<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom"><channel><title>Regression | Meng's Page</title><link>https://www.zhangmeng43.com/tags/regression/</link><atom:link href="https://www.zhangmeng43.com/tags/regression/index.xml" rel="self" type="application/rss+xml"/><description>Regression</description><generator>Hugo Blox Builder (https://hugoblox.com)</generator><language>en-us</language><lastBuildDate>Thu, 26 Oct 2023 00:00:00 +0000</lastBuildDate><image><url>https://www.zhangmeng43.com/media/icon_hu_3c4bb17454bfe3f5.png</url><title>Regression</title><link>https://www.zhangmeng43.com/tags/regression/</link></image><item><title>Modeling Human-Like Interaction Between Cyclists and Vehicles</title><link>https://www.zhangmeng43.com/projects/poster/</link><pubDate>Thu, 26 Oct 2023 00:00:00 +0000</pubDate><guid>https://www.zhangmeng43.com/projects/poster/</guid><description>&lt;div class="text-base text-justify leading-relaxed max-w-prose mx-auto"&gt;
&lt;h3 id="introduction"&gt;Introduction&lt;/h3&gt;
&lt;p&gt;The study, using real-world data, aims to model the interaction between &lt;strong&gt;crossing bicycles&lt;/strong&gt; and &lt;strong&gt;right-turning vehicles&lt;/strong&gt;, attempting to alter the simulator&amp;rsquo;s guidance at the tactical level. In ten days of video recordings from an urban intersection, &lt;strong&gt;517 valid cases&lt;/strong&gt; were collected.&lt;/p&gt;
&lt;figure class="my-6 text-center"&gt;
&lt;img src="plot.png"
alt="Interaction overview plot"
class="mx-auto rounded-xl shadow-md w-3/4" /&gt;
&lt;figcaption class="mt-2 text-sm text-gray-600"&gt;
Figure 1. Trajectories of crossing bicycles and right-turning vehicles.
&lt;/figcaption&gt;
&lt;/figure&gt;
&lt;hr&gt;
&lt;h3 id="modeling"&gt;Modeling&lt;/h3&gt;
&lt;p&gt;A &lt;strong&gt;logistic regression model&lt;/strong&gt; of crossing order was employed with features of bicycles (0) and vehicles (1):&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;speed (&lt;em&gt;v&lt;/em&gt;)&lt;/li&gt;
&lt;li&gt;speed difference (&lt;em&gt;dv&lt;/em&gt;)&lt;/li&gt;
&lt;li&gt;distance to crossing point (&lt;em&gt;d2x&lt;/em&gt;)&lt;/li&gt;
&lt;li&gt;predicted PET (&lt;em&gt;ppet&lt;/em&gt;).&lt;/li&gt;
&lt;/ul&gt;
&lt;p&gt;The dataset was split into &lt;strong&gt;training (80%)&lt;/strong&gt; and &lt;strong&gt;testing (20%)&lt;/strong&gt; subsets. Models with different feature combinations were cross-validated.&lt;/p&gt;
$$
\log\left(\frac{p}{1-p}\right)
= \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \ldots + \beta_k x_k
$$&lt;iframe src="highchart1.html"
class="w-full h-[520px] my-6 rounded-xl border border-gray-200 shadow-sm"
loading="lazy" allowfullscreen&gt;&lt;/iframe&gt;
&lt;hr&gt;
&lt;h3 id="simulation"&gt;Simulation&lt;/h3&gt;
&lt;p&gt;The selected model was implemented in &lt;strong&gt;SUMO&lt;/strong&gt;: At 20 m before the crossing point, the crossing order was estimated, and the lagging object was forced to slow down. A comparison was performed between &lt;strong&gt;real data&lt;/strong&gt;, &lt;strong&gt;SUMO’s default model&lt;/strong&gt;, and &lt;strong&gt;this new model&lt;/strong&gt;.&lt;/p&gt;
&lt;ul&gt;
&lt;li&gt;In reality, &lt;strong&gt;74%&lt;/strong&gt; of bicycles crossed before vehicles.&lt;/li&gt;
&lt;li&gt;In the default model, vehicles were more conservative - bicycles crossed first in about 90% of cases.&lt;/li&gt;
&lt;li&gt;The new model brings this ratio &lt;strong&gt;closer to 50%&lt;/strong&gt;, though still not identical to real data.&lt;/li&gt;
&lt;li&gt;In the default model, &lt;strong&gt;PET distributions&lt;/strong&gt; vary strongly by crossing order, whereas in the real-world data and new model, PET distributions are similar (yet differ by ~1 s).&lt;/li&gt;
&lt;/ul&gt;
&lt;iframe src="highchart2.html"
class="w-full h-[520px] my-6 rounded-xl border border-gray-200 shadow-sm"
loading="lazy" allowfullscreen&gt;&lt;/iframe&gt;
&lt;hr&gt;
&lt;h3 id="conclusion"&gt;Conclusion&lt;/h3&gt;
&lt;p&gt;The study of &lt;strong&gt;interactions between bicycles and vehicles&lt;/strong&gt; in real traffic contributes to improving &lt;strong&gt;simulator realism&lt;/strong&gt;.&lt;br&gt;
Although the new model did not perfectly reproduce the crossing-order distribution, it significantly improved the &lt;strong&gt;PET distribution&lt;/strong&gt;, bringing it closer to reality.&lt;/p&gt;
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