Symplectic Principal Component Analysis: A New Method for Time Series Analysis

<table><svg height="14.2375" id="M150" style="vertical-align:-3.13504pt" version="1.1" viewbox="0 0 18.5625 14.2375" width="18.5625" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.2375)">
<g transform="translate(72,-60.61)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐷</tspan>
</text>
<text transform="matrix(1,0,0,-1,-62.07,60.66)">
<tspan style="font-size: 8.75px; " x="0" y="0">2</tspan>
</text>
</g>
</g>
</svg> versus embedding dimension <svg height="10.75" id="M151" style="vertical-align:-0.15048pt" version="1.1" viewbox="0 0 9.375 10.75" width="9.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.75)">
<g transform="translate(72,-63.4)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑑</tspan>
</text>
</g>
</g>
</svg>.</table>

Mathematical Problems in Engineering

fig8

Figure 8

Figure 8: Symplectic Principal Component Analysis: A New Method for Time Series Analysis 