# A Functional Data Approach to Outlier Detection and Imputation for Traffic Density Data on Urban Arterial Roads

• Bin Tang School of Mathematics and Statistics, Guizhou University
• Yao Hu School of Mathematics and Statistics, Guizhou University
• Huan Chen School of Mathematics and Statistics, Guizhou University
Keywords: functional data, functional principal component analysis, traffic density, outliers, s-FPCA

### Abstract

In traffic monitoring data analysis, the magnitude of traffic density plays an important role in determin-ing the level of traffic congestion. This study proposes a data imputation method for spatio-functional principal component analysis (s-FPCA) and unifies anomaly curve detection, outlier confirmation and imputation of traf-fic density at target intersections. Firstly, the detection of anomalous curves is performed based on the binary principal component scores obtained from the function-al data analysis, followed by the determination of the presence of outliers through threshold method. Secondly, an improved method for missing traffic data estimation based on upstream and downstream is proposed. Final-ly, a numerical study of the actual traffic density data is carried out, and the accuracy of s-FPCA for imputation is improved by 8.28%, 8.91% and 7.48%, respective-ly, when comparing to functional principal component analysis (FPCA) with daily traffic density data missing rates of 5%, 10% and 20%, proving the superiority of the method. This method can also be applied to the detection of outliers in traffic flow, imputation and other longitudi-nal data analysis with periodic fluctuations.

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Published
2022-09-30
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Tang B, Hu Y, Chen H. A Functional Data Approach to Outlier Detection and Imputation for Traffic Density Data on Urban Arterial Roads. Promet [Internet]. 2022Sep.30 [cited 2022Dec.2];34(5):755-6. Available from: https://traffic.fpz.hr/index.php/PROMTT/article/view/4069
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