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Converging evidence increasingly suggests that psychiatric disorders, such as major depressive disorder (MDD) and autism spectrum disorder (ASD), are not unitary diseases, but rather heterogeneous syndromes that involve diverse, co-occurring symptoms and divergent responses to treatment. This clinical heterogeneity has hindered the progress of precision diagnosis and treatment effectiveness in psychiatric disorders. In this study, we propose BPI-GNN, a new interpretable graph neural network (GNN) framework for analyzing functional magnetic resonance images (fMRI), by leveraging the famed prototype learning. In addition, we introduce a novel generation process of prototype subgraph to discover essential edges of distinct prototypes and employ total correlation (TC) to ensure the independence of distinct prototype subgraph patterns. BPI-GNN can effectively discriminate psychiatric patients and healthy controls (HC), and identify biological meaningful subtypes of psychiatric disorders. We evaluate the performance of BPI-GNN against 11 popular brain network classification methods on three psychiatric datasets and observe that our BPI-GNN always achieves the highest diagnosis accuracy. More importantly, we examine differences in clinical symptom profiles and gene expression profiles among identified subtypes and observe that our identified brain-based subtypes have the clinical relevance. It also discovers the subtype biomarkers that align with current neuro-scientific knowledge.

This paper investigates the selection of voxels for functional Magnetic Resonance Imaging (fMRI) brain data. We aim to identify a comprehensive set of discriminative voxels associated with human learning when exposed to a neutral visual stimulus that predicts an aversive outcome. However, due to the nature of the unconditioned stimuli (typically a noxious stimulus), it is challenging to obtain sufficient sample sizes for psychological experiments, given the tolerability of the subjects and ethical considerations. We propose a stable hierarchical voting (SHV) mechanism based on stability selection to address this challenge. This mechanism enables us to evaluate the quality of spatial random sampling and minimizes the risk of false and missed detections. We assess the performance of the proposed algorithm using simulated and publicly available datasets. The experiments demonstrate that the regularization strategy choice significantly affects the results' interpretability. When applying our algorithm to our collected fMRI dataset, it successfully identifies sparse and closely related patterns across subjects and displays stable weight maps for three experimental phases under the fear conditioning paradigm. These findings strongly support the causal role of aversive conditioning in altering visual-cortical activity.

Accurate monitoring of the depth of anesthesia (DOA) is essential to ensure the safety of the operation. In this study, a new index using near-infrared spectroscopy (NIRS) signal was proposed to assess the relationship between the DOA and cerebral hemodynamic variables. Methods: Four cerebral hemodynamic variables of 15 patients were collected, including left, right, proximal, distal, oxygenated (HbO $_{{2}}{)}$ and deoxygenated (Hb) hemoglobin concentration changes. The Phase-Amplitude coupling (PAC), an adaptation of cross-frequency coupling to reflect the modulation of the amplitude of high-frequency signals by the phase of low-frequency signals, was measured and the modulation index (MI) was obtained to monitor the DOA afterwards. Meanwhile, the BIS value based on electroencephalogram is also measured and compared. Results: Compared with awake period, in anesthesia maintenance period, the PAC was strengthened. The analysis of receiver operating characteristic (ROC) curve showed that the MI, especially the MI of rp-HbO2, could effectively discriminate these two periods. Additionally, during the whole anesthesia process, the BIS value was statistically consistent with the MI of cerebral hemodynamic variables, and cerebral hemodynamic variables were immune from interference by clinical electric devices. Conclusion: The MI of cerebral hemodynamic variables was appropriate to be used as a new index to monitor the DOA. Significance: This study is of great significance to the development of new modes of anesthesia monitoring and new decoding methods, and is expected to develop a high-performance anesthesia monitoring system.

The early prediction of epileptic seizures holds paramount significance in patient care and medical research. Extracting useful spatial-temporal features to facilitate seizure prediction represents a primary challenge in this field. This study proposes GAMRNN, a novel methodology integrating a dual-layer gated recurrent unit (GRU) model with a convolutional attention module. GAMRNN aims to capture intricate spatial-temporal characteristics by highlighting informative feature channels and spatial pattern dynamics. We employ the Lion optimization algorithm to enhance the model's generalization capability and predictive accuracy. Our evaluation of GAMRNN on the widely utilized CHB-MIT EEG dataset demonstrates its effectiveness in seizure prediction. The results include an impressive average classification accuracy of 91.73%, sensitivity of 88.09%, specificity of 92.09%, and a low false positive rate of 0.053/h. Notably, GAMRNN enables early seizure prediction with a lead time ranging from 5 to 35 min, exhibiting remarkable performance improvements compared to similar prediction models.

