TSBP: Tangent Space Belief Propagation for Manifold Learning

We present Tangent Space Belief Propagation (TSBP) as a method for graph denoising to improve the robustness of manifold learning algorithms. Dimension reduction by manifold learning relies heavily on the accurate selection of nearest neighbors, which has proven an open problem for sparse and noisy datasets. TSBP uses global nonparametric belief propagation to accurately estimate the tangent spaces of the underlying manifold at each data point. Edges of the neighborhood graph that deviate from the tangent spaces are then removed. The resulting denoised graph can then be embedded into a lower-dimensional space using methods from existing manifold learning algorithms. Artificially generated manifold data, simulated sensor data from a mobile robot, and high dimensional tactile sensory data are used to demonstrate the efficacy of our TSBP method.