ximated to further improve speed. This opens up the possibility that a data point may receive an assignment that is <em>worse</em> than the current one. This is avoided by checking that the new assignment estimated by using ANN is an improvement; otherwise the old assignment is kept.</li>
<li><b>Center estimation.</b> Each center \(\bc_q\) is updated to minimize its average distances to the points assigned to it. It is easy to show that the best center is the mean or median of the points, respectively if th