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</div><!-- fragment --><p>See the <a href="https://libscran.github.io/qdtsne/">reference documentation</a> for more details.</p>
<h1>Approximations for speed</h1>
<p>van der Maaten (2014) proposed the use of the Barnes-Hut approximation for the repulsive force calculations in t-SNE. The algorithm consolidates a group of distant points into a single center of mass, avoiding the need to calculate forces between individual points. The definition of "distant" is determined by the <code>theta</code> parameter, where larger values sacrifice accuracy for speed.</p>
<p>In <b>qdtsne</b>, we introduce an extra <code>max_depth</code> parameter that bounds the depth of the tree used for the Barnes-Hut force calculations. A maximum depth of <picture><source srcset="form_3_dark.png" media="(prefers-color-scheme: dark)"/><img class="formulaInl" alt="$m$" src="form_3.png"/></picture> is equivalent to the following procedure:</p>
<p>In <b>qdtsne</b>, we introduce an extra <code>max_depth</code> parameter that bounds the depth of the tree used for the Barnes-Hut force calculations. A maximum depth of \(m\) is equivalent to the following procedure:</p>
<ol type="1">
<li>Define the bounding box/hypercube for our dataset and partition it along each dimension into $2^m$ intervals, forming a high-dimensional grid.</li>
<li>In each grid cell, move all data points in that cell to the cell's center of mass.</li>
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