# Symmetric low-rank representation for subspace clustering

arXiv: https://arxiv.org/abs/1410.8618 · HTML: https://mlsanity.com/paper/1410.8618/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2014.

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

- [Multilayer Graph Approach to Deep Subspace Clustering](https://mlsanity.com/paper/2401.17033/) (2024)

## Abstract (arXiv)

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which preserves the subspace structures of high-dimensional data. In contrast to performing iterative singular value decomposition in some existing low-rank representation based algorithms, the symmetric low-rank representation in the SLRR method can be calculated as a closed form solution by solving the symmetric low-rank optimization problem. By making use of the angular information of the principal directions of the symmetric low-rank representation, an affinity graph matrix is constructed for spectral clustering. Extensive experimental results show that it outperforms state-of-the-art subspace clustering algorithms.