier-rejected k-nearest neighbour regression model for short-term traffic flow forecasting,”
IEEE Access
8
,
22686
22696
(
2020
).
24.
W.-C.
Hong
,
Y.
Dong
,
F.
Zheng
, and
C.-Y.
Lai
, “
Forecasting urban traffic flow by SVR with continuous ACO
,”
Appl. Math. Model.
35
(
3
),
1282
1291
(
2011
).
25.
W.
Cai
,
D.
Yu
,
Z.
Wu
,
X.
Du
, and
T.
Zhou
, “
A hybrid ensemble learning framework for basketball outcomes prediction
,”
Phys. A Stat. Mech. Appl.
528
,
121461
(
2019
).
26.
L.
Cai
,
Q.
Chen
,
W.
Cai
,
X.
Xu
,
T.
Zhou
, and
J.
Qin
, “
Svrgsa: A hybrid learning based model for short-term traffic flow forecasting
,”
IET Intell. Transp. Syst.
13
(
9
),
1348
1355
(
2019
).
27.
Y.
LeCun
,
Y.
Bengio
, and
G.
Hinton
, “
Deep learning
,”
Nature
521
,
436
(
2015
).
28.
W.
Huang
,
G.
Song
,
H.
Hong
, and
K.
Xie
, “
Deep architecture for traffic flow prediction: Deep belief networks with multitask learning
,”
IEEE Trans. Intell. Transp. Syst.
15
(
5
),
2191
2201
(
2014
).
29.
T.
Zhou
,
G.
Han
,
X.
Xu
,
Z.
Lin
,
C.
Han
,
Y.
Huang
, and
J.
Qin
, “
δ-agree AdaBoost stacked autoencoder for short-term traffic flow forecasting
,”
Neurocomputing
247
,
31
38
(
2017
).
30.
T.
Zhou
,
G.
Han
,
X.
Xu
,
C.
Han
,
Y.
Huang
, and
J.
Qin
, “
A learning-based multimodel integrated framework for dynamic traffic flow forecasting
,”
Neural Process. Lett.
49
,
407
430
(
2019
).
31.
Y.
Lv
,
Y.
Duan
,
W.
Kang
,
Z.
Li
, and
F.
Wang
, “
Traffic flow prediction with big data: A deep learning approach
,”
IEEE Trans. Intell. Transp. Syst.
16
(
2
),
865
873
(
2015
).
32.
P.
Lingras
,
S.
Sharma
, and
M.
Zhong
, “
Prediction of recreational travel using genetically designed regression and time-delay neural network models
,”
Transp. Res. Rec.
1805
(
2
),
16
24
(
2002
).
33.
R.
Pascanu
,
T.
Mikolov
, and
Y.
Bengio
, “On the difficulty of training recurrent neural networks,” in Proceedings of the 30th International Conference on International Conference on Machine Learning - Volume 28, ICML’13 (JMLR.org, 2013), pp. III-1310–III-1318.
34.
S.
Hochreiter
and
J.
Schmidhuber
, “
Long short-term memory
,”
Neural Comput.
9
,
1735
1780
(
1997
).
35.
F. A.
Gers
,
J.
Schmidhuber
, and
F.
Cummins
, “Learning to forget: Continual prediction with LSTM,” in 1999 Ninth International Conference on Artificial Neural Networks ICANN 99 (Conference Publication No. 470) (IET, 1999), Vol. 2, pp. 850–855.
36.
X.
Ma
,
Z.
Tao
,
Y.
Wang
,
H.
Yu
, and
Y.
Wang
, “
Long short-term memory neural network for traffic speed prediction using remote microwave sensor data
,”
Transp. Res. Part C Emerg. Technol.
54
,
187
197
(
2015
).
37.
T.
Yongxue
and
P.
Li
, “Predicting short-term traffic flow by long short-term memory recurrent neural network,” in 2015 IEEE International Conference on Smart City/SocialCom/SustainCom (SmartCity) (IEEE, 2015), pp. 153–158.
38.
L.
Canyi
,
J.
Tang
,
M.
Lin
,
L.
Lin
,
S.
Yan
, and
Z.
Lin
, “Correntropy induced l2 graph for robust subspace clustering,” in 2013 IEEE International Conference on Computer Vision (IEEE, 2013), pp. 1801–1808.
39.
W.
Liu
,
P. P.
Pokharel
, and
J. C.
Príncipe
, “
Correntropy: Properties and applications in non-Gaussian signal processing
,”
IEEE Trans. Signal Process.
55
,
5286
5298
(
2007
).
40.
R.
He
,
W.
Zheng
, and
B.
Hu
, “
Maximum correntropy criterion for robust face recognition
,”
IEEE Trans. Pattern Anal. Mach. Intell.
33
(
8
),
1561
1576
(
2011
).
41.
R. J.
Bessa
,
V.
Miranda
, and
J.
Gama
, “
Entropy and correntropy against minimum square error in offline and online three-day ahead wind power forecasting
,”
IEEE Trans. Power Syst.
