LSTM deep learning long-term traffic volume prediction model based on Markov state description

ABSTRACT

When applying long short-term memory (LSTM) neural network model to traffic prediction, there are limitations in exploiting spatial-temporal traffic state features. The interpretability of models has not received enough attention. This study suggests an LSTM traffic flow prediction model that can anticipate traffic volume 24 h in advance. The model makes use of the traffic flow state information obtained from the fuzzy C-means clustering method by clustering the multi-day historical traffic flow data. Markov chain is used to capture the label feature of traffic flow using transition probability matrix information. To show the efficacy of the suggested technique, experiments were conducted using real traffic volume data from a city in China. The simulation results demonstrate that the proposed model can attain greater prediction accuracy, and the network training time may be significantly reduced.

CO EDITOR-IN-CHIEF:

• Su, Shun-Feng

ASSOCIATE EDITOR:

• Su, Shun-Feng

KEYWORDS:

• Traffic volume
• long-term prediction
• deep-learning
• LSTM model

Nomenclature

$\mathbf{b}$	=	the bias vector (e.g. is the input gate bias vector)
$\mathit{c}$	=	the number of clusters
$c_{\mathit{t}-1}$	=	LSTM’s cell state
CNN	=	convolutional neural network
$d_{ij}^2$	=	the square Euclidean distance
DNN	=	deep neural network
$f_{\mathit{ij}}(t_k)$	=	the transition frequency at the $k_{\mathit{th}}$ time interval $t_k$
$f_t,i_t,C_t,O_t$	=	the basic modules contain input gate, forget gate, output gate, input modulation gate, and memory cell state
FCM	=	Fuzzy C-means
GCN	=	graph convolutional network
$h_{\mathit{t}-1}$	=	LSTM’s hidden state
$\mathbf{H}=\left[h_1,h_2\cdots ,h_t,h_T\right]$	=	the hidden vector sequence
$l_{max}$	=	the maximum step size
LSTM	=	long short -term memory
$\mathit{m}$	=	the fuzzifier
MAPE	=	the mean absolute percentage error
MSE	=	the mean square error
$\mathit{N}$	=	the total number of traffic volume states
$\mathbf{P}\mathbf{(}{\mathbf{t}}_{\mathbf{k}}\mathbf{)}$	=	a one-step transition probability matrix
${\mathbf{P}}^{{\mathbf{t}}_{\mathbf{s}}}\mathbf{(}{\mathbf{t}}_{\mathbf{k}}\mathbf{)}$	=	a multi-step transition probability matrix
$p_{\mathit{ij}}\left(t_k\right)$	=	the transition probability
${\mathbf{p}}_{\mathbf{ij}}^{{\mathbf{t}}_{\mathbf{s}}}\mathbf{(}{\mathbf{t}}_{\mathbf{k}}\mathbf{)}$	=	the transition probability at the time $t_k$
$p_j(t_k)$	=	the marginal probability
RNN	=	recurrent neural network
$tanh\left(\cdot \right)$	=	hyperbolic tangent function
$u_{\mathit{ij}}$	=	the membership degree of data object $x_j$ in cluster $\mathit{i}$
$\mathbf{U}$	=	the initial membership matrix
$\mathbf{V}=\{\mathit{v}(t_k)\}$	=	the daily of traffic volume
$v^{\left(\mathit{l}\right)}$	=	the cluster center
$v_k$	=	the real traffic volume at $\mathit{kth}$ time period
${\hat{v}}_{\mathit{k}}$	=	the predicted traffic volume at $\mathit{kth}$ time period
$\mathit{v}{s}_i$	=	the states of the other days traffic volume at $t_k$
${\mathbf{W}}_{\mathbf{c}}$	=	the cell update gate weig ht matrix
${\mathbf{W}}_{\mathbf{f}}$	=	the forget gate weight matrix
${\mathbf{W}}_{\mathbf{i}}$	=	the input gate weight matrix
${\mathbf{W}}_{\mathbf{o}}$	=	the output gate weight matrix
$x_t$	=	input variable
$\mathbf{X}=\left[x_1,x_2\cdots ,x_t,x_T\right]$	=	a sliding window
$\mathbf{Y}=\left[y_1,y_2\cdots ,y_t,y_T\right]$	=	an output sequence
$\mathit{\alpha }$	=	a given significance level
$\mathit{\sigma }\left(\cdot \right)$	=	sigmoid function
${\chi }^2\left(t_k\right)$	=	chi-square statistics

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under [Grant No. 62176019].