  Modeling data as being sampled from a union of independent subspaces has been
widely applied to a number of real world applications. However, dimensionality
reduction approaches that theoretically preserve this independence assumption
have not been well studied. Our key contribution is to show that $2K$
projection vectors are sufficient for the independence preservation of any $K$
class data sampled from a union of independent subspaces. It is this
non-trivial observation that we use for designing our dimensionality reduction
technique. In this paper, we propose a novel dimensionality reduction algorithm
that theoretically preserves this structure for a given dataset. We support our
theoretical analysis with empirical results on both synthetic and real world
data achieving \textit{state-of-the-art} results compared to popular
dimensionality reduction techniques.
