Hi oofbey, If you look at Figure 3 of our paper, the baseline "Sculley" is precisely the well tuned mini batch kmeans of scikit-learn. We swept on batch sizes and threshold for dead cluster reassignment (Batch size: 256, 512, 1024, 2048, 4096, 65536, 262144, 524288. Dead-cluster threshold : 0, 0.001, 0.01, 0.05, 0.1, 0.5). The reason e-means outperforms previous mini-batch methods is because it is a robust optimization framework powered by scaling laws, specializing techniques inspired from the deep learning literature for the k-means problem. Meanwhile mini-batch k-means methods rely on the MacQueen update rule introduced in 1967, which is known to be highly suboptimal and converge to a lesser solution than Lloyd (See Darken and Moody, 1990, Note on Learning Rate Schedules for Stochastic Optimization).