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.

翻译：我们提出了一种高效的在线字典学习算法，用于基于核的稀疏表示。在此框架中，输入信号被非线性映射到高维特征空间，并使用虚拟字典进行稀疏表示。在每一步中，字典通过一种基于递归最小二乘（RLS）方法的新颖算法进行递归更新。该更新机制适用于单样本或小批量数据，并保持较低的计算复杂度。在四个不同领域的数据集上的实验表明，我们的方法不仅优于现有的在线核字典学习方法，而且达到了接近批量训练模型的分类精度，同时保持了显著更高的计算效率。