Correntropy Algorithm Research Articles

Bias-compensated based diffusion affine projection like maximum correntropy algorithm

A distributed network with highly colored input signal is often located in a scenario where the output signal is subject to impulse noise. Under the above scenario, the performance of the diffusion adaptive algorithms will suffer from performance degradation, which includes distributed parameter estimation accuracy and convergence/tracking rate. To solve these problems, the diffusion affine projection like maximum correntropy (DAPLMC) algorithm is proposed. Moreover, highly colored input signals tend to be mixed with noise, which will lead to biased estimation. To deal with the adverse impact of biased estimation, based on the bias compensation (BC) strategy, the bias-compensated DAPLMC (BC-DAPLMC) algorithm is proposed in this paper. By analyzing the convergence performance of the BC-DAPLMC algorithm, a range of its step size is obtained, and the steady-state error of the BC-DAPLMC algorithm is studied. The superior performance of the BC-DAPLMC algorithm and theoretical steady-state error analysis is validated by simulation results.

Fractional-order modified blake–zisserman-based correntropy algorithm in [formula omitted]-stable environment

Traditional robust adaptive filtering algorithms are commonly designed by incorporating error nonlinearity cost functions and stochastic gradient descent (SGD) method to mitigate the effects of non-Gaussian/impulsive noises that can distort systems. However, these methods often face significant challenges when the input signal itself contains sharp spikes. This paper addresses the challenge of managing spikes and outliers often encountered in both input and noise signals within adaptive filtering settings. We propose utilizing the α-stable distribution model for both input and noise signals. Our approach centres on optimizing the modified Blake-Zisserman-based correntropy (MBZC) cost function and employing the fractional-order SGD (FoSGD) method, leading to the development of a new method called fractional-order MBZC (FoMBZC), that offers increased flexibility and broader applicability across various signal and noise types. We provide a detailed analysis of the mean stability and mean square steady-state behaviour of the FoMBZC under Gaussian conditions. Finally, simulation experiments in various non-Gaussian environments are performed to highlight the superiority of the proposed method compared to existing algorithms.

A Kernel Normalized Data-Reusing Generalized Maximum Correntropy Algorithm

A Kernel Normalized Data-Reusing Generalized Maximum Correntropy Algorithm

A Novel Combinatoric Correntropy Algorithm: Properties and its Performance Analysis

In order to improve the flexibility of the correntropy that is usually in the form of a single kernel, this brief proposes a novel combinatoric maximum correntropy criterion (C-MCC), where the combinatoric correntropy (C-C) consists of two different single-type kernels. As a new form of correntropy, the C-C has a more generalized form than the traditional single-kernel correntropy, and the corresponding properties and proofs of the C-C are given in this brief. It is noticed that the combined kernel can become a single kernel by changing the combined parameters. Moreover, the adaptive filtering algorithm based on C-MCC is derived and the theoretical performance analysis of the C-MCC algorithm is also provided. Finally, the experimental simulations show that the proposed algorithm has better convergence speed and steady-state performance than MCC-type and other algorithms, and the proposed method of the theoretical analysis of C-MCC agrees well with simulation results.

Maximum Total Improper Complex Correntropy Algorithm for Widely Linear Adaptive Filtering

The maximum total complex correntropy (MTCC) algorithm improves the performance of adaptive filtering under the error in variable (EIV) model by integrating both input and output noise information into the total complex correntropy. However, the MTCC algorithm cannot be applied to the widely linear model, directly. Compared with a strictly linear model, the widely linear model provides the complete statistical information of signals for adaptive filtering. This paper first constructs a novel cost function for the widely linear model by incorporating the input and output noise information into the improper complex correntropy. Then, a novel widely linear adaptive filter algorithm named widely linear maximum total improper complex correntropy (WL-MTICC) is proposed using the gradient descent method under the maximum total improper correntropy criterion. Finally, the analysis of local stability and convergence in the mean sense regarding the proposed WL-MTICC algorithm is provided. Simulations are used to show the performance advantage of the proposed WL-MTICC algorithm in the presence of both input and output noises.

