  In this paper, we consider the problem of manifold approximation with affine
subspaces. Our objective is to discover a set of low dimensional affine
subspaces that represents manifold data accurately while preserving the
manifold's structure. For this purpose, we employ a greedy technique that
partitions manifold samples into groups that can be each approximated by a low
dimensional subspace. We start by considering each manifold sample as a
different group and we use the difference of tangents to determine appropriate
group mergings. We repeat this procedure until we reach the desired number of
sample groups. The best low dimensional affine subspaces corresponding to the
final groups constitute our approximate manifold representation. Our
experiments verify the effectiveness of the proposed scheme and show its
superior performance compared to state-of-the-art methods for manifold
approximation.