IntroductionAutomatic sleep staging is a classification process with severe class imbalance and suffers from instability of scoring stage N1. Decreased accuracy in classifying stage N1 significantly impacts the staging of individuals with sleep disorders. We aim to achieve automatic sleep staging with expert-level performance in both N1 stage and overall scoring.MethodsA neural network model combines an attention-based convolutional neural network and a classifier with two branches is developed. A transitive training strategy is employed to balance universal feature learning and contextual referencing. Parameter optimization and benchmark comparisons are conducted using a large-scale dataset, followed by evaluation on seven datasets in five cohorts.ResultsThe proposed model achieves an accuracy of 88.16%, Cohen’s kappa of 0.836, and MF1 score of 0.818 on the SHHS1 test set, also with comparable performance to human scorers in scoring stage N1. Incorporating multiple cohort data improves its performance. Notably, the model maintains high performance when applied to unseen datasets and patients with neurological or psychiatric disorders.DiscussionThe proposed algorithm demonstrates strong performance and generalizablility, and its direct transferability is noteworthy among similar studies on automated sleep staging. It is publicly available, which is conducive to expanding access to sleep-related analysis, especially those associated with neurological or psychiatric disorders.

The Partial Least Square Regression (PLSR) method has shown admirable competence for predicting continuous variables from inter-correlated electrocorticography signals in the brain-computer interface. However, PLSR is essentially formulated with the least square criterion, thus, being considerably prone to the performance deterioration caused by the brain recording noises. To address this problem, this study aims to propose a new robust variant for PLSR. To this end, the maximum correntropy criterion (MCC) is utilized to propose a new robust implementation of PLSR, called Partial Maximum Correntropy Regression (PMCR). The half-quadratic optimization is utilized to calculate the robust projectors for the dimensionality reduction, and the regression coefficients are optimized by a fixed-point optimization method. The proposed PMCR is evaluated with a synthetic example and a public electrocorticography dataset under three performance indicators. For the synthetic example, PMCR realized better prediction results compared with the other existing methods. PMCR could also abstract valid information with a limited number of decomposition factors in a noisy regression scenario. For the electrocorticography dataset, PMCR achieved superior decoding performance in most cases, and also realized the minimal neurophysiological pattern deterioration with the interference of the noises. The experimental results demonstrate that, the proposed PMCR could outperform the existing methods in a noisy, inter-correlated, and high-dimensional decoding task. PMCR could alleviate the performance degradation caused by the adverse noises and ameliorate the electrocorticography decoding robustness for the brain-computer interface.

Abstract 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.

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.

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.

Brain-computer interfaces (BCIs) based on motor imagery (MI) utilizing multi-channel electroencephalogram (EEG) data are commonly used to improve motor function of people with motor disabilities. EEG channel selection can enhance MI classification accuracy by selecting informative channels, accordingly reducing redundant information. The sequential backward floating search (SBFS) approach has been considered as one of the best feature selection methods. In this paper, SBFS is first implemented to select the optimal EEG channels in MI-BCI. Further, to reduce the time complexity of SBFS, the modified SBFS is proposed and applied to left and right hand MI tasks. In the modified SBFS, based on the map of EEG channels at the scalp, the symmetrical channels are selected as channel pairs and acceleration is thus realized by removing or adding multiple channels in each iteration. Extensive experiments were conducted on four public BCI datasets. Experimental results show that the SBFS achieves significantly higher classification accuracy (p < 0.001) than using all channels and conventional MI channels (i.e., C3, C4, and Cz). Moreover, the proposed method outperforms the state-of-the-art selection methods.

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.

