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Knowl. Discov. Data"],"published-print":{"date-parts":[[2023,11,30]]},"abstract":"<jats:p>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 article 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. 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