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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 tangentsdoi:10.1016/j.sigpro.2014.03.047 fatcat:t2qqcud4brdofg2lu22nhxueim