  Currently the amount of data produced worldwide is increasing beyond measure,
thus a high volume of unsupervised data must be processed continuously. One of
the main unsupervised data analysis is clustering. In streaming data scenarios,
the data is composed by an increasing sequence of batches of samples where the
concept drift phenomenon may happen. In this paper, we formally define the
Streaming $K$-means(S$K$M) problem, which implies a restart of the error
function when a concept drift occurs. We propose a surrogate error function
that does not rely on concept drift detection. We proof that the surrogate is a
good approximation of the S$K$M error. Hence, we suggest an algorithm which
minimizes this alternative error each time a new batch arrives. We present some
initialization techniques for streaming data scenarios as well. Besides
providing theoretical results, experiments demonstrate an improvement of the
converged error for the non-trivial initialization methods.
