Manifold Blurring Mean Shift Algorithms for Manifold Denoising

Abstract

We propose a new family of algorithms for denoising data assumed to lie on a low-dimensional manifold. The algorithms are based on the blurring mean-shift update, which moves each data point towards its neighbors, but constrain the motion to be orthogonal to the manifold. The resulting algorithms are nonparametric, simple to implement and very effective at removing noise while preserving the curvature of the manifold and limiting shrinkage. They deal well with extreme outliers and with variations of density along the manifold. We apply them as preprocessing for dimensionality reduction; and for nearest-neighbor classification of MNIST digits, with consistent improvements up to 36% over the original data.

Cite

Text

Wang and Carreira-Perpiñán. "Manifold Blurring Mean Shift Algorithms for Manifold Denoising." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2010. doi:10.1109/CVPR.2010.5539845

Markdown

[Wang and Carreira-Perpiñán. "Manifold Blurring Mean Shift Algorithms for Manifold Denoising." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2010.](https://mlanthology.org/cvpr/2010/wang2010cvpr-manifold/) doi:10.1109/CVPR.2010.5539845

BibTeX

@inproceedings{wang2010cvpr-manifold,
  title     = {{Manifold Blurring Mean Shift Algorithms for Manifold Denoising}},
  author    = {Wang, Weiran and Carreira-Perpiñán, Miguel Á.},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {2010},
  pages     = {1759-1766},
  doi       = {10.1109/CVPR.2010.5539845},
  url       = {https://mlanthology.org/cvpr/2010/wang2010cvpr-manifold/}
}