Attention-Driven Recurrent Imputation for Traffic Speed

Abstract

In practice, traffic data collection is often warned by missing data due to communication errors, sensor failures, storage loss, among other factors, leading to impaired data collection and hampering the effectiveness of downstream applications. However, existing imputation approaches focus exclusively on estimating the lost value from incomplete observations and ignore historical data. In this paper, we propose a novel neural network model, namely, Attention-Driven Recurrent Imputation Network (ADRIN), to address the problem of missing traffic data. Specifically, in ADRIN, we devise an Imputation-targeted Long Short-Term Memory (LSTM-I) module for filling in missing data. Meanwhile, we consider the periodicity of historical data and design a historical average calculation module in ADRIN. On this basis, we employ the multi-head self-attention mechanism for further extracting latent temporal features from the output of the two modules. ADRIN is capable of modeling both incomplete observation inputs and historical averages independently to estimate the missing values. We conducted comprehensive experiments on three real-world traffic datasets, to demonstrate that ADRIN consistently outperforms other baselines in a variety of scenarios. Furthermore, ablation experiments are conducted on the various modules of the model, and it is concluded that historical data can significantly enhance the imputation effect.

On the Limitations of Physics-Informed Deep Learning: Illustrations Using First-Order Hyperbolic Conservation Law-Based Traffic Flow Models

“…Plugging the relationship between variables ρ, v, and q from (22) into the Eulerian formulation of conservation law in (8), the physical law can be written as (23) and (24).…”

“…Observe that both the equations provide the same physical law -the only difference is their dependent variable. Equation (23) formulates the law in terms of velocity v(x, t), whereas (24) formulates it in terms of density ρ(x, t). Both ( 23) and ( 24) are hyperbolic PDEs.…”

“…A second order diffusive term can be added to make the PDE become parabolic and secure a strong solution. For example, (24) will become (25) where ϵ is a constant of a small value.…”

“…We first generate the dataset shown in Fig. 5a, by using the LWR conservation law (hyperbolic PDE) in (24). Based on the same initial and boundary conditions, and only adding a diffusion term to the LWR PDE to make it parabolic, as explained in (25), we are able to configure the dataset illustrated in Fig.…”

“…Databased approaches [19]- [23] utilize the insights derived from historical data and apply statistical or machine learning techniques to reconstruct and predict traffic states. For instance, the method of attention-driven recurrent imputation is proposed to estimate the missing vehicle velocity data [24]. The third category of streaming-data-based approaches [25], [26] contains methods that do not necessitate a priori knowledge of historical observation, instead take advantage of real-time data, with a weak assumption of traffic relationship acquired from empirical evidence.…”