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maths-cs-ai-compendium-zh/images/graph_laplacian_smoothness.svg
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 700 230" width="700" height="230">
<text x="350" y="22" text-anchor="middle" font-family="Arial, sans-serif" font-size="14" font-weight="bold" fill="#333">Graph Laplacian: Measuring Signal Smoothness</text>
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<!-- Smooth signal (left) -->
<text x="175" y="50" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#27ae60">Smooth Signal (low x^T L x)</text>
<circle cx="100" cy="110" r="22" fill="#27ae60" fill-opacity="0.7" stroke="#1e8449" stroke-width="1.5"/>
<text x="100" y="115" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">0.9</text>
<circle cx="180" cy="90" r="22" fill="#27ae60" fill-opacity="0.8" stroke="#1e8449" stroke-width="1.5"/>
<text x="180" y="95" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">1.0</text>
<circle cx="250" cy="120" r="22" fill="#27ae60" fill-opacity="0.65" stroke="#1e8449" stroke-width="1.5"/>
<text x="250" y="125" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">0.8</text>
<circle cx="175" cy="170" r="22" fill="#27ae60" fill-opacity="0.75" stroke="#1e8449" stroke-width="1.5"/>
<text x="175" y="175" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">0.9</text>
<line x1="120" y1="105" x2="160" y2="95" stroke="#666" stroke-width="1.2"/>
<line x1="200" y1="95" x2="230" y2="115" stroke="#666" stroke-width="1.2"/>
<line x1="175" y1="110" x2="175" y2="148" stroke="#666" stroke-width="1.2"/>
<line x1="115" y1="125" x2="158" y2="160" stroke="#666" stroke-width="1.2"/>
<text x="175" y="210" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#27ae60">neighbours have similar values</text>
<!-- Non-smooth signal (right) -->
<text x="525" y="50" text-anchor="middle" font-family="Arial, sans-serif" font-size="12" font-weight="bold" fill="#e74c3c">Non-Smooth Signal (high x^T L x)</text>
<circle cx="450" cy="110" r="22" fill="#e74c3c" fill-opacity="0.8" stroke="#c0392b" stroke-width="1.5"/>
<text x="450" y="115" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">0.9</text>
<circle cx="530" cy="90" r="22" fill="#3498db" fill-opacity="0.5" stroke="#2980b9" stroke-width="1.5"/>
<text x="530" y="95" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">-0.8</text>
<circle cx="600" cy="120" r="22" fill="#e74c3c" fill-opacity="0.6" stroke="#c0392b" stroke-width="1.5"/>
<text x="600" y="125" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">0.7</text>
<circle cx="525" cy="170" r="22" fill="#3498db" fill-opacity="0.7" stroke="#2980b9" stroke-width="1.5"/>
<text x="525" y="175" text-anchor="middle" font-family="Arial, sans-serif" font-size="11" font-weight="bold" fill="white">-0.5</text>
<line x1="470" y1="105" x2="510" y2="95" stroke="#666" stroke-width="1.2"/>
<line x1="550" y1="95" x2="580" y2="115" stroke="#666" stroke-width="1.2"/>
<line x1="525" y1="110" x2="525" y2="148" stroke="#666" stroke-width="1.2"/>
<line x1="465" y1="125" x2="508" y2="160" stroke="#666" stroke-width="1.2"/>
<text x="525" y="210" text-anchor="middle" font-family="Arial, sans-serif" font-size="10" fill="#e74c3c">neighbours have very different values</text>
</svg>