Design a Metric Robust to Complicated High Dimensional Noise for Efficient Manifold Denoising
This work addresses denoising for data on manifolds in high-dimensional spaces, but it appears incremental as it builds on existing tools and defers theoretical guarantees to a future paper.
The authors tackled the problem of manifold denoising under complex high-dimensional noise by proposing an efficient denoiser based on landmark diffusion and optimal shrinkage, which handles various setups like colored and dependent noise, and they provided systematic comparisons on simulated and real datasets.
In this manuscript, we propose an efficient manifold denoiser based on landmark diffusion and optimal shrinkage under the complicated high dimensional noise and compact manifold setup. It is flexible to handle several setups, including the high ambient space dimension with a manifold embedding that occupies a subspace of high or low dimensions, and the noise could be colored and dependent. A systematic comparison with other existing algorithms on both simulated and real datasets is provided. This manuscript is mainly algorithmic and we report several existing tools and numerical results. Theoretical guarantees and more comparisons will be reported in the official paper of this manuscript.