  In this work, two new initialization methods for K-means clustering are
proposed. Both proposals are based on applying a divide-and-conquer approach
for the K-means|| type of an initialization strategy. The second proposal also
utilizes multiple lower-dimensional subspaces produced by the random projection
method for the initialization. The proposed methods are scalable and can be run
in parallel, which make them suitable for initializing large-scale problems. In
the experiments, comparison of the proposed methods to the K-means++ and
K-means|| methods is conducted using an extensive set of reference and
synthetic large-scale datasets. Concerning the latter, a novel high-dimensional
clustering data generation algorithm is given. The experiments show that the
proposed methods compare favorably to the state-of-the-art. We also observe
that the currently most popular K-means++ initialization behaves like the
random one in the very high-dimensional cases.
