Manifold Denoising

Part of Advances in Neural Information Processing Systems 19 (NIPS 2006)

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Matthias Hein, Markus Maier


We consider the problem of denoising a noisily sampled submanifold M in Rd, where the submanifold M is a priori unknown and we are only given a noisy point sample. The presented denoising algorithm is based on a graph-based diffusion process of the point sample. We analyze this diffusion process using recent re- sults about the convergence of graph Laplacians. In the experiments we show that our method is capable of dealing with non-trivial high-dimensional noise. More- over using the denoising algorithm as pre-processing method we can improve the results of a semi-supervised learning algorithm.