>-dimensional vectors. Specifically, there will be <span class="math inline">\(N\)</span> items to be
clustered, each represented 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 unnumbered">
<h3>Geometric Hard <span class="math inline">\(K\)</span>-Means Clustering</h3>
<p><span class="math i