  Consider a high-dimensional data set, in which for every data-point there is
incomplete information. Each object in the data set represents a real entity,
which is described by a point in high-dimensional space. We model the lack of
information for a given object as an affine subspace in $\mathbb{R}^d$ whose
dimension $k$ is the number of missing features.
  Our goal in this study is to find clusters of objects where the main problem
is to cope with partial information and high dimension. Assuming the data set
is separable, namely, its emergence from clusters that can be modeled as a set
of disjoint ball in $\mathbb{R}^d$, we suggest a simple data clustering
algorithm. Our suggested algorithm use the affine subspaces minimum distance
and calculates pair-wise projection of the data achieving poly-logarithmic time
complexity.
  We use probabilistic considerations to prove the algorithm's correctness.
These probabilistic results are of independent interest, and can serve to
better understand the geometry of high dimensional objects.
