e
(i.e., <span class="math inline">\(L_2\)</span> distance). Other distributions relate to other
geometries. For instance, replacing the normal distribution with the
double exponential (Laplace) distribution produces a clustering model
based on <span class="math inline">\(L_1\)</span> distance (i.e., Manhattan or taxicab
distance).</p>
<p>Within the multivariate normal version of <span class="math inline">\(K\)</span>-means, replacing the
unit covariance matrix with a shared covariance matrix amounts to
wor