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

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

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

We apologize for this error.

张 T. T.、金 P. J.、Piccoli, B. 和 Sartipi, M. (2024)。用于车辆轨迹验证和细化的深度时空嵌入。计算机辅助土木和基础设施工程，39，1597−1615。 https://doi.org/10.1111/mice.13160

在“方法论”部分，公式(2)“ $$ ”不正确。正确的等式应该写成“ $$ ”

在“方法论”部分，方程(3) $$ 不正确。正确的方程(3)应该写成 $$

在“方法论”部分，方程(4) $$ 不正确。正确的方程（4）应该写成 $$

对于这个错误，我们深表歉意。