With the rapid development of information theoretic learning, the maximum correntropy criterion (MCC) has been widely used in time series prediction area. Especially, the kernel recursive least squares (KRLS) based on MCC is studied recently due to its online recursive form and the ability to resist noise and be robust in non-Gaussian environments. However, it is not always an optimal choice that using the correntropy, which is calculated by default Gaussian kernel function, to describe the local similarity between variables. Besides, the computational burden of MCC based KRLS will raise as data size increases, thus causing difficulties in accommodating time-varying environments. Therefore, this paper proposes a quantized generalized MCC (QGMCC) to solve the above problem. Specifically, a generalized MCC (GMCC) is utilized to enhance the accuracy and flexibility in calculating the correntropy. In order to solve the problem of computational complexity, QGMCC quantizes the input space and upper bounds the network size by vector quantization (VQ) method. Furthermore, QGMCC is applied to KRLS and forming a computationally efficient and precisely predictive algorithm. After that, the improved algorithm named quantized kernel recursive generalized maximum correntropy (QKRGMC) is set up and the derivation process is also given. Experimental results of one benchmark dataset and two real-world datasets are present to verify the effectiveness of the online prediction algorithm.

随着信息理论学习的飞速发展，最大熵准则（MCC）已广泛应用于时间序列预测领域。尤其是，最近由于基于MCC的内核递归最小二乘（KRLS）的在线递归形式以及在非高斯环境下具有抗噪声和鲁棒性的能力，因此对其进行了研究。但是，使用默认由高斯核函数计算的熵来描述变量之间的局部相似性并不总是一种最佳选择。此外，基于MCC的KRLS的计算负担将随着数据大小的增加而增加，从而在适应时变环境方面造成困难。因此，本文提出了一种量化的广义MCC（QGMCC）来解决上述问题。特别，利用通用的MCC（GMCC）可以提高计算熵的准确性和灵活性。为了解决计算复杂性的问题，QGMCC通过矢量量化（VQ）方法对输入空间进行量化，并限制网络的上限。此外，将QGMCC应用于KRLS，并形成了计算有效且精确预测的算法。然后，建立了改进的算法，称为量化核递归广义最大熵（QKRGMC），并给出了推导过程。给出了一个基准数据集和两个实际数据集的实验结果，以验证在线预测算法的有效性。QGMCC通过矢量量化（VQ）方法量化输入空间并限制网络大小的上限。此外，将QGMCC应用于KRLS，并形成了计算有效且精确预测的算法。然后，建立了改进的算法，称为量化核递归广义最大熵（QKRGMC），并给出了推导过程。给出了一个基准数据集和两个实际数据集的实验结果，以验证在线预测算法的有效性。QGMCC通过矢量量化（VQ）方法量化输入空间并限制网络大小的上限。此外，将QGMCC应用于KRLS，并形成了计算高效且精确预测的算法。然后，建立了改进的算法，称为量化核递归广义最大熵（QKRGMC），并给出了推导过程。给出了一个基准数据集和两个实际数据集的实验结果，以验证在线预测算法的有效性。