arXiv subjects

Badong Chen

Publications and source records attributed to Badong Chen.

At least 91 records · Page 5Linked to original sources

arXiv2017

A Novel Brain Decoding Method: a Correlation Network Framework for Revealing Brain Connections

Brain decoding is a hot spot in cognitive science, which focuses on reconstructing perceptual images from brain activities. Analyzing the correlations of collected data from human brain activities and representing activity patterns are two problems in brain decoding based on functional magnetic resonance imaging (fMRI) signals. However, existing correlation analysis methods mainly focus on the strength information of voxel, which reveals functional connectivity in the cerebral cortex. They tend to neglect the structural information that implies the intracortical or intrinsic connections; that is, structural connectivity. Hence, the effective connectivity inferred by these methods is relatively unilateral. Therefore, we proposed a correlation network (CorrNet) framework that could be flexibly combined with diverse pattern representation models. In the CorrNet framework, the topological correlation was introduced to reveal structural information. Rich correlations were obtained, which contributed to specifying the underlying effective connectivity. We also combined the CorrNet framework with a linear support vector machine (SVM) and a dynamic evolving spike neuron network (SNN) for pattern representation separately, thus providing a novel method for decoding cognitive activity patterns. Experimental results verified the reliability and robustness of our CorrNet framework and demonstrated that the new method achieved significant improvement in brain decoding over comparable methods.

cs.CV↗

arXiv2017

Robustness of Maximum Correntropy Estimation Against Large Outliers

The maximum correntropy criterion (MCC) has recently been successfully applied in robust regression, classification and adaptive filtering, where the correntropy is maximized instead of minimizing the well-known mean square error (MSE) to improve the robustness with respect to outliers (or impulsive noises). Considerable efforts have been devoted to develop various robust adaptive algorithms under MCC, but so far little insight has been gained as to how the optimal solution will be affected by outliers. In this work, we study this problem in the context of parameter estimation for a simple linear errors-in-variables (EIV) model where all variables are scalar. Under certain conditions, we derive an upper bound on the absolute value of the estimation error and show that the optimal solution under MCC can be very close to the true value of the unknown parameter even with outliers (whose values can be arbitrarily large) in both input and output variables. Illustrative examples are presented to verify and clarify the theory.

stat.ML↗

arXiv2017

Bias-Compensated Normalized Maximum Correntropy Criterion Algorithm for System Identification with Noisy Input

This paper proposed a bias-compensated normalized maximum correntropy criterion (BCNMCC) algorithm charactered by its low steady-state misalignment for system identification with noisy input in an impulsive output noise environment. The normalized maximum correntropy criterion (NMCC) is derived from a correntropy based cost function, which is rather robust with respect to impulsive noises. To deal with the noisy input, we introduce a bias-compensated vector (BCV) to the NMCC algorithm, and then an unbiasedness criterion and some reasonable assumptions are used to compute the BCV. Taking advantage of the BCV, the bias caused by the input noise can be effectively suppressed. System identification simulation results demonstrate that the proposed BCNMCC algorithm can outperform other related algorithms with noisy input especially in an impulsive output noise environment.

stat.ML↗

arXiv2017

Quantized Minimum Error Entropy Criterion

Comparing with traditional learning criteria, such as mean square error (MSE), the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyis entropy estimator, called information potential (IP), is a popular MEE cost in information theoretic learning (ITL). The computational complexity of IP is however quadratic in terms of sample number due to double summation. This creates computational bottlenecks especially for large-scale datasets. To address this problem, in this work we propose an efficient quantization approach to reduce the computational burden of IP, which decreases the complexity from O(N*N) to O (MN) with M << N. The new learning criterion is called the quantized MEE (QMEE). Some basic properties of QMEE are presented. Illustrative examples are provided to verify the excellent performance of QMEE.

stat.ML↗

arXiv2017

KLMAT: A Kernel Least Mean Absolute Third Algorithm

In this paper, a kernel least mean absolute third (KLMAT) algorithm is developed for adaptive prediction. Combining the benefits of the kernel method and the least mean absolute third (LMAT) algorithm, the proposed KLMAT algorithm performs robustly against noise with different probability densities. To further enhance the convergence rate of the KLMAT algorithm, a variable step-size version (VSS-KLMAT algorithm) is proposed based on a Lorentzian function. Moreover, the stability and convergence property of the proposed algorithms are analyzed. Simulation results in the context of time series prediction demonstrate that the effectiveness of proposed algorithms.

eess.SY↗

arXiv2017

Associations among Image Assessments as Cost Functions in Linear Decomposition: MSE, SSIM, and Correlation Coefficient

The traditional methods of image assessment, such as mean squared error (MSE), signal-to-noise ratio (SNR), and Peak signal-to-noise ratio (PSNR), are all based on the absolute error of images. Pearson's inner-product correlation coefficient (PCC) is also usually used to measure the similarity between images. Structural similarity (SSIM) index is another important measurement which has been shown to be more effective in the human vision system (HVS). Although there are many essential differences among these image assessments, some important associations among them as cost functions in linear decomposition are discussed in this paper. Firstly, the selected bases from a basis set for a target vector are the same in the linear decomposition schemes with different cost functions MSE, SSIM, and PCC. Moreover, for a target vector, the ratio of the corresponding affine parameters in the MSE-based linear decomposition scheme and the SSIM-based scheme is a constant, which is just the value of PCC between the target vector and its estimated vector.

