  We provide the first streaming algorithm for computing a provable
approximation to the $k$-means of sparse Big data. Here, sparse Big Data is a
set of $n$ vectors in $\mathbb{R}^d$, where each vector has $O(1)$ non-zeroes
entries, and $d\geq n$. E.g., adjacency matrix of a graph, web-links, social
network, document-terms, or image-features matrices.
  Our streaming algorithm stores at most $\log n\cdot k^{O(1)}$ input points in
memory. If the stream is distributed among $M$ machines, the running time
reduces by a factor of $M$, while communicating a total of $M\cdot k^{O(1)}$
(sparse) input points between the machines.
  % Our main technical result is a deterministic algorithm for computing a
sparse $(k,\epsilon)$-coreset, which is a weighted subset of $k^{O(1)}$ input
points that approximates the sum of squared distances from the $n$ input points
to every $k$ centers, up to $(1\pm\epsilon)$ factor, for any given constant
$\epsilon>0$. This is the first such coreset of size independent of both $d$
and $n$.
  Existing algorithms use coresets of size at least polynomial in $d$, or
project the input points on a subspace which diminishes their sparsity, thus
require memory and communication $\Omega(d)=\Omega(n)$ even for $k=2$.
  Experimental results real public datasets shows that our algorithm boost the
performance of such given heuristics even in the off-line setting. Open code is
provided for reproducibility.
