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The normalized subband adaptive filtering algorithm provides fast convergence rate for colored input signals as compared to the normalized least mean square algorithm, but it suffers from a poor convergence issue in the α -stable noise. In light of this, the normalized subband p-norm (NSPN) algorithm, which is based on the least mean p-power error (MPE) criterion, is proposed in this study. This technique is not only robust against impulsive noise samples, but it also maintains a fast convergence rate when colored input signals are used. In addition to this, we develop both the steady-state and the transient models of the NSPN algorithm and provide some insights. Then, in order to solve the problem of making a choice regarding the order p in the NSPN algorithm, we design an autonomous system and come up with the NSPN algorithm with a variable p-norm (VP-NSPN). In addition, we offer the TFC-based VP-NSPN algorithm with a fast convergence rate and low steady-state misadjustment simultaneously by making use of the tap-weights feedback-based convex combination (TFC) scheme. In conclusion, simulation results on system identification and acoustic echo cancellation are undertaken in order to validate the superiority of the proposed algorithms and validate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent work, the concept of mixture correntropy (MC) was proposed to improve the learning performance, where the kernel function is a mixture Gaussian kernel, namely, a linear combination of several zero-mean Gaussian kernels with different widths. In both correntropy and MC, the center of the kernel function is, however, always located at zero. In the present work, to further improve the learning performance, we propose the concept of multikernel correntropy (MKC), in which each component of the mixture Gaussian kernel can be centered at a different location. The properties of the MKC are investigated and an efficient approach is proposed to determine the free parameters in MKC. Experimental results show that the learning algorithms under the maximum MKC criterion (MMKCC) can outperform those under the original maximum correntropy criterion (MCC) and the maximum MC criterion (MMCC). [ABSTRACT FROM AUTHOR]

The multivariate autoregressive (MVAR) model is widely used in describing the dynamics of nonlinear systems, in which the estimates of model parameters and underlying states can be achieved by dual extended Kalman filter (DEKF). However, when the measurements are corrupted by complicated non-Gaussian noises, the DEKF based on the minimum mean-square error (MMSE) criterion may provide biased estimates. In the present article, we develop a novel dual Kalman-type filter, referred to as DEKF under minimum error entropy (MEE) with fiducial points (MEEFs-DEKF) to deal with the non-Gaussian noises. First, the equivalent state-space model and parameter-space model are presented based on the MVAR model. Then, an optimality criterion based on MEE with fiducial points (MEEFs) is applied in the batch-mode regression equation to improve the robustness. Finally, a fixed-point iteration algorithm gives the posterior estimates of state and parameter. Simulation results confirm that the proposed MEEF-DEKF can achieve excellent performance in various noises with different distributions, especially in heavy-tailed and multimodal noises. [ABSTRACT FROM AUTHOR]

In this article, a novel normal-skew mixture (NSM) distribution is presented to model the normal and/or heavy-tailed and/or skew nonstationary distributed noises. The NSM distribution can be formulated as a hierarchically Gaussian presentation by leveraging a Bernoulli distributed random variable. Based on this, a novel robust Kalman filtering framework can be developed utilizing the variational Bayesian method, where the one-step prediction and measurement-likelihood densities are modeled as NSM distributions. For implementation, several exemplary robust Kalman filters (KFs) are derived based on some specific cases of NSM distribution. The relationships between some existing robust KFs and the presented framework are also revealed. The superiority of the proposed robust Kalman filtering framework is validated by a target tracking simulation example. [ABSTRACT FROM AUTHOR]

Multi-view clustering has received widespread attention owing to its effectiveness by integrating multi-view data appropriately, but traditional algorithms have limited applicability to large-scale real-world data due to their high computational complexity and low robustness. Focusing on the aforementioned issues, we propose an efficient and robust multi-view clustering algorithm with anchor graph regularization (ERMC-AGR). In this work, a novel anchor graph regularization (ARG) is designed to improve the quality of the learned embedded anchor graph (EAG), and the obtained EAG is decomposed by nonnegative matrix factorization (NMF) under correntropy criterion to acquire clustering results directly. Different from the traditional graph regularization that needs to construct a large-scale Laplacian matrix pertaining to the all-sample graph, our lightweight AGR, constructed from the perspective of anchors, can reduce the computational complexity significantly while improving the EAG quality. Moreover, a factor matrix of NMF is constrained to be the cluster indicator matrix to omit additional k-means after optimization. Subsequently, correntropy is utilized to improve the effectiveness and robustness of ERMC-AGR owing to its promising performance to complex noises and outliers. Extensive experiments on real-world datasets and noisy datasets show that ERMC-ARG can improve the clustering efficiency and robustness while ensuring comparable or even better effectiveness. [ABSTRACT FROM AUTHOR]

