## What is/are Kernel Adaptive?

Kernel Adaptive - Therefore, for the accurate estimation of DOD, DOA and Doppler shift, an efficient, kernel adaptive filter (KAF) based estimation approach is proposed.^{[1]}In this paper, we propose a nonlinear recurrent kernel normalized LMS (NR-KNLMS) algorithm based on the algorithmic framework of multikernel adaptive filtering for nonlinear autoregressive systems.

^{[2]}Furthermore, SPMKC proposes a kernel group self-expressiveness term and a kernel adaptive local structure learning term to preserve the global and local structure of the input data in kernel space, respectively, rather than the original space.

^{[3]}To alleviate this problem and realize as fully as possible the potential of SSIM, an anisotropic implementation is put forward in this letter in which a kernel adaptive to image local structures is integrated in SSIM computation.

^{[4]}Moreover, we emphasize recent advances of NLANC algorithms, such as spline ANC algorithms, kernel adaptive filters, and nonlinear distributed ANC algorithms.

^{[5]}The Cauchy loss (CL) is a high-order loss function which has been successfully used to overcome large outliers in kernel adaptive filters.

^{[6]}To further tackle complex nonlinear issues, novel multiple random Fourier features (MRFF) spaces are then constructed in finite-dimensional features spaces, which is proven effective for approximation of multi-kernel adaptive filter (MKAF), theoretically.

^{[7]}In this brief, a kernel adaptive filter based on the Student’s

^{[8]}The kernel adaptive filters (KAFs) can better solve the nonlinear problem by mapping the filtered reference signal to the high dimensional reproductive kernel Hilbert feature space (RKHFS).

^{[9]}The kernel least mean square (KLMS) algorithm is the simplest algorithm in kernel adaptive filters.

^{[10]}The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems.

^{[11]}This paper presents an automatic kernel weighting technique for multikernel adaptive filtering.

^{[12]}A learning task is sequential if its data samples become available over time; kernel adaptive filters (KAFs) are sequential learning algorithms.

^{[13]}In this paper, we develop a kernel adaptive filter for quaternion domain data, based on information theoretic learning cost function which could be useful for quaternion based kernel applications of nonlinear filtering.

^{[14]}An outlier detection and elimination method based on kernel adaptive filtering with variable step size for trajectory data of vehicle test was proposed.

^{[15]}Random Fourier mapping (RFM) in kernel adaptive filters (KAFs) provides an efficient method to curb the linear growth of the dictionary by projecting the original input data into a finite-dimensional space.

^{[16]}To overcome these drawbacks, we propose a recurrent kernel-based approach for image processing using the Kernel Adaptive Autoregressive Moving Average algorithm (KAARMA).

^{[17]}In this paper, we develop a kernel adaptive filter for quaternion data, using stochastic information gradient (SIG) cost function based on the information theoretic learning (ITL) approach.

^{[18]}Firstly, it is modified to operate as a kernel adaptive filter, i.

^{[19]}Next, borrowing sparsification methods from kernel adaptive filtering, the continuous action-space approximation in the online least-squares policy iteration algorithm can be efficiently automated as well.

^{[20]}The proposed KMEC is derived in the context of the kernel adaptive filter and it provides good performance for identifying the nonlinear channels in different mixed noise environments in terms of the mean square error (MSE) at its steady-state and convergence performance.

^{[21]}For nonlinear channels, Kernel Adaptive Filters (KAFs) have been used since they are able to solve nonlinear problems implicitly projecting the input vector into a larger dimension space, where they can be linearly solved.

^{[22]}We present an online method for multiscale data classification, using the multikernel adaptive filtering framework.

^{[23]}Kernel conjugate gradient (KCG) algorithms have been proposed to improve the convergence rate and filtering accuracy of kernel adaptive filters (KAFs).

^{[24]}In recent years, the kernel adaptive filter (KAF) has been widely adopted to solve the robust regression problem due to its low-complexity and high-approximation capability and robustness while the applications in battery RUL prediction are still few and far between.

^{[25]}

## kernel recursive least

ABSTRACT Aiming at the problems of strong nonlinearity and complicated mechanism for chemical processes, a class of soft sensor modeling methods based on kernel adaptive filtering (KAF) algorithms are proposed, including sliding-window kernel recursive least-squares (SW-KRLS), fixed-budget kernel recursive least-squares (FBKRLS) and quantization kernel least mean squares (Q-KLMS).^{[1]}To improve the robustness of the kernel recursive least squares algorithm (KRLS) and reduce its network size, two robust recursive kernel adaptive filters, namely recursive minimum kernel risk-sensitive mean p-power error algorithm (RMKRP) and its quantized RMKRP (QRMKRP), are proposed in the RKHS under the minimum kernel risk-sensitive mean p-power error (MKRP) criterion, respectively.

^{[2]}

## kernel adaptive filter

Therefore, for the accurate estimation of DOD, DOA and Doppler shift, an efficient, kernel adaptive filter (KAF) based estimation approach is proposed.^{[1]}Moreover, we emphasize recent advances of NLANC algorithms, such as spline ANC algorithms, kernel adaptive filters, and nonlinear distributed ANC algorithms.

