  K-means is one of the most widely used algorithms for clustering in Data
Mining applications, which attempts to minimize the sum of the square of the
Euclidean distance of the points in the clusters from the respective means of
the clusters. However, K-means suffers from local minima problem and is not
guaranteed to converge to the optimal cost. K-means++ tries to address the
problem by seeding the means using a distance-based sampling scheme. However,
seeding the means in K-means++ needs $O\left(K\right)$ sequential passes
through the entire dataset, and this can be very costly for large datasets.
Here we propose a method of seeding the initial means based on factorizations
of higher order moments for bounded data. Our method takes $O\left(1\right)$
passes through the entire dataset to extract the initial set of means, and its
final cost can be proven to be within $O(\sqrt{K})$ of the optimal cost. We
demonstrate the performance of our algorithm in comparison with the existing
algorithms on various benchmark datasets.
