Corrigendum to “Deep spatial-temporal embedding for vehicle trajectory validation and refinement”

Abstract

Zhang, T. T., Jin, P. J., Piccoli, B., & Sartipi, M. (2024). Deep spatial-temporal embedding for vehicle trajectory validation and refinement. Computer-Aided Civil and Infrastructure Engineering, 39, 1597−1615. https://doi.org/10.1111/mice.13160

In the “Methodology” section, Equation (2) “$S\left(e_i,e_j\right)=\frac{1}{2}\left(1+\frac{e_i^T\ast e_j}{e_{i}2e_{j}2}\right)$” was incorrect. The correct equation should have been written as “$S\left(e_i,e_j\right)=\frac{1}{2}\left(1+\frac{e_i^T\ast e_j}{{\parallel e_i\parallel }_2{\parallel e_j\parallel }_2}\right)$”

In the “Methodology” section, Equation (3) $L_{ST}=\hat{Y}-Y_2=\frac{1}{H\ast W\ast N}\sum _{i=1}^N\sum _{j=1}^{H\ast W}{\hat{s}}_{i,j-}{s}_{i,j}$ was incorrect. The correct Equation (3) should have been written as $L_{ST}={\left(\hat{Y},-,Y\right)}_2=\frac{1}{H\ast W\ast N}\sum _{i=1}^N\sum _{j=1}^{H\ast W}\parallel {\hat{s}}_{i,j-}{s}_{i,j}\parallel$

In the “Methodology” section, Equation (4) $L_d=\sum _{d\in \left(\frac{1}{2},\frac{1}{4},\frac{1}{8}\frac{1}{16},\right)}{\parallel \widehat{Y_d}-Y_d\parallel }_2$ was incorrect. The correct Equation (4) should have written as $L_d=\sum _{d\in \left(\frac{1}{2},\frac{1}{4},\frac{1}{8}\frac{1}{16}\right)}{\parallel \widehat{Y_d}-Y_d\parallel }_2$

We apologize for this error.