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{"title":"用于车辆轨迹验证和完善的深度时空嵌入 \"的更正","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":null,"pages":null},"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":"{\"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\":null,\"pages\":null},\"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}","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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Corrigendum to “Deep spatial-temporal embedding for vehicle trajectory validation and refinement”
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.