class="p">(</span><span class="n">df</span><span class="p">)</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">U</span><span class="p">[:,</span> <span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
  <span class="n">df</span><span class="o">.</span><span class="n">columns</span><span class="o">=</span><span class="p">[</span><span class="s1">&#39;Scatter Points&#39;</sp