A Polarized Random Fourier Feature Kernel Least-Mean-Square Algorithm

Abstract

This paper presents a polarized random Fourier feature kernel least-mean-square algorithm that aims to overcome the dimension curve of the random Fourier feature kernel least-mean-square (RFFKLMS) algorithm. RFFKLMS is an effective nonlinear adaptive filtering algorithm based on the kernel approximation technique. However, random samples drawn from the distribution need more dimensions to achieve better-generalized performance because they are independent of the training data. To overcome this weakness, a kernel polarization method is adopted to optimize the random samples. Polarized random Fourier features demonstrate a clear advantage over a method without using the polarization method. The experimental results in the context of Lorenz time series prediction and channel equalization verify the effectiveness of the proposed method.INDEX TERMS Kernel adaptive filtering, kernel polarization method, polarized random Fourier features, random Fourier features.

Expanded Neo-Fuzzy Adaptive Decayed Brain Emotional Learning Network for Online Time Series Predication

“…We simulated the ENF-ADBEL to predict the x-dynamics of the Lorenz chaotic time series. This series has also been used in various studies to verify the performance of prediction algorithms [18]- [19]. The series is generated by [17] from the coupled differential equations; for more details, refer to [2].…”

Accelerate Convergence of Polarized Random Fourier Feature-Based Kernel Adaptive Filtering With Variable Forgetting Factor and Step Size

“…To evaluate the tracking speed of the proposed algorithm, an initial set of 800 data points were generated using Eq. (21). Then, for n > 800, the system model was changed to…”

“…The time and memory complexity of the RFFKLMS algorithm, in contrast to the sparsification method, are merely constant, which improved the online computation ability of KLMS algorithm in the case of real-time and large-scale signal processing. A polarized random Fourier features-based kernel least-meansquare(PRFFKLMS) algorithm was proposed, where the polarization preprocessing method further improved the accuracy performance of RFFKLMS [21]. Although PRFFKLMS algorithm is the most representative RFF-based KLMS algorithm at present, the convergence speed and tracking speed of PRFFKLMS algorithm still need to be improved for nonstationary signal processing cases.…”

“…Although PRFFKLMS algorithm is the most representative RFF-based KLMS algorithm at present, the convergence speed and tracking speed of PRFFKLMS algorithm still need to be improved for nonstationary signal processing cases. In [18], [21], the RFFbased kernel adaptive filtering algorithm such as RFFKLMS and PRFFKLMS algorithm use the fixed step size strategy.…”

An Efficient Scheme for Determining the Power Loss in Wind-PV Based on Deep Learning

“…Let denote the regenerated kernel Hilbert space (RKHS)[32], (•): → denote the nonlinear feature mapping function from the original feature space to RKHS. Since RKHS is usually a high-dimensional or even infinite space, the corresponding kernel generally chooses to represent an infinite-dimensional Gaussian kernel[33][34]: Deep learning model based on DBN-DNN.…”