T(x-\bar x_k)\|^2.\non
\end{eqnarray}\]</div>
<p>When <span class="arithmatex">\(L=K-1\)</span>, the second term vanishes, and we recover (a). </p>
<p>When <span class="arithmatex">\(L&lt;K-1\)</span>, the first term <span class="arithmatex">\(\|z-\bar z_k\|^2\)</span> is just the Mahalanobis squared distances for the distributions projected onto the subspace spanned by <span class="arithmatex">\(U\)</span>.</p>
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