Corrigendum to “Deep spatial-temporal embedding for vehicle trajectory validation and refinement”
IF 8.5
1区 工程技术
Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
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{"title":"Corrigendum to “Deep spatial-temporal embedding for vehicle trajectory validation and refinement”","authors":"","doi":"10.1111/mice.13303","DOIUrl":null,"url":null,"abstract":"<p>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</p><p>In the “Methodology” section, Equation (2) “<span></span><math>\n <semantics>\n <mrow>\n <mi>S</mi>\n <mspace></mspace>\n <mrow>\n <mo>(</mo>\n <mrow>\n <msub>\n <mi>e</mi>\n <mi>i</mi>\n </msub>\n <mo>,</mo>\n <msub>\n <mi>e</mi>\n <mi>j</mi>\n </msub>\n </mrow>\n <mo>)</mo>\n </mrow>\n <mo>=</mo>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <mspace></mspace>\n <mfenced>\n <mrow>\n <mn>1</mn>\n <mo>+</mo>\n <mfrac>\n <mrow>\n <msubsup>\n <mi>e</mi>\n <mi>i</mi>\n <mi>T</mi>\n </msubsup>\n <mo>∗</mo>\n <msub>\n <mi>e</mi>\n <mi>j</mi>\n </msub>\n </mrow>\n <mrow>\n <msub>\n <mi>e</mi>\n <mi>i</mi>\n </msub>\n <mn>2</mn>\n <msub>\n <mi>e</mi>\n <mi>j</mi>\n </msub>\n <mn>2</mn>\n </mrow>\n </mfrac>\n </mrow>\n </mfenced>\n </mrow>\n <annotation>$S\\ ( {{{e}_i},{{e}_j}} ) = \\frac{1}{2}\\ \\left( {1 + \\frac{{e_i^T{\\mathrm{*}}{{e}_j}}}{{{{e}_i}2{{{\\mathrm{e}}}_{\\mathrm{j}}}2}}} \\right)$</annotation>\n </semantics></math>” was incorrect. The correct equation should have been written as “<span></span><math>\n <semantics>\n <mrow>\n <mi>S</mi>\n <mspace></mspace>\n <mrow>\n <mo>(</mo>\n <mrow>\n <msub>\n <mi>e</mi>\n <mi>i</mi>\n </msub>\n <mo>,</mo>\n <msub>\n <mi>e</mi>\n <mi>j</mi>\n </msub>\n </mrow>\n <mo>)</mo>\n </mrow>\n <mo>=</mo>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <mspace></mspace>\n <mfenced>\n <mrow>\n <mn>1</mn>\n <mo>+</mo>\n <mfrac>\n <mrow>\n <msubsup>\n <mi>e</mi>\n <mi>i</mi>\n <mi>T</mi>\n </msubsup>\n <mo>∗</mo>\n <msub>\n <mi>e</mi>\n <mi>j</mi>\n </msub>\n </mrow>\n <mrow>\n <msub>\n <mrow>\n <mrow>\n <mo>∥</mo>\n </mrow>\n <msub>\n <mi>e</mi>\n <mi>i</mi>\n </msub>\n <mrow>\n <mo>∥</mo>\n </mrow>\n </mrow>\n <mn>2</mn>\n </msub>\n <msub>\n <mrow>\n <mrow>\n <mo>∥</mo>\n </mrow>\n <msub>\n <mi>e</mi>\n <mi>j</mi>\n </msub>\n <mrow>\n <mo>∥</mo>\n </mrow>\n </mrow>\n <mn>2</mn>\n </msub>\n </mrow>\n </mfrac>\n </mrow>\n </mfenced>\n </mrow>\n <annotation>$S\\ ( {{{e}_i},{{e}_j}} ) = \\frac{1}{2}\\ \\left( {1 + \\frac{{e_i^T{\\mathrm{*}}{{e}_j}}}{{{\\|{{e}_i}\\|}_2 {\\|{{e}_j}\\|}_2}}} \\right)$</annotation>\n </semantics></math>”</p><p>In the “Methodology” section, Equation (3) <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>L</mi>\n <mrow>\n <mi>S</mi>\n <mi>T</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <mover>\n <mi>Y</mi>\n <mo>̂</mo>\n </mover>\n <mspace></mspace>\n <mo>−</mo>\n <msub>\n <mi>Y</mi>\n <mn>2</mn>\n </msub>\n <mspace></mspace>\n <mo>=</mo>\n <mfrac>\n <mn>1</mn>\n <mrow>\n <mi>H</mi>\n <mo>∗</mo>\n <mi>W</mi>\n <mo>∗</mo>\n <mi>N</mi>\n </mrow>\n </mfrac>\n <mspace></mspace>\n <munderover>\n <mo>∑</mo>\n <mrow>\n <mi>i</mi>\n <mspace></mspace>\n <mo>=</mo>\n <mspace></mspace>\n <mn>1</mn>\n </mrow>\n <mi>N</mi>\n </munderover>\n <munderover>\n <mo>∑</mo>\n <mrow>\n <mi>j</mi>\n <mspace></mspace>\n <mo>=</mo>\n <mspace></mspace>\n <mn>1</mn>\n </mrow>\n <mrow>\n <mi>H</mi>\n <mo>∗</mo>\n <mi>W</mi>\n </mrow>\n </munderover>\n <msub>\n <mover>\n <mi>s</mi>\n <mo>̂</mo>\n </mover>\n <mrow>\n <mi>i</mi>\n <mo>,</mo>\n <mi>j</mi>\n <mspace></mspace>\n <mo>−</mo>\n <mspace></mspace>\n </mrow>\n </msub>\n <msub>\n <mi>s</mi>\n <mrow>\n <mi>i</mi>\n <mo>,</mo>\n <mi>j</mi>\n </mrow>\n </msub>\n </mrow>\n <annotation>${{\\mathcal{L}}_{ST}} = \\hat{Y}\\ - {{Y}_2}\\ = \\frac{1}{{H{\\mathrm{*}}W{\\mathrm{*}}N}}\\ \\mathop \\sum \\limits_{i\\ = \\ 1}^N \\mathop \\sum \\limits_{j\\ = \\ 1}^{H{\\mathrm{*}}W} {{\\hat{s}}_{i,j\\ - \\ }}{{s}_{i,j}}$</annotation>\n </semantics></math> was incorrect. The correct Equation (3) should have been written as <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>L</mi>\n <mrow>\n <mi>S</mi>\n <mi>T</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <msub>\n <mfenced>\n <mover>\n <mi>Y</mi>\n <mo>̂</mo>\n </mover>\n <mo>−</mo>\n <mi>Y</mi>\n </mfenced>\n <mn>2</mn>\n </msub>\n <mo>=</mo>\n <mfrac>\n <mn>1</mn>\n <mrow>\n <mi>H</mi>\n <mo>∗</mo>\n <mi>W</mi>\n <mo>∗</mo>\n <mi>N</mi>\n </mrow>\n </mfrac>\n <mspace></mspace>\n <munderover>\n <mo>∑</mo>\n <mrow>\n <mi>i</mi>\n <mspace></mspace>\n <mo>=</mo>\n <mspace></mspace>\n <mn>1</mn>\n </mrow>\n <mi>N</mi>\n </munderover>\n <munderover>\n <mo>∑</mo>\n <mrow>\n <mi>j</mi>\n <mspace></mspace>\n <mo>=</mo>\n <mspace></mspace>\n <mn>1</mn>\n </mrow>\n <mrow>\n <mi>H</mi>\n <mo>∗</mo>\n <mi>W</mi>\n </mrow>\n </munderover>\n <mrow>\n <mo>∥</mo>\n <msub>\n <mover>\n <mi>s</mi>\n <mo>̂</mo>\n </mover>\n <mrow>\n <mi>i</mi>\n <mo>,</mo>\n <mi>j</mi>\n <mspace></mspace>\n <mo>−</mo>\n <mspace></mspace>\n </mrow>\n </msub>\n <msub>\n <mi>s</mi>\n <mrow>\n <mi>i</mi>\n <mo>,</mo>\n <mi>j</mi>\n </mrow>\n </msub>\n <mo>∥</mo>\n </mrow>\n </mrow>\n <annotation>${{\\mathcal{L}}_{ST}} = \\left \\| \\widehat{Y} - Y \\right \\|_2 = \\frac{1}{{H{\\mathrm{*}}W{\\mathrm{*}}N}}\\ \\mathop \\sum \\limits_{i\\ = \\ 1}^N \\mathop \\sum \\limits_{j\\ = \\ 1}^{H{\\mathrm{*}}W} \\|{{\\hat{s}}_{i,j\\ - \\ }}{{s}_{i,j}}\\|$</annotation>\n </semantics></math></p><p>In the “Methodology” section, Equation (4) <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>L</mi>\n <mi>d</mi>\n </msub>\n <mo>=</mo>\n <mspace></mspace>\n <munder>\n <mo>∑</mo>\n <mrow>\n <mi>d</mi>\n <mspace></mspace>\n <mo>∈</mo>\n <mspace></mspace>\n <mfenced>\n <mrow>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <mo>,</mo>\n <mspace></mspace>\n <mfrac>\n <mn>1</mn>\n <mn>4</mn>\n </mfrac>\n <mo>,</mo>\n <mspace></mspace>\n <mfrac>\n <mn>1</mn>\n <mn>8</mn>\n </mfrac>\n <mspace></mspace>\n <mfrac>\n <mn>1</mn>\n <mn>16</mn>\n </mfrac>\n <mo>,</mo>\n </mrow>\n </mfenced>\n <mspace></mspace>\n </mrow>\n </munder>\n <msub>\n <mrow>\n <mrow>\n <mo>∥</mo>\n </mrow>\n <mover>\n <msub>\n <mi>Y</mi>\n <mi>d</mi>\n </msub>\n <mo>̂</mo>\n </mover>\n <mo>−</mo>\n <msub>\n <mi>Y</mi>\n <mi>d</mi>\n </msub>\n <mrow>\n <mo>∥</mo>\n </mrow>\n </mrow>\n <mn>2</mn>\n </msub>\n </mrow>\n <annotation>${{\\mathcal{L}}_d} = \\ \\mathop \\sum \\limits_{d\\ \\in \\ \\left\\{ {\\frac{1}{2},\\ \\frac{1}{4},\\ \\frac{1}{8}\\ \\frac{1}{{16}},} \\right\\}\\ } {\\|\\widehat {{{Y}_d}} - {{Y}_d}\\|}_2$</annotation>\n </semantics></math> was incorrect. The correct Equation (4) should have written as <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>L</mi>\n <mi>d</mi>\n </msub>\n <mo>=</mo>\n <mspace></mspace>\n <munder>\n <mo>∑</mo>\n <mrow>\n <mi>d</mi>\n <mspace></mspace>\n <mo>∈</mo>\n <mspace></mspace>\n <mfenced>\n <mrow>\n <mfrac>\n <mn>1</mn>\n <mn>2</mn>\n </mfrac>\n <mo>,</mo>\n <mspace></mspace>\n <mfrac>\n <mn>1</mn>\n <mn>4</mn>\n </mfrac>\n <mo>,</mo>\n <mspace></mspace>\n <mfrac>\n <mn>1</mn>\n <mn>8</mn>\n </mfrac>\n <mspace></mspace>\n <mfrac>\n <mn>1</mn>\n <mn>16</mn>\n </mfrac>\n </mrow>\n </mfenced>\n <mspace></mspace>\n </mrow>\n </munder>\n <msub>\n <mrow>\n <mrow>\n <mo>∥</mo>\n </mrow>\n <mover>\n <msub>\n <mi>Y</mi>\n <mi>d</mi>\n </msub>\n <mo>̂</mo>\n </mover>\n <mo>−</mo>\n <msub>\n <mi>Y</mi>\n <mi>d</mi>\n </msub>\n <mrow>\n <mo>∥</mo>\n </mrow>\n </mrow>\n <mn>2</mn>\n </msub>\n </mrow>\n <annotation>${{\\mathcal{L}}_d} = \\ \\mathop \\sum \\limits_{d\\ \\in \\ \\left\\{ {\\frac{1}{2},\\ \\frac{1}{4},\\ \\frac{1}{8}\\ \\frac{1}{{16}}} \\right\\}\\ } {\\|\\widehat {{{Y}_d}} - {{Y}_d}\\|}_2$</annotation>\n </semantics></math></p><p>We apologize for this error.</p>","PeriodicalId":156,"journal":{"name":"Computer-Aided Civil and Infrastructure Engineering","volume":"39 16","pages":"2553"},"PeriodicalIF":8.5000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1111/mice.13303","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer-Aided Civil and Infrastructure Engineering","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/mice.13303","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
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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
(
e
i
,
e
j
)
=
1
2
1
+
e
i
T
∗
e
j
e
i
2
e
j
2
$S\ ( {{{e}_i},{{e}_j}} ) = \frac{1}{2}\ \left( {1 + \frac{{e_i^T{\mathrm{*}}{{e}_j}}}{{{{e}_i}2{{{\mathrm{e}}}_{\mathrm{j}}}2}}} \right)$
” was incorrect. The correct equation should have been written as “
S
(
e
i
,
e
j
)
=
1
2
1
+
e
i
T
∗
e
j
∥
e
i
∥
2
∥
e
j
∥
2
$S\ ( {{{e}_i},{{e}_j}} ) = \frac{1}{2}\ \left( {1 + \frac{{e_i^T{\mathrm{*}}{{e}_j}}}{{{\|{{e}_i}\|}_2 {\|{{e}_j}\|}_2}}} \right)$
”
In the “Methodology” section, Equation (3)
L
S
T
=
Y
̂
−
Y
2
=
1
H
∗
W
∗
N
∑
i
=
1
N
∑
j
=
1
H
∗
W
s
̂
i
,
j
−
s
i
,
j
${{\mathcal{L}}_{ST}} = \hat{Y}\ - {{Y}_2}\ = \frac{1}{{H{\mathrm{*}}W{\mathrm{*}}N}}\ \mathop \sum \limits_{i\ = \ 1}^N \mathop \sum \limits_{j\ = \ 1}^{H{\mathrm{*}}W} {{\hat{s}}_{i,j\ - \ }}{{s}_{i,j}}$
