\) can be skipped when the new assignment for \(\bx_i\) is searched. Checking this requires keeping track of all the inter-center distances, but centers are typically a small fraction of the training data, so overall this can be a significant saving. In particular, if this condition is satisfied for all the centers \(\bc \not= \bc_{q_i}\), the point \(\bx_i\) can be skipped completely. Furthermore, the condition can be tested also based on an upper bound \(UB_i\) of \(\|\bx_i - \bc_{q_i}\|_p\).</p>
<p>Secon