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

arXiv: https://arxiv.org/abs/2401.03921 · HTML: https://mlsanity.com/paper/2401.03921/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 12 of 12)

- [ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise](https://mlsanity.com/paper/2009.12297/) (2020)
- [OptShrink: An algorithm for improved low-rank signal matrix denoising by optimal, data-driven singular value shrinkage](https://mlsanity.com/paper/1306.6042/) (2013)
- [Impact of signal-to-noise ratio and bandwidth on graph Laplacian spectrum from high-dimensional noisy point cloud](https://mlsanity.com/paper/2011.10725/) (2020)
- [Non-Parametric Estimation of Manifolds from Noisy Data](https://mlsanity.com/paper/2105.04754/) (2021)
- [Manifold Approximation by Moving Least-Squares Projection (MMLS)](https://mlsanity.com/paper/1606.07104/) (2016)
- [Manifold Fitting under Unbounded Noise](https://mlsanity.com/paper/1909.10228/) (2019)
- [Manifold Learning Using Kernel Density Estimation and Local Principal Components Analysis](https://mlsanity.com/paper/1709.03615/) (2017)
- [Inferring manifolds using Gaussian processes](https://mlsanity.com/paper/2110.07478/) (2021)
- [Optimal Recovery of Precision Matrix for Mahalanobis Distance from High Dimensional Noisy Observations in Manifold Learning](https://mlsanity.com/paper/1904.09204/) (2019)
- [Matrix Denoising with Partial Noise Statistics: Optimal Singular Value Shrinkage of Spiked F-Matrices](https://mlsanity.com/paper/2211.00986/) (2022)
- [Diffusion geometry approach to efficiently remove electrical stimulation artifacts in intracranial electroencephalography](https://mlsanity.com/paper/1811.08428/) (2018)
- [Recovery of the fetal electrocardiogram for morphological analysis from two trans-abdominal channels via optimal shrinkage](https://mlsanity.com/paper/1904.09525/) (2019)

## Built on by (most cited first, 1 of 1)

- [Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators](https://mlsanity.com/paper/2405.12317/) (2024)

## Abstract (arXiv)

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.