# Dynamic Tensor Modeling for Missing Data Completion in Electronic Toll Collection Gantry Systems
## 2 Related Works  
A comprehensive analysis of prior research will enable us to identify the challenges and gaps that this study seeks to address, making an exploration of related work essential. Facing these challenges, missing data completion has emerged as a vital research frontier. Established methods encompass statistical, deep learning, and tensor-based approaches. On the basis of statistical methods, regression analysis methods using techniques such as linear regression, polynomial regression, and regression trees, are suitable for situations in which there are few missing data but that do not capture the complex relationships among data [10; 11; 12]. Clustering methods can group the samples in a dataset and then use other samples within the same cluster to estimate the missing values, but clustering methods need to pre-specify the number of clusters, which is limited for high-dimensional data analysis [13]. Methods based on moment decomposition include Singular Value Decomposition (SVD) and Nonnegative Matrix Factorization (NMF), which are widely used in recommender systems and image processing. However, SVD and NMF may be sensitive to outliers, may not work well when dealing with sparse matrices, and are usually used for numerical data, not for categorical data [14]. Bayesian methods allow for the introduction of uncertainty into the estimation of missing values and provide estimates of probability distributions. Markov Chain Monte Carlo (MCMC) and Bayesian networks are part of the Bayesian approach. However, in the case of high-dimensional and large-scale data, the computational complexity of Bayesian methods increases and requires a priori knowledge to specify the probability distribution [15]. Deep learning techniques, such as Recurrent Neural Networks (RNNs) and transformers, have made significant progress in data completion tasks. They can handle complex data patterns and long-term dependencies. However, complex machine learning models may require more computational resources and a large amount of labeled data for training, which, in some cases, may not be easily accessible [16; 17; 18; 19; 20]. For tensor-based complementation methods applied to high-dimensional tensors, the increase in dimensionality may lead to dimensionality catastrophe, i.e., the data become very sparse, increasing the probability of missing data points, increasing the difficulty in the complementation problem, leading to an increase in uncertainty in the results of the complementation, and the model suffers from overfitting or difficulty in generalizing to new data [21; 22; 23]. The intricacy of traffic flow data, with its multifaceted correlations and patterns, necessitates analytical approaches that can adeptly manage their complexity. Tensor models have risen to prominence in this context, offering a robust framework for capturing high-order correlations and multimodal data interactions inherent in traffic systems [24; 25]. These models are particularly valued for their ability to exploit the intrinsic low-rank properties of traffic data, thus enhancing the precision and interpretability of the analyses. A significant contribution in this domain has been made by [PERSON] et al., who utilized Gaussian regular polynomial decomposition to unravel the latent structures within the data, applying Bayesian networks to fill in the gaps of incomplete datasets [15]. Their work stands out for integrating probabilistic models with tensor decomposition, providing a powerful tool for data restoration and uncertainty quantification in traffic flow analysis. Expanding upon these foundational models, subsequent research has delved into dynamic tensor flow models that aim to capture the spatiotemporal dynamics of traffic flow. These models are sophisticated, as they are designed to analyze data across both macroscales, which consider long-term trends and cyclic patterns, and microscales, which focus on the minute-by-minute fluctuations of traffic flow [26; 27; 28].