was incorrect. The correct Equation (3) should have been written as
L
S
T
=
Y
̂
−
Y
2
=
1
H
∗
W
∗
N
∑
i
=
1
N
∑
j
=
1
H
∗
W
∥
s
̂
i
,
j
−
s
i
,
j
∥
${{\mathcal{L}}_{ST}} = \left \| \widehat{Y} - Y \right \|_2 = \frac{1}{{H{\mathrm{*}}W{\mathrm{*}}N}}\ \mathop \sum \limits_{i\ = \ 1}^N \mathop \sum \limits_{j\ = \ 1}^{H{\mathrm{*}}W} \|{{\hat{s}}_{i,j\ - \ }}{{s}_{i,j}}\|$
In the “Methodology” section, Equation (4)
L
d
=
∑
d
∈
1
2
,
1
4
,
1
8
1
16
,
∥
Y
d
̂
−
Y
d
∥
2
${{\mathcal{L}}_d} = \ \mathop \sum \limits_{d\ \in \ \left\{ {\frac{1}{2},\ \frac{1}{4},\ \frac{1}{8}\ \frac{1}{{16}},} \right\}\ } {\|\widehat {{{Y}_d}} - {{Y}_d}\|}_2$
was incorrect. The correct Equation (4) should have written as
L
d
=
∑
d
∈
1
2
,
1
4
,
1
8
1
16
∥
Y
d
̂
−
Y
d
∥
2
${{\mathcal{L}}_d} = \ \mathop \sum \limits_{d\ \in \ \left\{ {\frac{1}{2},\ \frac{1}{4},\ \frac{1}{8}\ \frac{1}{{16}}} \right\}\ } {\|\widehat {{{Y}_d}} - {{Y}_d}\|}_2$
We apologize for this error.
用于车辆轨迹验证和完善的深度时空嵌入 "的更正
正确的公式应该写成 " S ( e i , e j ) = 1 2 1 + e i T ∗ e j ∥ e i ∥ 2 ∥ e j ∥ 2 $S\ ( {{{e}_i},{{e}_j}} ) = \frac{1}{2}}\left( {1 + \frac{{e_i^T{\mathrm{*}}{{e}_j}}}{{{\|{e}_i}|}\_2 {\|{e}_j}\}{{e}_j}|_2}}})\在 "方法论 "部分，公式 (3) L S T = Y ̂ - Y 2 = 1 H ∗ W ∗ N ∑ i = 1 N ∑ j = 1 H ∗ W s ̂ i , j - s i , j ${{mathcal{L}}_{ST}} = \hat{Y}\ - {{Y}_2}} = \frac{1}{{H{\mathrm{*}}W{\mathrm{*}}N}}} \mathop \sum \limits_{i\ = \ 1}^N \mathop \sum \limits_{j\ = \ 1}^{H{\mathrm{*}}W}}{{hat{s}}_{i,j\ - \ }}{s}_{i,j}}$ 是不正确的。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
来源期刊
期刊介绍：
Computer-Aided Civil and Infrastructure Engineering stands as a scholarly, peer-reviewed archival journal, serving as a vital link between advancements in computer technology and civil and infrastructure engineering. The journal serves as a distinctive platform for the publication of original articles, spotlighting novel computational techniques and inventive applications of computers. Specifically, it concentrates on recent progress in computer and information technologies, fostering the development and application of emerging computing paradigms.
Encompassing a broad scope, the journal addresses bridge, construction, environmental, highway, geotechnical, structural, transportation, and water resources engineering. It extends its reach to the management of infrastructure systems, covering domains such as highways, bridges, pavements, airports, and utilities. The journal delves into areas like artificial intelligence, cognitive modeling, concurrent engineering, database management, distributed computing, evolutionary computing, fuzzy logic, genetic algorithms, geometric modeling, internet-based technologies, knowledge discovery and engineering, machine learning, mobile computing, multimedia technologies, networking, neural network computing, optimization and search, parallel processing, robotics, smart structures, software engineering, virtual reality, and visualization techniques.
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