^{[2]}The Cauchy loss (CL) is a high-order loss function which has been successfully used to overcome large outliers in kernel adaptive filters.

^{[3]}To further tackle complex nonlinear issues, novel multiple random Fourier features (MRFF) spaces are then constructed in finite-dimensional features spaces, which is proven effective for approximation of multi-kernel adaptive filter (MKAF), theoretically.

^{[4]}In this brief, a kernel adaptive filter based on the Student’s

^{[5]}The kernel adaptive filters (KAFs) can better solve the nonlinear problem by mapping the filtered reference signal to the high dimensional reproductive kernel Hilbert feature space (RKHFS).

^{[6]}The complex kernel adaptive filter (CKAF) has been widely applied to the complex-valued nonlinear problem in signal processing and machine learning.

^{[7]}The kernel least mean square (KLMS) algorithm is the simplest algorithm in kernel adaptive filters.

^{[8]}5 concentration called Weather Research and Forecasting model based quantized kernel adaptive filter (WRF-QKAF) is proposed in this paper.

^{[9]}A learning task is sequential if its data samples become available over time; kernel adaptive filters (KAFs) are sequential learning algorithms.

^{[10]}In this paper, we develop a kernel adaptive filter for quaternion domain data, based on information theoretic learning cost function which could be useful for quaternion based kernel applications of nonlinear filtering.

^{[11]}To improve the robustness of the kernel recursive least squares algorithm (KRLS) and reduce its network size, two robust recursive kernel adaptive filters, namely recursive minimum kernel risk-sensitive mean p-power error algorithm (RMKRP) and its quantized RMKRP (QRMKRP), are proposed in the RKHS under the minimum kernel risk-sensitive mean p-power error (MKRP) criterion, respectively.

^{[12]}Random Fourier mapping (RFM) in kernel adaptive filters (KAFs) provides an efficient method to curb the linear growth of the dictionary by projecting the original input data into a finite-dimensional space.

^{[13]}In this paper, we develop a kernel adaptive filter for quaternion data, using stochastic information gradient (SIG) cost function based on the information theoretic learning (ITL) approach.

^{[14]}Firstly, it is modified to operate as a kernel adaptive filter, i.

^{[15]}The proposed KMEC is derived in the context of the kernel adaptive filter and it provides good performance for identifying the nonlinear channels in different mixed noise environments in terms of the mean square error (MSE) at its steady-state and convergence performance.

^{[16]}For nonlinear channels, Kernel Adaptive Filters (KAFs) have been used since they are able to solve nonlinear problems implicitly projecting the input vector into a larger dimension space, where they can be linearly solved.

^{[17]}Kernel conjugate gradient (KCG) algorithms have been proposed to improve the convergence rate and filtering accuracy of kernel adaptive filters (KAFs).

^{[18]}In recent years, the kernel adaptive filter (KAF) has been widely adopted to solve the robust regression problem due to its low-complexity and high-approximation capability and robustness while the applications in battery RUL prediction are still few and far between.

^{[19]}

## kernel adaptive filtering

In this paper, we propose a nonlinear recurrent kernel normalized LMS (NR-KNLMS) algorithm based on the algorithmic framework of multikernel adaptive filtering for nonlinear autoregressive systems.^{[1]}ABSTRACT Aiming at the problems of strong nonlinearity and complicated mechanism for chemical processes, a class of soft sensor modeling methods based on kernel adaptive filtering (KAF) algorithms are proposed, including sliding-window kernel recursive least-squares (SW-KRLS), fixed-budget kernel recursive least-squares (FBKRLS) and quantization kernel least mean squares (Q-KLMS).

^{[2]}In this paper, two new multi-output kernel adaptive filtering algorithms are developed that exploit the temporal and spatial correlations among the input-output multivariate time series.

^{[3]}The purpose of kernel adaptive filtering (KAF) is to map input samples into reproducing kernel Hilbert spaces and use the stochastic gradient approximation to address learning problems.

^{[4]}This paper presents an automatic kernel weighting technique for multikernel adaptive filtering.

^{[5]}Although the sparse kernel adaptive filtering algorithms have been proposed to address the problem of redundant dictionary in non-stationary environments, there is few attempt of analyzing their stochastic convergence behaviors.

^{[6]}An outlier detection and elimination method based on kernel adaptive filtering with variable step size for trajectory data of vehicle test was proposed.

^{[7]}Simulations are conducted to illustrate the performance benefits of RFF-EW-KRLP related to the typical kernel adaptive filtering algorithms based on the second statistic error criterion in the impulsive noise environment.

^{[8]}Next, borrowing sparsification methods from kernel adaptive filtering, the continuous action-space approximation in the online least-squares policy iteration algorithm can be efficiently automated as well.

^{[9]}Simulations demonstrate the EW-KRLP algorithm has better convergence performance than the existing kernel adaptive filtering approaches in identifying the non-stationary nonlinear system under the assumption of non-Gaussian impulsive noise modeled by the symmetric α-stable distribution.

^{[10]}We present an online method for multiscale data classification, using the multikernel adaptive filtering framework.

^{[11]}An interpolation method based on bidirectional unequal interval kernel adaptive filtering was proposed to solve the missing data problem of trajectory measurement for the vehicle test.

^{[12]}