In this letter, a novel kernel function named qq-Rényi kernel is proposed. Based on it, a new online adaptive learning algorithm is presented, which is derived based on the recursive adaptive filtering paradigm under the reproducing kernel Hilbert space. The proposed learning algorithm is different from the conventional kernel-based learning paradigm in two senses: first, the reproducing kernel so-called q\boldsymbol {q}-Rényi kernel is firstly derived and employed; and second, a sparsity constraint is utilized to generate a small size of neural networks while maintaining a high learning performance. The effectiveness of the proposed algorithm is demonstrated via numerical simulations.

中文翻译：

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基于$q$-Renyi核函数的稀疏鲁棒自适应滤波算法


在这封信中，提出了一种名为 qq-Rényi 核的新型核函数。在此基础上，基于再生核希尔伯特空间下的递归自适应滤波范式，提出了一种新的在线自适应学习算法。所提出的学习算法在两个意义上不同于传统的基于核的学习范式：首先，首先导出并使用了所谓的 q\boldsymbol {q}-Rényi 核的再现核；其次，利用稀疏约束来生成小规模的神经网络，同时保持较高的学习性能。通过数值模拟证明了所提出算法的有效性。