Kernel Recursive Least Squares Dictionary Learning Algorithm

We propose an efficient online dictionary learning algorithm for kernel-based sparse representations. In this framework, input signals are nonlinearly mapped to a high-dimensional feature space and represented sparsely using a virtual dictionary. At each step, the dictionary is updated recursively using a novel algorithm based on the recursive least squares (RLS) method. This update mechanism works with single samples or mini-batches and maintains low computational complexity. Experiments on four datasets across different domains show that our method not only outperforms existing online kernel dictionary learning approaches but also achieves classification accuracy close to that of batch-trained models, while remaining significantly more efficient.

@article{alipoor2025_2507.01636,
  title={ Kernel Recursive Least Squares Dictionary Learning Algorithm },
  author={ Ghasem Alipoor and Karl Skretting },
  journal={arXiv preprint arXiv:2507.01636},
  year={ 2025 }
}