## 5 Conclusions and Future Work  
This study proposes a novel approach of imputation of missing traffic data by identifying SBTS of a target location, and determining customized tempo-spatial dependencies for each SBTS, which consists of multiple spot-states of the desired road-section, utilizing the data from different time periods at up- and down-stream traffic detectors in the vicinity of the target area with the missing data.  
The proposed \(Ang_{t}\)-based approach more effectively divided the traffic data into different SBTS compared to the traditional average-speed approach which merely identifies states by drawing fundamental diagrams. The proposed method combined with the support vector regression, that can separate the SBTS and identify the spatiotemporal dependencies, showed consistent improvements in terms of performance of imputations. Additionally, the proposed approach showed the best performance exceeding comparison methods including linear interpolation, k-NN and ANN approaches when dealing with varying missing rates or relatively large and continuous missing patterns. The spatiotemporal dependencies detected by the method can be used as a constructive clue to identify the hidden congestion mechanism associated with the study section. In this study, the spatiotemporal dependency was widely distributed in SBTS II while it was narrowly distributed in SBTS III. The value of the \(Ang_{t}\) identifying the SBTS has been utilized as an input to overcome the narrow dependency in the SBTS III, and the performance of imputation has been improved.  
Although the proposed approach can improve the imputation performance of missing values, and it is relatively easy to apply, there is room for further improvement. For example, the current model still requires a certain amount of historical data of the missing target in order to train with the proposed method. The directions of future research still remain to be explored. The segmentation of the SBTS in this study can branch out to various ITS applications. An automatic segmentation rule can be designed for a fluent application of the proposed approach and can be applied in the emerging data-driven ITS environments. For example, hierarchical or expectation-maximization clustering approaches using the angle value can be a near-foreseeable enhancement from this study. Furthermore, more sophisticated regression model such as deep learning models can be combined with the proposed approach to further improve the performances. Also, additional datasets can be incorporated to ensure the transferability of the proposed model.  
**Author Contributions:** In this study, all of the authors contributed to the writing of the manuscript. [PERSON] designed the overall modeling framework and mainly writing the initial version. [PERSON] performed the data analysis  
Figure 7: Traffic speed profile of real and predicted data by ANN and proposed model.  
and interpretation and writing the initial version. [PERSON] and [PERSON] contributed the data analysis and result interpretation, revised and improved the overall draft. S.K. contributed to drafting the initial paper, advised the data analysis and coordinated the overall effort.  
This research was funded by a Jungseok Logistics Foundation grant, the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (Grant No. 2018R1A2B6005729), and Abu Dhabi Department of Education and Knowledge (ADEK) Award for Research Excellence AARE 2017-263 (Grant No. 8-434000104).  
The authors declare no conflict of interest.