Target tracking plays an important role in the construction, operation, and maintenance of the space station by the robot, which puts forward high requirements on the accuracy of target tracking. However, the special space environment may cause complex non-Gaussian noise in target tracking data. And the performance of traditional Kalman Filter will deteriorate seriously when the error signals are non-Gaussian, which may lead to mission failure. In the paper, a novel Kalman Filter algorithm with Generalized Maximum Correntropy Criterion (GMCKF) is proposed to improve the tracking accuracy with non-Gaussian noise. The GMCKF algorithm, which replaces the default Gaussian kernel with the generalized Gaussian density function as kernel, can adapt to multi-type non-Gaussian noises and evaluate the noise accurately. A parameter automatic selection algorithm is proposed to determine the shape parameter of GMCKF algorithm, which helps the GMCKF algorithm achieve better performance for complex non-Gaussian noise. The performance of the proposed algorithm has been evaluated by simulations and the ground experiments. Then, the algorithm has been applied in the maintenance experiments in TianGong-2 space laboratory of China. The results validated the feasibility of the proposed method with the target tracking precision improved significantly in complex non-Gaussian environment.

This paper addresses the stability issues of the least mean absolute third (LMAT) algorithm using the normalization based on the third order in the estimation error. A novel robust normalized least mean absolute third (RNLMAT) algorithm is therefore proposed to be stable for all statistics of the input, noise, and initial weights. For further improving the filtering performance of RNLMAT in different noises and initial conditions, the variable step-size RNLMAT (VSSRNLMAT) and the switching RNLMAT (SWRNLMAT) algorithms are proposed using the statistics of the estimation error and a switching method, respectively. The filtering performance of RNLMAT is improved by VSSRNLMAT and SWRNLMAT at the expense of affordable computational cost. RNLMAT with less computational complexity than other normalized adaptive filtering algorithms, can provide better filtering accuracy and robustness against impulsive noises. The steady-state performance of RNLMAT and SWRNLMAT in terms of the excess mean-square error is performed for theoretical analysis. Simulations conducted in system identification under different noise environments confirm the theoretical results and the superiorities of the proposed algorithms from the aspects of filtering accuracy and robustness against large outliers.

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.

Real industrial processes usually are equipped with onboard control or diagnostic systems and limit to store a complicated model. Also, measurement samples from real processes are contaminated with noises of different statistical characteristics and are produced by one-by-one way. In this case, learning algorithms with better learning performance and compact model for systems with noises of various statistics are necessary. This paper proposes a new online extreme learning machine (ELM) algorithm, namely, sparse recursive least mean p-power ELM (SRLMP-ELM). In SRLMP-ELM, a novel cost function, i.e., the sparse least mean p-power (SLMP) error criterion, provides a mechanism to update the output weights sequentially and automatically tune some parameters of the output weights to zeros. The SLMP error criterion aims to minimize the combination of the mean p-power of the errors and a sparsity penalty constraint of the output weights. For real industrial system requirements, the proposed on-line learning algorithm is able to provide more higher accuracy, compact model, and better generalization ability than ELM and online sequential ELM, whereas the non-Gaussian noises impact the processes, especially impulsive noises. Simulations are reported to demonstrate the performance and effectiveness of the proposed methods.

Frequent itemsets mining with differential privacy refers to the problem of mining all frequent itemsets whose supports are above a given threshold in a given transactional dataset, with the constraint that the mined results should not break the privacy of any single transaction. Current solutions for this problem cannot well balance efficiency, privacy, and data utility over large-scale data. Toward this end, we propose an efficient, differential private frequent itemsets mining algorithm over large-scale data. Based on the ideas of sampling and transaction truncation using length constraints, our algorithm reduces the computation intensity, reduces mining sensitivity, and thus improves data utility given a fixed privacy budget. Experimental results show that our algorithm achieves better performance than prior approaches on multiple datasets.

In order to solve the system identification problems, the normalized least mean absolute deviation (NLMAD) algorithm was developed as an effective and robust method. In this paper, aiming at the system identification problems with sparsity characteristic, and taking the advantage of the NLMAD algorithm to suppress impulsive output measurement noise interference, we introduce the L1-norm as a sparse penalty constraint into the NLMAD algorithm to design a robust sparse adaptive filtering algorithm. Furthermore, considering the biased estimation caused by the input noise, we employ an unbiasedness criterion to derive an effective bias-compensated vector which can compensate the bias efficiently for the proposed sparse NLMAD algorithm. The desirable performance of the new method is measured with simulations of two stages. The proposed bias-compensated sparse NLMAD algorithm achieves better performance compared to other existing methods in both stages. Simulation results demonstrate the excellent performance of the proposed algorithm in solving sparse system identification problems. The promising results in this paper suggest that the bias-compensated sparse NLMAD algorithm may become a useful tool for system identification with noisy input and impulsive output noise.

