  \begin{algorithmic}[1]
  \item \textbf{Input:} $X = \langle X_{(t-T+1)}, X_{(t-T+2)}, \ldots, X_{t}\rangle; \quad X \in \mathbb{R}^{N \times T \times 1}$
  \item \textbf{Output:} $ \widetilde{Y} = \langle  X_{(t+1)}, X_{(t+2)}, \ldots, X_{\left(t+T^{\prime}\right)}\rangle; \quad \widetilde{Y} \in \mathbb{R}^{N \times T \times 1}$
  \item \textbf{Parameters:} \texttt{Randomly initialize $\Theta$ and hidden state $H_{t-1}$}

      \For{\texttt{all} $T$}
        \State $X_{t^{\prime}} \gets X[:,t,:]; \quad   X_{t^{\prime}} \in \mathbb{R}^{N \times 1} $ 
        \State $X_t=\xi_{\theta}\left(X_{t^{\prime}}\right) ;  \quad X_t\in R^{N \times C^{\prime}}$ \Comment{followed by eq. ~\ref{eqn:eqn2}}
        \State $H_{t-1} = {STLGRU}_{\Theta} \left( X_t,H_{t-1} \right)$
      \EndFor
      \State $H_t= H_{t-1}$
      \State $\hat{Y} = OutputLayer(H_t)$  \Comment{followed by eq. ~\ref{function}}
      \State calculate loss $L$ using eq. ~\ref{final}
      \State \textbf{return} $\hat{Y} $
  \end{algorithmic}

\begin{algorithmic}
[1]
\item \textbf{Input:} $X = \langle X_{(t-T+1)}, X_{(t-T+2)}, \ldots, X_{t}\rangle; \quad X \in \mathbb{R}^{N \times T \times 1}$
\item \textbf{Output:} $ \widetilde{Y} = \langle X_{(t+1)}, X_{(t+2)}, \ldots, X_{\left(t+T^{\prime}\right)}\rangle; \quad \widetilde{Y} \in \mathbb{R}^{N \times T \times 1}$
\item \textbf{Parameters:} \texttt{Randomly initialize $\Theta$ and hidden state $H_{t-1}$}
\For{\texttt{all} $T$}
\State $X_{t^{\prime}} \gets X[:,t,:]; \quad X_{t^{\prime}} \in \mathbb{R}^{N \times 1} $
\State $X_t=\xi_{\theta}\left(X_{t^{\prime}}\right) ; \quad X_t\in R^{N \times C^{\prime}}$ \Comment{followed by eq. ~\ref{eqn:eqn2}}
\State $H_{t-1} = {STLGRU}_{\Theta} \left( X_t,H_{t-1} \right)$
\EndFor
\State $H_t= H_{t-1}$
\State $\hat{Y} = OutputLayer(H_t)$ \Comment{followed by eq. ~\ref{function}}
\State calculate loss $L$ using eq. ~\ref{final}
\State \textbf{return} $\hat{Y} $
\end{algorithmic}
{
    "title": "stlgru: spatio-temporal lightweight graph gru for traffic flow   prediction",
    "id": "2212.04548",
    "abstract": "reliable forecasting of traffic flow requires efficient modeling of traffic data. indeed, different correlations and influences arise in a dynamic traffic network, making modeling a complicated task. existing literature has proposed many different methods to capture traffic networks' complex underlying spatial-temporal relations. however, given the heterogeneity of traffic data, consistently capturing both spatial and temporal dependencies presents a significant challenge. also, as more and more sophisticated methods are being proposed, models are increasingly becoming memory-heavy and, thus, unsuitable for low-powered devices. to this end, we propose spatio-temporal lightweight graph gru, namely stlgru, a novel traffic forecasting model for predicting traffic flow accurately. specifically, our proposed stlgru can effectively capture dynamic local and global spatial-temporal relations of traffic networks using memory-augmented attention and gating mechanisms in a continuously synchronized manner. moreover, instead of employing separate temporal and spatial components, we show that our memory module and gated unit can successfully learn the spatial-temporal dependencies with reduced memory usage and fewer parameters. extensive experimental results on three real-world public traffic datasets demonstrate that our method can not only achieve state-of-the-art performance but also exhibit competitive computational efficiency. our code is available at https://github.com/kishor-bhaumik/stlgru",
    "categories": "cs.lg",
    "doi": "",
    "created": "2022-12-08",
    "updated": "2024-02-19",
    "authors": [
        "kishor kumar bhaumik",
        "fahim faisal niloy",
        "saif mahmud",
        "simon woo"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2212.04548"
}
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