Bilateral tangent projection for manifold smoothing

In this paper, we propose a bilateral tangent projection (BTP) algorithm to smooth a set of noisy data assumed to lie on a low-dimensional manifold. The data points are smoothed by a family of local tangent projections adaptively. The BTP algorithm utilizes not only the location information of the data point but also the fitness of the tangent space estimation. The local tangent space with better fitness plays more important role in the smoothing procedure. The experimental results show that our algorithm is effective for noise reduction and preserves the structure of the underlying manifold.