Turbocharging Mini-Batch K-Means

We propose an accelerated Mini-Batch k-means algorithm which combines three key improvements. The first is a modified center update which results in convergence to a local minimum in fewer iterations. The second is an adaptive increase of batchsize to meet an increasing requirement for centroid accuracy. The third is the inclusion of distance bounds based on the triangle inequality, which are used to eliminate distance calculations along the same lines as Elkan's algorithm. The combination of the two latter constitutes a very powerful scheme to reuse computation already done over samples until statistical accuracy requires the use of additional data points.