Unmanned aerial vehicles (UAVs) can be deployed as base stations (BSs) for emergency communications of user equipments (UEs) in 5G/6G networks. In multi-UAV communication networks, UAVs’ load balancing and UEs’ data rate fairness are two challenging problems and can be optimized by UAV deployment strategies. In this work, we found that these two problems are related by the same performance metric, which makes it possible to optimize the two problems simultaneously. To solve this joint optimization problem, we propose a UAV diffusion deployment algorithm based on the virtual force field method. Firstly, according to the unique performance metric, we define two new virtual forces, which are the UAV-UAV force and UE-UAV force defined by FU and FV, respectively. FV is the main contributor to load balancing and UEs’ data rate fairness, and FU contributes to fine tuning the UEs’ data rate fairness performance. Secondly, we propose a diffusion control stratedy to the update UAV-UAV force, which optimizes FV in a distributed manner. In this diffusion strategy, each UAV optimizes the local parameter by exchanging information with neighbor UAVs, which achieve global load balancing in a distributed manner. Thirdly, we adopt the successive convex optimization method to update FU, which is a non-convex problem. The resultant force of FV and FU is used to control the UAVs’ motion. Simulation results show that the proposed algorithm outperforms the baseline algorithm on UAVs’ load balancing and UEs’ data rate fairness.

A diffusion general mixed-norm (DGMN) algorithm for distributed estimation over network (DEoN) is proposed. The standard diffusion adaptive filtering algorithm with a single error norm exhibits slow convergence speed and poor misadjustments under specific environments. To overcome this drawback, the DGMN is developed by using a convex mixture of p and textit q norms as the cost function to improve the convergence rate and substantially reduce the steady-state coefficient errors. Especially, it can be used to solve the DEoN under Gaussian and non-Gaussian noise environments, including measurement noises with long-tail and short-tail distributions, and impulsive noises with α-stable distributions. In addition, the analysis of the mean and mean square convergence is performed. Simulation results show the advantages of the proposed algorithm with mixing error norms for DEoN.

For linear systems, the original Kalman filter under the minimum mean square error (MMSE) criterion is an optimal filter under a Gaussian assumption. However, when the signals follow non-Gaussian distributions, the performance of this filter deteriorates significantly. An efficient way to solve this problem is to use the maximum correntropy criterion (MCC) instead of the MMSE criterion to develop the filters. In a recent work, the maximum correntropy Kalman filter (MCKF) was derived. The MCKF performs very well in filtering heavy-tailed non-Gaussian noise, and its performance can be further improved when some prior information about the system is available (e.g., the system states satisfy some equality constraints). In this paper, to address the problem of state estimation under equality constraints, we develop a new filter, called the MCKF with state constraints, which combines the advantages of the MCC and constrained estimation technology. The performance of the new algorithm is confirmed with two illustrative examples.

Neurorobotics is one of the most ambitious fields in robotics, driving integration of interdisciplinary data and knowledge. One of the most productive areas of interdisciplinary research in this area has been the implementation of biologically-inspired mechanisms in the development of autonomous systems. Specifically, enabling such systems to display adaptive behavior such as learning from good and bad outcomes, has been achieved by quantifying and understanding the neural mechanisms of the brain networks mediating adaptive behaviors in humans and animals. For example, associative learning from aversive or dangerous outcomes is crucial for an autonomous system, to avoid dangerous situations in the future. A body of neuroscience research has suggested that the neurocomputations in the human brain during associative learning involve re-shaping of sensory responses. The nature of these adaptive changes in sensory processing during learning however are not yet well enough understood to be readily implemented into on-board algorithms for robotics application. Toward this overall goal, we record the simultaneous electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI), characterizing one candidate mechanism, i.e., large-scale brain oscillations. The present report examines the use of Functional Source Separation (FSS) as an optimization step in EEG-fMRI fusion that harnesses timing information to constrain the solutions that satisfy physiological assumptions. We applied this approach to the voxel-wise correlation of steady-state visual evoked potential (ssVEP) amplitude and blood oxygen level-dependent imaging (BOLD), across both time series. The results showed the benefit of FSS for the extraction of robust ssVEP signals during simultaneous EEG-fMRI recordings. Applied to data from a 3-phase aversive conditioning paradigm, the correlation maps across the three phases (habituation, acquisition, extinction) show converging results, notably major overlapping areas in both primary and extended visual cortical regions, including calcarine sulcus, lingual cortex, and cuneus. In addition, during the acquisition phase when aversive learning occurs, we observed additional correlations between ssVEP and BOLD in the anterior cingulate cortex (ACC) as well as the precuneus and superior temporal gyrus.