Random Fourier feature kernel recursive maximum mixture correntropy algorithm for online time series prediction

In the paper, a novel kernel recursive least-squares (KRLS) algorithm named random Fourier feature kernel recursive maximum mixture correntropy (RFF-RMMC) algorithm is proposed, which improves the prediction efficiency and robustness of the KRLS algorithm. Random Fourier feature (RFF) method as well as maximum mixture correntropy criterion (MMCC) are combined and applied into KRLS algorithm afterwards. Using RFF to approximate the kernel function in KRLS with a fixed cost can greatly reduce the computational complexity and simultaneously improve the prediction efficiency. In addition, the MMCC maintains the robustness like the maximum correntropy criterion (MCC). More importantly, it can enhance the accuracy of the similarity measurement between predicted and true values by more flexible parameter settings, and then make up for the loss of prediction accuracy caused by RFF to a certain extent. The performance of the RFF-RMMC algorithm for online time series prediction is verified by the simulation results based on three datasets.

Fractional‐order complex correntropy algorithm for adaptive filtering in α‐stable environment

In adaptive filtering applications, the Gaussian distribution cannot be used to model the signal/noise with frequent spikes accurately. In fact, the rational model to simulate the behaviour of such signal/noise is the α-stable distribution process. In this letter, a fractional-order complex correntropy algorithm is proposed to deal with the case that both signal and noise processes are modelled as complex-valued α-stable signals. Compared with the classical approaches, the proposed fractional-order complex correntropy extends the Gaussian assumption of signal/noise in the complex domain to the assumption of α-stable distributions without second-order and higher order statistical moments. Benefitting from the fractional-order calculus and correntropy criterion, fractional-order complex correntropy shows great robustness to the jittery behaviour of complex-valued α-stable signal/noise. In addition, a convergence analysis for fractional-order complex correntropy has been carried out. Simulations on system identification revealed that the filtering performance is significantly improved by using fractional-order complex correntropy.

A novel visualization system of using augmented reality in knee replacement surgery: Enhanced bidirectional maximum correntropy algorithm.

Image registration and alignment are the main limitations of augmented reality (AR)-based knee replacement surgery. This research aims to decrease the registration error, eliminate outcomes that are trapped in local minima to improve the alignment problems, handle the occlusion and maximize the overlapping parts. Markerless image registration method was used for AR-based knee replacement surgery to guide and visualize the surgical operation. While weight least square algorithm was used to enhance stereo camera-based tracking by filling border occlusion in right-to-left direction and non-border occlusion from left-to-right direction. This study has improved video precision to 0.57-0.61mm alignment error. Furthermore, with the use of bidirectional points, that is, forward and backward directional cloud point, the iteration on image registration was decreased. This has led to improve the processing time as well. The processing time of video frames was improved to 7.4-11.74 frames per second. It seems clear that this proposed system has focused on overcoming the misalignment difficulty caused by the movement of patient and enhancing the AR visualization during knee replacement surgery. The proposed system was reliable and favourable which helps in eliminating alignment error by ascertaining the optimal rigid transformation between two cloud points and removing the outliers and non-Gaussian noise. The proposed AR system helps in accurate visualization and navigation of anatomy of knee such as femur, tibia, cartilage, blood vessels and so forth.

Fixed-Point Maximum Total Complex Correntropy Algorithm for Adaptive Filter

Adaptive filtering for complex-valued data plays a key role in the field of signal processing. So far, there has been very little research for the adaptive filtering in complex-valued errors-in-variables (EIV) model. Compared with the complex correntropy, the total complex correntropy has shown superior performance in the EIV model. However, the current gradient based maximum total complex correntropy (MTCC) adaptive filtering algorithm has suffered from the tradeoff between fast convergence rate and low weight error power. In order to improve the performance of MTCC, we develop a fixed point maximum total complex correntropy (FP-MTCC) adaptive filtering algorithm in this study. The convergence analysis of the FP-MTCC is also provided in the paper. Furthermore, we develop two recursive FP-MTCC (RFP-MTCC) algorithms for the online adaptive filtering and provide the transient analysis of RFP-MTCC. Finally, the validity of the convergence and the superiority of the proposed algorithms are verified by simulations.

