  In recent years, there have been major efforts to develop data stream
algorithms that process inputs in one pass over the data with little memory
requirement. For the $k$-means problem, this has led to the development of
several $(1+\varepsilon)$-approximations (under the assumption that $k$ is a
constant), but also to the design of algorithms that are extremely fast in
practice and compute solutions of high accuracy. However, when not only the
length of the stream is high but also the dimensionality of the input points,
then current methods reach their limits.
  We propose two algorithms, piecy and piecy-mr that are based on the recently
developed data stream algorithm BICO that can process high dimensional data in
one pass and output a solution of high quality. While piecy is suited for high
dimensional data with a medium number of points, piecy-mr is meant for high
dimensional data that comes in a very long stream. We provide an extensive
experimental study to evaluate piecy and piecy-mr that shows the strength of
the new algorithms.
