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In this manuscript, we propose an efficient manifold denoiser based onlandmark diffusion and optimal shrinkage under the complicated high dimensionalnoise and compact manifold setup. It is flexible to handle several setups,including the high ambient space dimension with a manifold embedding thatoccupies a subspace of high or low dimensions, and the noise could be coloredand dependent. A systematic comparison with other existing algorithms on bothsimulated and real datasets is provided. This manuscript is mainly algorithmicand we report several existing tools and numerical results. Theoreticalguarantees and more comparisons will be reported in the official paper of thismanuscript.

Design a Metric Robust to Complicated High Dimensional Noise for Efficient Manifold Denoising