Brain-computer interface (BCI) is a technology that connects the human brain and external devices. Many studies have shown the possibility of using it to restore motor control in stroke patients. One specific challenge of such BCI is that the classification accuracy is not high enough for multi-class movements. In this study, by using Multivariate Empirical Mode Decomposition (MEMD) and Convolutional Neural Network (CNN), a novel algorithm (MECN) was proposed to decode EEG signals for four kinds of hand movements. Firstly, the MEMD was used to decompose the movement-related electroencephalogram (EEG) signals to obtain the multivariate intrinsic empirical functions (MIMFs). Then, the optimal MIMFs fusion was performed based on sequential forward selection algorithm. Finally, the selected MIMFs were input to the CNN model for discriminating four kinds of hand movements. The average classification accuracy of thirteen subjects over the six-fold cross-validation reached 81.14% for 2s-data before the movement onset and 81.08% for 2s-data after the movement onset. The MECN method achieved statistically significant improvement on the state-of-the-art methods. The results showed that the algorithm proposed in this study can effectively decode four kinds of hand movements based on EEG signals. [ABSTRACT FROM AUTHOR]

Monitoring the consciousness states of patients and ensuring the appropriate depth of anesthesia (DOA) is critical for the safe implementation of surgery. In this study, a high-density electroencephalogram (EEG) combined with blood drug concentration and behavioral response indicators was used to monitor propofol-induced sedation and evaluate the alterations in consciousness states. Microstate analysis, which can reflect the semi-stable state of the sub-second activation of the brain functional network, can be used to assess the brain’s consciousness states. In this research, the EEG microstate sequences were constructed to compare the characteristics of corresponding sequences. Compared with the baseline (BS) state, the microstate sequences in the moderate sedation (MD) state exhibited higher complexity indexes of the multiscale sample entropy. With respect to the transition probability (TP) of microstates, most microstates tended to be converted into microstate C in the BS state. In contrast, they tended to be converted into microstate F in the MD state. The significant difference between the expected TP and observed TP could lead to the conclusion that hidden layers were present when there were changes in the consciousness states. According to the hidden Markov model, the accuracy of distinguishing the BS and MD states was 80.16%. The characteristics of microstate sequence revealed the variations in the brain states caused by alterations in consciousness states during anesthesia from a new perspective and presented a new idea for monitoring the DOA. [ABSTRACT FROM AUTHOR]

Spiking neural networks (SNNs) are regarded as a promising candidate to deal with the major challenges of current machine learning techniques, including the high energy consumption induced by deep neural networks. However, there is still a great gap between SNNs and the few-shot learning performance of artificial neural networks. Importantly, existing spike-based few-shot learning models do not target robust learning based on spatiotemporal dynamics and superior machine learning theory. In this paper, we propose a novel spike-based framework with the entropy theory, namely, heterogeneous ensemble-based spike-driven few-shot online learning (HESFOL). The proposed HESFOL model uses the entropy theory to establish the gradient-based few-shot learning scheme in a recurrent SNN architecture. We examine the performance of the HESFOL model based on the few-shot classification tasks using spiking patterns and the Omniglot data set, as well as the few-shot motor control task using an end-effector. Experimental results show that the proposed HESFOL scheme can effectively improve the accuracy and robustness of spike-driven few-shot learning performance. More importantly, the proposed HESFOL model emphasizes the application of modern entropy-based machine learning methods in state-of-the-art spike-driven learning algorithms. Therefore, our study provides new perspectives for further integration of advanced entropy theory in machine learning to improve the learning performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic systems. [ABSTRACT FROM AUTHOR]