The maximum correntropy criterion (MCC) has recently been successfully applied to adaptive filtering. Adaptive algorithms under MCC show strong robustness against large outliers. In this work, we apply the MCC criterion to develop a robust Hammerstein adaptive filter. Compared with the traditional Hammerstein adaptive filters, which are usually derived based on the well-known mean square error (MSE) criterion, the proposed algorithm can achieve better convergence performance especially in the presence of impulsive non-Gaussian (e.g., α-stable) noises. Additionally, some theoretical results concerning the convergence behavior are also obtained. Simulation examples are presented to confirm the superior performance of the new algorithm.

The minimum error entropy (MEE) criterion is an important learning criterion in information theoretical learning (ITL). However, the MEE solution cannot be obtained in closed form even for a simple linear regression problem, and one has to search it, usually, in an iterative manner. The fixed-point iteration is an efficient way to solve the MEE solution. In this work, we study a fixed-point MEE algorithm for linear regression, and our focus is mainly on the convergence issue. We provide a sufficient condition (although a little loose) that guarantees the convergence of the fixed-point MEE algorithm. An illustrative example is also presented.

Sparse system identification has received a great deal of attention due to its broad applicability. The proportionate normalized least mean square (PNLMS) algorithm, as a popular tool, achieves excellent performance for sparse system identification. In previous studies, most of the cost functions used in proportionate-type sparse adaptive algorithms are based on the mean square error (MSE) criterion, which is optimal only when the measurement noise is Gaussian. However, this condition does not hold in most real-world environments. In this work, we use the minimum error entropy (MEE) criterion, an alternative to the conventional MSE criterion, to develop the proportionate minimum error entropy (PMEE) algorithm for sparse system identification, which may achieve much better performance than the MSE based methods especially in heavy-tailed non-Gaussian situations. Moreover, we analyze the convergence of the proposed algorithm and derive a sufficient condition that ensures the mean square convergence. Simulation results confirm the excellent performance of the new algorithm.

Recently, sparse adaptive learning algorithms have been developed to exploit system sparsity as well as to mitigate various noise disturbances in many applications. In particular, in sparse channel estimation, the parameter vector with sparsity characteristic can be well estimated from noisy measurements through a sparse adaptive filter. In previous studies, most works use the mean square error (MSE) based cost to develop sparse filters, which is rational under the assumption of Gaussian distributions. However, Gaussian assumption does not always hold in real-world environments. To address this issue, we incorporate in this work an l1-norm or a reweighted l1-norm into the minimum error entropy (MEE) criterion to develop new sparse adaptive filters, which may perform much better than the MSE based methods, especially in heavy-tailed non-Gaussian situations, since the error entropy can capture higher-order statistics of the errors. In addition, a new approximator of l0-norm, based on the correntropy induced metric (CIM), is also used as a sparsity penalty term (SPT). We analyze the mean square convergence of the proposed new sparse adaptive filters. An energy conservation relation is derived and a sufficient condition is obtained, which ensures the mean square convergence. Simulation results confirm the superior performance of the new algorithms.

Colorectal cancer (CRC), as a result of a multistep process and under multiple factors, is one of the most common life-threatening cancers worldwide. To identify the “high risk” populations is critical for early diagnosis and improvement of overall survival rate. Of the complicated genetic and environmental factors, which group is mostly concerning colorectal carcinogenesis remains contentious. For this reason, this study collects relatively complete information of genetic variations and environmental exposure for both CRC patients and cancer-free controls; a multimethod ensemble model for CRC-risk prediction is developed by employing such big data to train and test the model. Our results demonstrate that (1) the explored genetic and environmental biomarkers are validated to connect to the CRC by biological function- or population-based evidences, (2) the model can efficiently predict the risk of CRC after parameter optimization by the big CRC-related data, and (3) our innovated heterogeneous ensemble learning model (HELM) and generalized kernel recursive maximum correntropy (GKRMC) algorithm have high prediction power. Finally, we discuss why the HELM and GKRMC can outperform the classical regression algorithms and related subjects for future study.

