A quantized kernel learning algorithm using a minimum kernel risk-sensitive loss criterion and bilateral gradient technique

Recently, inspired by correntropy, kernel risk-sensitive loss (KRSL) has emerged as a novel nonlinear similarity measure defined in kernel space, which achieves a better computing performance. After applying the KRSL to adaptive filtering, the corresponding minimum kernel risk-sensitive loss (MKRSL) algorithm has been developed accordingly. However, MKRSL as a traditional kernel adaptive filter (KAF) method, generates a growing radial basis functional (RBF) network. In response to that limitation, through the use of online vector quantization (VQ) technique, this article proposes a novel KAF algorithm, named quantized MKRSL (QMKRSL) to curb the growth of the RBF network structure. Compared with other quantized methods, e.g., quantized kernel least mean square (QKLMS) and quantized kernel maximum correntropy (QKMC), the efficient performance surface makes QMKRSL converge faster and filter more accurately, while maintaining the robustness to outliers. Moreover, considering that QMKRSL using traditional gradient descent method may fail to make full use of the hidden information between the input and output spaces, we also propose an intensified QMKRSL using a bilateral gradient technique named QMKRSL_BG, in an effort to further improve filtering accuracy. Short-term chaotic time-series prediction experiments are conducted to demonstrate the satisfactory performance of our algorithms.