  The independence clustering problem is considered in the following
formulation: given a set $S$ of random variables, it is required to find the
finest partitioning $\{U_1,\dots,U_k\}$ of $S$ into clusters such that the
clusters $U_1,\dots,U_k$ are mutually independent. Since mutual independence is
the target, pairwise similarity measurements are of no use, and thus
traditional clustering algorithms are inapplicable. The distribution of the
random variables in $S$ is, in general, unknown, but a sample is available.
Thus, the problem is cast in terms of time series. Two forms of sampling are
considered: i.i.d.\ and stationary time series, with the main emphasis being on
the latter, more general, case. A consistent, computationally tractable
algorithm for each of the settings is proposed, and a number of open directions
for further research are outlined.