The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate unless some constraints on the conditional distribution are imposed. A recent paper has proved that if the conditional density is conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate (with Shannon entropy) equals the conditional median. In this study, we extend this result to the generalized MEE estimation where the optimality criterion is the Renyi entropy or equivalently, the α-order information potential (IP).

The minimum error entropy (MEE) estimation is concerned with the estimation of a certain random variable (unknown variable) based on another random variable (observation), so that the entropy of the estimation error is minimized. This estimation method may outperform the well-known minimum mean square error (MMSE) estimation especially for non-Gaussian situations. There is an important performance bound on the MEE estimation, namely the W-S lower bound, which is computed as the conditional entropy of the unknown variable given observation. Though it has been known in the literature for a considerable time, up to now there is little study on this performance bound. In this paper, we reexamine the W-S lower bound. Some basic properties of the W-S lower bound are presented, and the characterization of Gaussian distribution using the W-S lower bound is investigated.

Recent studies suggest that the minimum error entropy (MEE) criterion can outperform the traditional mean square error criterion in supervised machine learning, especially in nonlinear and non-Gaussian situations. In practice, however, one has to estimate the error entropy from the samples since in general the analytical evaluation of error entropy is not possible. By the Parzen windowing approach, the estimated error entropy converges asymptotically to the entropy of the error plus an independent random variable whose probability density function (PDF) corresponds to the kernel function in the Parzen method. This quantity of entropy is called the smoothed error entropy, and the corresponding optimality criterion is named the smoothed MEE (SMEE) criterion. In this paper, we study theoretically the SMEE criterion in supervised machine learning where the learning machine is assumed to be nonparametric and universal. Some basic properties are presented. In particular, we show that when the smoothing factor is very small, the smoothed error entropy equals approximately the true error entropy plus a scaled version of the Fisher information of error. We also investigate how the smoothing factor affects the optimal solution. In some special situations, the optimal solution under the SMEE criterion does not change with increasing smoothing factor. In general cases, when the smoothing factor tends to infinity, minimizing the smoothed error entropy will be approximately equivalent to minimizing error variance, regardless of the conditional PDF and the kernel.

The minimum error entropy (MEE) criterion has been receiving increasing attention due to its promising perspectives for applications in signal processing and machine learning. In the context of Bayesian estimation, the MEE criterion is concerned with the estimation of a certain random variable based on another random variable, so that the error’s entropy is minimized. Several theoretical results on this topic have been reported. In this work, we present some further results on the MEE estimation. The contributions are twofold: (1) we extend a recent result on the minimum entropy of a mixture of unimodal and symmetric distributions to a more general case, and prove that if the conditional distributions are generalized uniformly dominated (GUD), the dominant alignment will be the MEE estimator; (2) we show by examples that the MEE estimator (not limited to singular cases) may be non-unique even if the error distribution is restricted to zero-mean (unbiased).

In this paper, robust first and second-order divided difference filtering algorithms based on correntropy are proposed, which not only retain the advantages of divided difference filters, but also exhibit robustness in the presence of non-Gaussian noises, especially when the measurements are contaminated by heavy-tailed noises. The proposed filters are then applied to the problem of ship positioning. In order to improve the accuracy and reliability of ship positioning, the positioning method combines the Dead Reckoning (DR) algorithm and the Global Positioning System (GPS). Experimental results of an illustrative example show the superior performance of the new algorithms when applied to ship positioning.

Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relationships between multivariate entropy (joint or total marginal) and traditional measures of multivariate variability, such as total dispersion and generalized variance, are investigated. It is shown that for the jointly Gaussian case, the joint entropy (or entropy power) is equivalent to the generalized variance, while total marginal entropy is equivalent to the geometric mean of the marginal variances and total marginal entropy power is equivalent to the total dispersion. The smoothed multivariate entropy (joint or total marginal) and the kernel density estimation (KDE)-based entropy estimator (with finite samples) are also studied, which, under certain conditions, will be approximately equivalent to the total dispersion (or a total dispersion estimator), regardless of the data distribution.