# Low Rank Representation on Grassmann Manifolds: An Extrinsic Perspective

arXiv: https://arxiv.org/abs/1504.01807 · HTML: https://mlsanity.com/paper/1504.01807/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Apr 2015.

## Built on by (most cited first, 2 of 2)

- [Polynomial Chaos Expansions on Principal Geodesic Grassmannian Submanifolds for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/2401.16683/) (2024)
- [Embedding Graphs on Grassmann Manifold](https://mlsanity.com/paper/2205.15068/) (2022)

## Abstract (arXiv)

Many computer vision algorithms employ subspace models to represent data. The Low-rank representation (LRR) has been successfully applied in subspace clustering for which data are clustered according to their subspace structures. The possibility of extending LRR on Grassmann manifold is explored in this paper. Rather than directly embedding Grassmann manifold into a symmetric matrix space, an extrinsic view is taken by building the self-representation of LRR over the tangent space of each Grassmannian point. A new algorithm for solving the proposed Grassmannian LRR model is designed and implemented. Several clustering experiments are conducted on handwritten digits dataset, dynamic texture video clips and YouTube celebrity face video data. The experimental results show our method outperforms a number of existing methods.