Clustering and Dimensionality Reduction on Riemannian Manifolds
Abstract
We propose a novel algorithm for clustering data sampled from multiple submanifolds of a Riemannian manifold. First, we learn a representation of the data using generalizations of local nonlinear dimensionality reduction algorithms from Euclidean to Riemannian spaces. Such generalizations exploit geometric properties of the Riemannian space, particularly its Riemannian metric. Then, assuming that the data points from different groups are separated, we show that the null space of a matrix built from the local representation gives the segmentation of the data. Our method is computationally simple and performs automatic segmentation without requiring user initialization. We present results on 2-D motion segmentation and diffusion tensor imaging segmentation.
Cite
Text
Goh and Vidal. "Clustering and Dimensionality Reduction on Riemannian Manifolds." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2008. doi:10.1109/CVPR.2008.4587422Markdown
[Goh and Vidal. "Clustering and Dimensionality Reduction on Riemannian Manifolds." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2008.](https://mlanthology.org/cvpr/2008/goh2008cvpr-clustering/) doi:10.1109/CVPR.2008.4587422BibTeX
@inproceedings{goh2008cvpr-clustering,
title = {{Clustering and Dimensionality Reduction on Riemannian Manifolds}},
author = {Goh, Alvina and Vidal, René},
booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
year = {2008},
doi = {10.1109/CVPR.2008.4587422},
url = {https://mlanthology.org/cvpr/2008/goh2008cvpr-clustering/}
}