d as a vector <span class="math inline">\(y_n \in \mathbb{R}^D\)</span>. In the
“soft” version of <span class="math inline">\(K\)</span>-means, the assignments to clusters will be
probabilistic.</p>
<div id="geometric-hard-k-means-clustering" class="section level3">
<h3 number="9.2.1"><span class="header-section-number">9.2.1</span> Geometric Hard <span class="math inline">\(K\)</span>-Means Clustering</h3>
<p><span class="math inline">\(K\)</span>-means clustering is typically described geometrically i