Symmetric low-rank representation for subspace clustering

TL;DR

The paper introduces a symmetric low-rank representation method for subspace clustering that efficiently captures subspace structures and improves clustering accuracy by using a closed-form solution and spectral clustering.

Contribution

It presents a novel symmetric low-rank representation approach that simplifies computation and enhances clustering performance over existing methods.

Findings

Outperforms state-of-the-art subspace clustering algorithms.

Provides a closed-form solution for symmetric low-rank representation.

Effectively preserves subspace structures in high-dimensional data.

Abstract

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.