This paper proposes a state estimation approach 'robust strong tracking unscented Kalman filter with unknown inputs' that can be applied to non‐linear systems with unknown inputs. Specifically, the non‐linear state and measurement equations are linearised by statistical linearisation. Then, the estimation equation of the unknown input is derived based on the weighted least squares method. The multiple suboptimal fading factor is introduced into a priori error covariance matrix to improve the tracking ability for the inaccuracy of the system model and the abrupt change of state variables caused by unknown inputs. Finally, based on the unbiased minimum variance estimation, the unbiased state estimation and the error covariance matrix are derived. Singular value decomposition is performed on the error covariance matrix to improve the stability of the algorithm. Simulated results validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The spiking neural network (SNN) is regarded as a promising candidate to deal with the great challenges presented by current machine learning techniques, including the high energy consumption induced by deep neural networks. However, there is still a great gap between SNNs and the online meta-learning performance of artificial neural networks. Importantly, existing spike-based online meta-learning models do not target the robust learning based on spatio-temporal dynamics and superior machine learning theory. In this invited article, we propose a novel spike-based framework with minimum error entropy, called MeMEE, using the entropy theory to establish the gradient-based online meta-learning scheme in a recurrent SNN architecture. We examine the performance based on various types of tasks, including autonomous navigation and the working memory test. The experimental results show that the proposed MeMEE model can effectively improve the accuracy and the robustness of the spike-based meta-learning performance. More importantly, the proposed MeMEE model emphasizes the application of the modern information theoretic learning approach on the state-of-the-art spike-based learning algorithms. Therefore, in this invited paper, we provide new perspectives for further integration of advanced information theory in machine learning to improve the learning performance of SNNs, which could be of great merit to applied developments with spike-based neuromorphic systems. [ABSTRACT FROM AUTHOR]

Least squares (LS) estimation is simple yet effective for parameter estimation. Most real-world problems are nonlinear. In practice, nonlinear LS problems are linearized first and then solved by a linear LS estimator. However, since these methods solve a nonlinear LS problem by a linear way, there is room for improvement only if estimators being nonlinear in the original measurement. In this article, an LS approach is proposed for nonlinear LS problems, along with theoretical analysis and justification. First, for a general nonlinear measurement model with any form of noise, a unified linearization (UL) approach is proposed under certain assumptions and a linearized least squares (LLS) estimator is defined based on the UL model. Second, an augmented nonlinear least squares (ANLS) estimator is proposed based on LLS estimation. In the ANLS estimator, the original measurement is augmented by its nonlinear conversion intended to further utilize the nonlinear measurement. Moreover, we prove that the ANLS estimator outperforms LLS estimation-based estimators. Finally, the UL and the ANLS estimator are applied to source localization with time difference of arrival and/or frequency difference of arrival measurement, and a two-step ANLS localization algorithm is developed. The performance of the proposed algorithm is evaluated via simulation of some typical localization scenarios. [ABSTRACT FROM AUTHOR]

In recent years, correntropy has been successfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this brief we propose a new variant of correntropy, named asymmetric correntropy, which uses an asymmetric Gaussian model as the kernel function. In addition, a robust adaptive filtering algorithm based on asymmetric correntropy is developed and its steady-state convergence performance is analyzed. Simulations are provided to confirm the theoretical results and good performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Partial discharge (PD) detection plays a vital role in on-line condition monitoring of electrical apparatus in the power systems. However, the noise of PD measurements significantly degrades the performance of detection algorithms. In this paper, we focus on developing an adaptive filtering technique for the PD denoising problem. Heretofore, there are just a few literature reviews addressing the PD denoising based on such a method. The proposed recursive continuous S-shaped (RCSS) algorithm integrates the advantages of recursive strategy and continuous S-shaped function into adaptive noise cancellation (ANC) system, yielding enhanced filtering performance. The proposed algorithm can tackle PD noises in both Gaussian and impulsive scenarios, which is easy to implement in practical applications. The convergence behavior is also analyzed. Extensive simulation and experimental results confirm that the proposed algorithm can address polluted PD pulses, even in excessively noisy conditions, resulting in smaller mean square error (MSE) as compared to other state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]