Discovering and Characterizing Hidden Variables Using a Novel Neural Network Architecture: LO-Net

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="193146.fig.0018a" src="https://static-preview.hindawi.com/articles/jr/volume-2011/193146/figures/193146.fig.0018a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Performance curve for predicting <svg height="11.375" id="M268" style="vertical-align:-3.49493pt" version="1.1" viewbox="0 0 25.737499 11.375" width="25.737499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.375)">
<g transform="translate(72,-62.9)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑥</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.07,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑡</tspan>
<tspan style="font-size: 8.75px; " x="2.7393761" y="0">+</tspan>
<tspan style="font-size: 8.75px; " x="8.7344961" y="0">1</tspan>
</text>
</g>
</g>
</svg> with different values of the weight (<svg height="7.4499998" id="M269" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 12.2375 7.4499998" width="12.2375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.45)">
<g transform="translate(72,-66.04)">
<text transform="matrix(1,0,0,-1,-71.95,66.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑤</tspan>
</text>
</g>
</g>
</svg>) for the distance penalty term (<svg height="10.6875" id="M270" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 17.225 10.6875" width="17.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
<tspan style="font-size: 12.50px; " x="7.4267821" y="0">1</tspan>
</text>
</g>
</g>
</svg>)</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="193146.fig.0018b" src="https://static-preview.hindawi.com/articles/jr/volume-2011/193146/figures/193146.fig.0018b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Performance curve for predicting <svg height="11.3625" id="M271" style="vertical-align:-3.49493pt" version="1.1" viewbox="0 0 24.887501 11.3625" width="24.887501" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.3625)">
<g transform="translate(72,-62.91)">
<text transform="matrix(1,0,0,-1,-71.95,66.45)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑦</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.75,63.32)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑡</tspan>
<tspan style="font-size: 8.75px; " x="2.7393761" y="0">+</tspan>
<tspan style="font-size: 8.75px; " x="8.7344961" y="0">1</tspan>
</text>
</g>
</g>
</svg> with different values of the weight (<svg height="7.4499998" id="M272" style="vertical-align:-0.11285pt" version="1.1" viewbox="0 0 12.2375 7.4499998" width="12.2375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.45)">
<g transform="translate(72,-66.04)">
<text transform="matrix(1,0,0,-1,-71.95,66.2)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑤</tspan>
</text>
</g>
</g>
</svg>) for the distance penalty term (<svg height="10.6875" id="M273" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 17.225 10.6875" width="17.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.6875)">
<g transform="translate(72,-63.45)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑃</tspan>
<tspan style="font-size: 12.50px; " x="7.4267821" y="0">1</tspan>
</text>
</g>
</g>
</svg>)</td></tr></table></td></tr></table>

Journal of Robotics

fig18

Figure 18

Figure 18: Discovering and Characterizing Hidden Variables Using a Novel Neural Network Architecture: LO-Net 