Low-Rank Representation with Empirical Kernel Space Embedding of Manifolds

Abstract

Low-Rank Representation (LRR) methods integrate low-rank constraints and projection operators to model the mapping from the sample space to low-dimensional manifolds. Nonetheless, existing approaches typically apply Euclidean algorithms directly to manifold data in the original input space, leading to suboptimal classification accuracy. To mitigate this limitation, we introduce an unsupervised low-rank projection learning method named Low-Rank Representation with Empirical Kernel Space Embedding of Manifolds (LRR-EKM). LRR-EKM leverages an empirical kernel mapping to project samples into the Reproduced Kernel Hilbert Space (RKHS), enabling the linear separability of non-linearly structured samples and facilitating improved low-dimensional manifold representations through Euclidean distance metrics. By incorporating a row sparsity constraint on the projection matrix, LRR-EKM not only identifies discriminative features and removes redundancies but also enhances the interpretability of the learned subspace. Additionally, we introduce a manifold structure preserving constraint to retain the original representation and distance information of the samples during projection. Comprehensive experimental evaluations across various real-world datasets validate the superior performance of our proposed method compared to the state-of-the-art methods. The code is publicly available at https://github.com/ff-raw-war/LRR-EKM.