  Clustering samples according to an effective metric and/or vector space
representation is a challenging unsupervised learning task with a wide spectrum
of applications. Among several clustering algorithms, k-means and its
kernelized version have still a wide audience because of their conceptual
simplicity and efficacy. However, the systematic application of the kernelized
version of k-means is hampered by its inherent square scaling in memory with
the number of samples. In this contribution, we devise an approximate strategy
to minimize the kernel k-means cost function in which the trade-off between
accuracy and velocity is automatically ruled by the available system memory.
Moreover, we define an ad-hoc parallelization scheme well suited for hybrid
cpu-gpu state-of-the-art parallel architectures. We proved the effectiveness
both of the approximation scheme and of the parallelization method on standard
UCI datasets and on molecular dynamics (MD) data in the realm of computational
chemistry. In this applicative domain, clustering can play a key role for both
quantitively estimating kinetics rates via Markov State Models or to give
qualitatively a human compatible summarization of the underlying chemical
phenomenon under study. For these reasons, we selected it as a valuable
real-world application scenario.
