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| <h1 id="visual-tutorial-multivariate-decomposition">Visual tutorial: multivariate decomposition</h1> |
| <p>Multivariate decomposition is easiest to understand when you can see channels |
| side by side.</p> |
| <h2 id="goal">Goal</h2> |
| <p>Compare:</p> |
| <ul> |
| <li>a true joint multivariate method (<code>MSSA</code>),</li> |
| <li>a channelwise baseline (<code>STD</code> run independently on each channel).</li> |
| </ul> |
| <h2 id="script">Script</h2> |
| <p>POSIX shell:</p> |
| <pre><code class="language-bash">PYTHONPATH=src python examples/visual_multivariate_walkthrough.py \ |
| --out-dir out/visual_multivariate |
| </code></pre> |
| <p>PowerShell:</p> |
| <pre><code class="language-powershell">$env:PYTHONPATH='src' |
| python examples/visual_multivariate_walkthrough.py --out-dir out/visual_multivariate |
| </code></pre> |
| <p>The script builds a three-channel synthetic panel with related but not |
| identical seasonal structure.</p> |
| <p>Published raw stdout:</p> |
| <ul> |
| <li><a href="../../assets/generated/tutorials/visual-multivariate/run_stdout.txt">run_stdout.txt</a></li> |
| </ul> |
| <h2 id="output-files">Output files</h2> |
| <p>The script writes:</p> |
| <ul> |
| <li><code>out/visual_multivariate/mssa_multivariate.png</code></li> |
| <li><code>out/visual_multivariate/std_channelwise_multivariate.png</code></li> |
| <li><code>out/visual_multivariate/channel0_trend_overlay.png</code></li> |
| <li><code>out/visual_multivariate/multivariate_summary.csv</code></li> |
| </ul> |
| <p>Published experiment record:</p> |
| <ul> |
| <li><a href="../../assets/generated/tutorials/visual-multivariate/multivariate_summary.csv">multivariate_summary.csv</a></li> |
| </ul> |
| <p>Published summary from the current docs build:</p> |
| <table> |
| <thead> |
| <tr> |
| <th>Channel</th> |
| <th>MSSA backend</th> |
| <th>STD backend</th> |
| <th style="text-align: right;">MSSA residual RMS</th> |
| <th style="text-align: right;">STD residual RMS</th> |
| <th style="text-align: right;">Mean abs trend gap</th> |
| </tr> |
| </thead> |
| <tbody> |
| <tr> |
| <td><code>sensor_a</code></td> |
| <td><code>python</code></td> |
| <td><code>native</code></td> |
| <td style="text-align: right;">0.0047</td> |
| <td style="text-align: right;">0.0000</td> |
| <td style="text-align: right;">0.0590</td> |
| </tr> |
| <tr> |
| <td><code>sensor_b</code></td> |
| <td><code>python</code></td> |
| <td><code>native</code></td> |
| <td style="text-align: right;">0.0038</td> |
| <td style="text-align: right;">0.0000</td> |
| <td style="text-align: right;">0.0260</td> |
| </tr> |
| <tr> |
| <td><code>sensor_c</code></td> |
| <td><code>python</code></td> |
| <td><code>native</code></td> |
| <td style="text-align: right;">0.0999</td> |
| <td style="text-align: right;">0.0000</td> |
| <td style="text-align: right;">0.0128</td> |
| </tr> |
| </tbody> |
| </table> |
| <p>Published example outputs:</p> |
| <p><img alt="MSSA multivariate components" src="../../assets/generated/tutorials/visual-multivariate/mssa_multivariate.png" /></p> |
| <p><img alt="Channelwise STD multivariate components" src="../../assets/generated/tutorials/visual-multivariate/std_channelwise_multivariate.png" /></p> |
| <p><img alt="Channel 0 trend overlay" src="../../assets/generated/tutorials/visual-multivariate/channel0_trend_overlay.png" /></p> |
| <h2 id="what-each-figure-tells-you">What each figure tells you</h2> |
| <p>These summary values come from a real local run of the tutorial script. They |
| show that the multivariate and channelwise paths are not identical even when |
| the figures look superficially similar.</p> |
| <p><code>mssa_multivariate.png</code>:</p> |
| <ul> |
| <li>look for cross-channel consistency in trend and seasonal extraction,</li> |
| <li>useful when channels share one latent mechanism.</li> |
| </ul> |
| <p><code>std_channelwise_multivariate.png</code>:</p> |
| <ul> |
| <li>shows what happens when each channel is decomposed independently,</li> |
| <li>useful as a baseline when you want interpretability per channel without joint |
| coupling.</li> |
| </ul> |
| <p><code>channel0_trend_overlay.png</code>:</p> |
| <ul> |
| <li>isolates one channel and overlays the trend from <code>MSSA</code> and channelwise |
| <code>STD</code>,</li> |
| <li>this is the fastest way to see whether joint structure is actually changing |
| the interpretation of one sensor.</li> |
| </ul> |
| <h2 id="when-this-tutorial-is-useful">When this tutorial is useful</h2> |
| <p>Use this pattern when:</p> |
| <ul> |
| <li>you have several sensors that probably share one seasonal driver,</li> |
| <li>you want to justify <code>MSSA</code> instead of a simpler channelwise baseline,</li> |
| <li>you need figures for a methods note, lab notebook, or internal review.</li> |
| </ul> |
| <p>If the multivariate and channelwise figures are nearly identical, a joint |
| method may not be buying you much.</p></div> |
| </div> |
| </div> |
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