Abstract
To construct an online kernel adaptive filter in a non-stationary environment, we propose a randomized feature networks-based kernel least mean square (KLMS-RFN) algorithm. In contrast to the Gaussian kernel, which implicitly maps the input to an infinite dimensional space in theory, the randomized feature mapping transform inputs samples into a relatively low-dimensional feature space, where the transformed samples are approximately equivalent to those in the feature space using a shift-invariant kernel. The mean square convergence process of the proposed algorithm is investigated under the uniform convergence analysis method of a nonlinear adaptive filter. The computational complexity is also evaluated. In Lorenz time series prediction and nonstationary channel equalization scenarios, the simulation results demonstrate the effectiveness of the proposed algorithm.
Highlights
In recent years, kernel-based learning has attracted much attention because the designed kernel-based nonlinear algorithm shows extraordinary improvements in performance as compared to the linear one
To evaluate the performance of the proposed kernel least mean square (KLMS)-RFN algorithm, extensive simulations based on chaotic time series prediction and nonlinear channel equalization are conducted
The KLMS-RFN algorithm is proposed to improve the performance of the online kernel-based LMS algorithm in a nonstationary environment by constructing the explicit mapping
Summary
Kernel-based learning has attracted much attention because the designed kernel-based nonlinear algorithm shows extraordinary improvements in performance as compared to the linear one ( at the cost of computational complexity). To restrict the growth of the weight network, several online sparsification criteria were proposed for KAFs to select valid samples in the learning process, such as approximate linear dependency (ALD) [5], the novelty criterion (NC) [11], the surprise criterion (SC) [12], the coherence criterion (CC) [13], the quantization criterion [14], and sparsity-promoting regularization [15,16] Among these criteria, the quantization criterion-based kernel least mean square (QKLMS) algorithm can perform better in the tradeoff between steady-state error and computational complexity [14]. The quantization criterion-based kernel least mean square (QKLMS) algorithm can perform better in the tradeoff between steady-state error and computational complexity [14] These methods are quite effective in restricting the growth of the weight network, for a nonstationary scenario, the scale of the selected samples will exhibit further growth when the feature of input signals changes because the redundant samples are not pruned during the adaptive learning process.
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