Robust Fractional Lower Order Correntropy Algorithm for DOA Estimation in Impulsive Noise Environments

Robust Fractional Lower Order Correntropy Algorithm for DOA Estimation in Impulsive Noise Environments

A Parallel Kernelized Data-Reusing Maximum Correntropy Algorithm

In this brief, a parallel kernel data-reusing maximum correntropy (PKDRMC) algorithm is proposed within the framework of nonlinear adaptive filtering. The PKDRMC algorithm consists of two branches, namely, the data-reusing maximum correntropy algorithm, and its kernelized form to combat the non-Gaussian interferences. Then, a new cost function is put forward based on the two different schemes, and it is investigated via nonlinear channel equalization (NCE). The proposed PKDRMC algorithm is robust against impulsive-noise environments. Simulations in the NCE under impulsive-noise settings perform that the PKDRMC algorithm outperforms the popular kernel adaptive algorithms.

Adaptive filtering based on recursive minimum error entropy criterion

In this paper, a robust adaptive algorithm, called recursive minimum error entropy, is derived under the minimum error entropy criterion. The new algorithm can perform robustly under impulsive noise. Theoretical analyses and numerical simulations revealed that the new algorithm performs better than the recursive least squares and recursive maximum correntropy algorithm.

Generalized maximum correntropy algorithm with affine projection for robust filtering under impulsive-noise environments

Combining affine projection (AP) with the generalized maximum correntropy (GMC) criterion, we propose a new family of AP-type filtering algorithms, called as APGMC, for system identification under impulsive-noise environments. By optimizing GMC of the a posterior error vector with a ℓ2-norm constraint on the filter weight vector, APGMC avoids the computation of the inversion of the input data matrix. Simulation results validate that APGMC achieves better filtering accuracy and faster convergence rate, compared to state-of-the-art algorithms.

Kernel Correntropy Conjugate Gradient Algorithms Based on Half-Quadratic Optimization.

As a nonlinear similarity measure defined in the kernel space, the correntropic loss (C-Loss) can address the stability issues of second-order similarity measures thanks to its ability to extract high-order statistics of data. However, the kernel adaptive filter (KAF) based on the C-Loss uses the stochastic gradient descent (SGD) method to update its weights and, thus, suffers from poor performance and a slow convergence rate. To address these issues, the conjugate gradient (CG)-based correntropy algorithm is developed by solving the combination of half-quadratic (HQ) optimization and weighted least-squares (LS) problems, generating a novel robust kernel correntropy CG (KCCG) algorithm. The proposed KCCG with less computational complexity achieves comparable performance to the kernel recursive maximum correntropy (KRMC) algorithm. To further curb the growth of the network in KCCG, the random Fourier features KCCG (RFFKCCG) algorithm is proposed by transforming the original input data into a fixed-dimensional random Fourier features space (RFFS). Since only one current error information is used in the loss function of RFFKCCG, it can provide a more efficient filter structure than the other KAFs with sparsification. The Monte Carlo simulations conducted in the prediction of synthetic and real-world chaotic time series and the regression for large-scale datasets validate the superiorities of the proposed algorithms in terms of robustness, filtering accuracy, and complexity.

