Low-rank representation with adaptive dimensionality reduction via manifold optimization for clustering

The dimensionality reduction techniques are often used to reduce data dimensionality for computational efficiency or other purposes in existing low-rank representation (LRR)-based methods. However, the two steps of dimensionality reduction and learning low-rank representation coefficients are implemented in an independent way; thus, the adaptability of representation coefficients to the original data space may not be guaranteed. This paper proposes a novel model, i.e., low-rank representation with adaptive dimensionality reduction (LRRARD) via manifold optimization for clustering, where dimensionality reduction and learning low-rank representation coefficients are integrated into a unified framework. This model introduces a low-dimensional projection matrix to find the projection that best fits the original data space. And the low-dimensional projection matrix and the low-rank representation coefficients interact with each other to simultaneously obtain the best projection matrix and representation coefficients. In addition, a manifold optimization method is employed to obtain the optimal projection matrix, which is an unconstrained optimization method in a constrained search space. The experimental results on several real datasets demonstrate the superiority of our proposed method.