Hilbert Functions and Applications to the Estimation of Subspace Arrangements

Yang, Allen Y.; Fossum, Robert M.

doi:10.1109/ICCV.2005.114

Hilbert Functions and Applications to the Estimation of Subspace Arrangements

Allen Y. Yang, Robert M. Fossum

ICCV 2005 pp. 158-165

doi:10.1109/ICCV.2005.114 /iccv/2005/yang2005iccv-hilbert/

Abstract

This paper develops a new mathematical framework for studying the subspace-segmentation problem. We examine some important algebraic properties of subspace arrangements that are closely related to the subspace-segmentation problem. More specifically, we introduce an important class of invariants given by the Hilbert functions. We show that there exist rich relations between subspace arrangements and their corresponding Hilbert functions. We propose a new subspace-segmentation algorithm, and showcase two applications to demonstrate how the new theoretical revelation may solve subspace segmentation and model selection problems under less restrictive conditions with improved results.

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Text

Yang and Fossum. "Hilbert Functions and Applications to the Estimation of Subspace Arrangements." IEEE/CVF International Conference on Computer Vision, 2005. doi:10.1109/ICCV.2005.114

Markdown

[Yang and Fossum. "Hilbert Functions and Applications to the Estimation of Subspace Arrangements." IEEE/CVF International Conference on Computer Vision, 2005.](https://mlanthology.org/iccv/2005/yang2005iccv-hilbert/) doi:10.1109/ICCV.2005.114

BibTeX

@inproceedings{yang2005iccv-hilbert,
  title     = {{Hilbert Functions and Applications to the Estimation of Subspace Arrangements}},
  author    = {Yang, Allen Y. and Fossum, Robert M.},
  booktitle = {IEEE/CVF International Conference on Computer Vision},
  year      = {2005},
  pages     = {158-165},
  doi       = {10.1109/ICCV.2005.114},
  url       = {https://mlanthology.org/iccv/2005/yang2005iccv-hilbert/}
}