24
(
4
),
1657
1666
(
2009
).
42.
R.
He
,
B.
Hu
,
W.
Zheng
, and
X.
Kong
, “
Robust principal component analysis based on maximum correntropy criterion
,”
IEEE Trans. Image Process.
20
(
6
),
1485
1494
(
2011
).
43.
A.
Garde
,
L.
Sörnmo
,
R.
Jané
, and
B. F.
Giraldo
, “
Correntropy-based spectral characterization of respiratory patterns in patients with chronic heart failure
,”
IEEE Trans. Biomed. Eng.
57
(
8
),
1964
1972
(
2010
).
44.
B.
Chen
,
L.
Xing
,
H.
Zhao
,
N.
Zheng
, and
J. C.
Príncipe
, “
Generalized correntropy for robust adaptive filtering
,”
IEEE Trans. Signal Process.
64
,
3376
3387
(
2016
).
45.
Y.
Wang
,
J. H.
van Schuppen
, and
J.
Vrancken
, “
Prediction of traffic flow at the boundary of a motorway network
,”
IEEE Trans. Intell. Transp. Syst.
15
(
1
),
214
227
(
2014
).
46.
B.
Yu
,
H.
Yin
, and
Z.
Zhu
, “Spatio-temporal graph convolutional networks: A deep learning framework for traffic forecasting,” in Proceedings of the 27th International Joint Conference on Artificial Intelligence (IJCAI) (IJCAI, 2018).
47.
S.
Arlot
and
A.
Celisse
, “
A survey of cross-validation procedures for model selection
,”
Stat. Surv.
4
,
40
79
(
2010
).
48.
F.
Chollet
et al., see https://keras.io for “Keras” (2015).
49.
M.
Lippi
,
M.
Bertini
, and
P.
Frasconi
, “
Short-term traffic flow forecasting: An experimental comparison of time-series analysis and supervised learning
,”
IEEE Trans. Intell. Transp. Syst.
14
(
2
),
871
882
(
2013
).
50.
Y.
Xie
,
Y.
Zhang
, and
Z.
Ye
, “
Short-term traffic volume forecasting using Kalman filter with discrete wavelet decomposition
,”
Comp. Aided Civil Infrastruct. Eng.
22
(
5
),
326
334
(
2007
).
51.
T.
Zhou
,
G.
Han
,
B. N.
Li
,
Z.
Lin
,
E. J.
Ciaccio
,
P. H.
Green
, and
J.
Qin
, “
Quantitative analysis of patients with celiac disease by video capsule endoscopy: A deep learning method
,”
Comput. Biol. Med.
85
,
1
6
(
2017
).
52.
B. N. N.
Li
,
X.
Wang
,
R.
Wang
,
T.
Zhou
,
R.
Gao
,
E. J.
Ciaccio
, and
P. H.
Green
, “Celiac disease detection from videocapsule endoscopy images using strip principal component analysis,”
IEEE/ACM Trans. Comput. Biol. Bioinform.
1
10
(2019).
53.
Y.
Song
,
Z.
Yu
,
T.
Zhou
,
J. Y.-C.
Teoh
,
B.
Lei
,
C.
Kup-Sze
, and
J.
Qin
, “CNN in CT image segmentation: Beyond loss function for exploiting ground truth images,” in 2020 IEEE International Symposium on Biomedical Imaging (ISBI) (IEEE, 2020), pp. 1–4.
54.
D.
Jiang
,
K.
Wu
,
D.
Chen
,
G.
Tu
,
T.
Zhou
,
A.
Garg
, and
L.
Gao
, “
A probability and integrated learning based classification algorithm for high-level human emotion recognition problems
,”
Measurement
150
,
107049
(
2019
).
55.
D.
Jiang
,
Z.
Liu
,
L.
Zheng
, and
J.
Chen
, “Factorization meets neural networks: A scalable and efficient recommender for solving the new user problem,”
IEEE Access
8
,
18350
18361
(
2020
).
56.
Y.
Chen
,
F.
Guo
,
Z.
Gong
, and
W.
Cai
, “
One note about the Tu-Deng conjecture in case w(t)=5
,”
IEEE Access
7
,
13799
13802
(
2019
).
57.
Y.
Chen
,
L.
Zhang
,
D.
Tang
, and
W.
Cai
, “
Translation equivalence of Boolean functions expressed by primitive element
,”
IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
102
,
672
675
(
2019
).
58.
Y.
Chen
,
F.
Guo
, and
J.
Ruan
, “
Constructing odd-variable RSBFS with optimal algebraic immunity, good nonlinearity and good behavior against fast algebraic attacks
,”
Discrete Appl. Math.
262
,
1
12
(
2019
).
59.
Y.
Chen
,
F.
Guo
,
H.
Xiang
,
W.
Cai
, and
X.
He
, “
Balanced odd-variable RSBFS with optimum AI, high nonlinearity and good behavior against FAAS
,”
IEICE Trans. Fundam. Electron. Commun. Comput. Sci.
102
,
818
824
(
2019
).
You do not currently have access to this content.