Tangent-based manifold approximation with locally linear models
 We relate manifold approximation with affine spaces to the structure of the manifold.  We employ the variation of local tangent spaces as a measure of manifold linearity.  We propose a new algorithm for manifold approximation based on our linearity measure.  We provide an effective upper bound for the dissimilarity measure used in our scheme.  We prove the effectiveness of our scheme in both synthetic and real signals.
manifold approximation tangent space affine subspaces flats