Linear manifold approximation based on differences of tangents

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 well approximated by low dimensional subspaces. We start with considering each manifold sample as a different group and we use the difference of tangents to determine advantageous group mergings. We repeat this procedure until we reach the desired number of significant groups. At the end, the best low dimensional affine subspaces corresponding to the final groups constitute the 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.