span class="math display">\[
z_n \sim \mathsf{Categorical}({\bf 1}/K),
\]</span>
where <span class="math inline">\({\bf 1}\)</span> is the unit vector of <span class="math inline">\(K\)</span> dimensions, so that <span class="math inline">\({\bf  1}/K\)</span> is the symmetric <span class="math inline">\(K\)</span>-simplex. Thus the model assumes that
each data point is drawn from a hard decision about cluster
membership. The softness arises only from the uncertainty about which
cluster generated a data poi