The Cauchy Conjugate Gradient Algorithm with Random Fourier Features

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. The commonly used measure in RFM-based KAFs is the minimum mean square error (MMSE), which causes performance deterioration in the presence of non-Gaussian noises. To address this issue, the minimum Cauchy loss (MCL) criterion has been successfully applied for combating non-Gaussian noises in KAFs. However, these KAFs using the well-known stochastic gradient descent (SGD) optimization method may suffer from slow convergence rate and low filtering accuracy. To this end, we propose a novel robust random Fourier features Cauchy conjugate gradient (RFFCCG) algorithm using the conjugate gradient (CG) optimization method in this paper. The proposed RFFCCG algorithm with low complexity can achieve better filtering performance than the KAFs with sparsification, such as the kernel recursive maximum correntropy algorithm with novelty criterion (KRMC-NC), in stationary and non-stationary environments. Monte Carlo simulations conducted in the time-series prediction and nonlinear system identification confirm the superiorities of the proposed algorithm.

Zero Attracting Maximum Total Correntropy Algorithm for Sparse System Identification

Recently, a robust maximum total correntropy (MTC) adaptive filtering algorithm has been used in errors-in-variables (EIV) model in which both input and output data are contaminated with noises. As an extension of the maximum correntropy criterion (MCC), the MTC algorithm shows desirable performance in non-Gaussian noise environments. However, the MTC algorithm may suffer from performance deterioration in the sparse system. To overcome this drawback, a robust and sparse adaptive filtering algorithm, called zero attracting maximum total correntropy (ZA-MTC), is derived by adding a l1 norm penalty term to the maximum total correntropy algorithm in this brief. In addition, in the reweighted version, a log-sum function is employed to replace the l1 norm penalty term. Simulation results demonstrate the advantages of the proposed algorithms under sparsity assumptions on the unknown parameter vector.

Projected Kernel Recursive Maximum Correntropy

In this brief, a different kernel recursive maximum correntropy algorithm is derived using the weighted output information, called KRMC-W. To curb the network growth, we propose a new online sparsification strategy in a feature space, named vector projection (VP) method. Applying the VP to KRMC-W, two novel sparsified kernel adaptive filters, called soft projected KRMC-W and hard projected KRMC-W, respectively, are developed to reduce the average computation complexity. Simulation results under the case of ${\alpha }$ -stable noise are conducted to demonstrate the efficiencies of the proposed algorithms.

Kernel Recursive Generalized Maximum Correntropy

In this letter, a novel kernel adaptive algorithm, called kernel recursive generalized maximum correntropy algorithm (KRGMC), is derived in a kernel space and under the generalized maximum correntropy (GMC) criterion. The proposed kernel algorithm can effectively scale down the dynamic recursive weight coefficients influenced by the impulsive estimate error to avoid the significant performance degradation. The superior performance of the proposed algorithm is verified by numerical simulations about short-time series prediction in alpha-stable noise environment.

Automatic dependent surveillance‐broadcast time delay estimation based on extended recursive maximum correntropy algorithm

In this study, a novel adaptive algorithm, termed extended recursive maximum correntropy (EX-RMC), is proposed to estimate the time delay of automatic dependent surveillance-broadcast (ADS-B), an up-to-date surveillance technology in civil aviation. The proposed algorithm is designed to deal with both the random time-varying delay and the impulsive noise. The superiority of EX-RMC in tracking time-varying state of an unknown plant has been verified by simulation experiments. On-site experiments are also carried out to demonstrate the practical value of the ADS-B time delay estimation method based on EX-RMC.

Convex regularized recursive maximum correntropy algorithm

In this brief, a robust and sparse recursive adaptive filtering algorithm, called convex regularized recursive maximum correntropy (CR-RMC), is derived by adding a general convex regularization penalty term to the maximum correntropy criterion (MCC). An approximate expression for automatically selecting the regularization parameter is also introduced. Simulation results show that the CR-RMC can significantly outperform the original recursive maximum correntropy (RMC) algorithm especially when the underlying system is very sparse. Compared with the convex regularized recursive least squares (CR-RLS) algorithm, the new algorithm also shows strong robustness against impulsive noise. The CR-RMC also performs much better than other LMS-type sparse adaptive filtering algorithms based on MCC.