cs.CV↗

arXiv2017

Set-membership improved normalized subband adaptive filter algorithms for acoustic echo cancellation

In order to improve the performances of recently-presented improved normalized subband adaptive filter (INSAF) and proportionate INSAF algorithms for highly noisy system, this paper proposes their set-membership versions by exploiting the theory of set-membership filtering. Apart from obtaining smaller steady-state error, the proposed algorithms significantly reduce the overall computational complexity. In addition, to further improve the steady-state performance for the algorithms, their smooth variants are developed by using the smoothed absolute subband output errors to update the step sizes. Simulation results in the context of acoustic echo cancellation have demonstrated the superiority of the proposed algorithms.

eess.SY↗

arXiv2017

Maximum Correntropy Adaptive Filtering Approach for Robust Compressive Sensing Reconstruction

Robust compressive sensing(CS) reconstruction has become an attractive research topic in recent years. Robust CS aims to reconstruct the sparse signals under non-Gaussian(i.e. heavy tailed) noises where traditional CS reconstruction algorithms may perform very poorly due to utilizing $l_2$ norm of the residual vector in optimization. Most of existing robust CS reconstruction algorithms are based on greedy pursuit method or convex relaxation approach. Recently, the adaptive filtering framework has been introduced to deal with the CS reconstruction, which shows desirable performance in both efficiency and reconstruction performance under Gaussian noise. In this paper, we propose an adaptive filtering based robust CS reconstruction algorithm, called $l_0$ regularized maximum correntropy criterion($l_0$-MCC) algorithm, which combines the adaptive filtering framework and maximum correntropy criterion(MCC). MCC has recently been successfully used in adaptive filtering due to its robustness to impulsive non-Gaussian noises and low computational complexity. We analyze theoretically the stability of the proposed $l_0$-MCC algorithm. A mini-batch based $l_0$-MCC(MB-$l_0$-MCC) algorithm is further developed to speed up the convergence. Comparison with existing robust CS reconstruction algorithms is conducted via simulations, showing that the proposed $l_0$-MCC and MB-$l_0$-MCC can achieve significantly better performance than other algorithms.

cs.IT↗

arXiv2017

Brain Inspired Cognitive Model with Attention for Self-Driving Cars

Perception-driven approach and end-to-end system are two major vision-based frameworks for self-driving cars. However, it is difficult to introduce attention and historical information of autonomous driving process, which are the essential factors for achieving human-like driving into these two methods. In this paper, we propose a novel model for self-driving cars named brain-inspired cognitive model with attention (CMA). This model consists of three parts: a convolutional neural network for simulating human visual cortex, a cognitive map built to describe relationships between objects in complex traffic scene and a recurrent neural network that combines with the real-time updated cognitive map to implement attention mechanism and long-short term memory. The benefit of our model is that can accurately solve three tasks simultaneously:1) detection of the free space and boundaries of the current and adjacent lanes. 2)estimation of obstacle distance and vehicle attitude, and 3) learning of driving behavior and decision making from human driver. More significantly, the proposed model could accept external navigating instructions during an end-to-end driving process. For evaluation, we build a large-scale road-vehicle dataset which contains more than forty thousand labeled road images captured by three cameras on our self-driving car. Moreover, human driving activities and vehicle states are recorded in the meanwhile.

cs.CV↗

arXiv2016

Robust Learning with Kernel Mean p-Power Error Loss

Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean-p power error (KMPE), including the correntropic loss (CLoss) as a special case. Some basic properties of KMPE are presented. In particular, we apply the KMPE to extreme learning machine (ELM) and principal component analysis (PCA), and develop two robust learning algorithms, namely ELM-KMPE and PCA-KMPE. Experimental results on synthetic and benchmark data show that the developed algorithms can achieve consistently better performance when compared with some existing methods.

stat.ML↗

arXiv2016

Constrained Maximum Correntropy Adaptive Filtering

Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (MSE) criterion, which is an ideal optimality criterion under Gaussian noises. This assumption however fails to model the behavior of non-Gaussian noises found in practice. Motivated by the robustness and simplicity of maximum correntropy criterion (MCC) in non-Gaussian impulsive noises, this paper proposes a new adaptive filtering algorithm called constrained maximum correntropy criterion (CMCC). Specifically, CMCC incorporates a linear constraint into a MCC filter to solve a constrained optimization problem explicitly. The proposed adaptive filtering algorithm is easy to implement and has low computational complexity, and in terms of convergence accuracy (say lower mean square deviation) and stability, can significantly outperform those MSE based constrained adaptive algorithms in presence of heavy-tailed impulsive noises. Additionally, the mean square convergence behaviors are studied under energy conservation relation, and a sufficient condition to ensure the mean square convergence and the steady-state mean square deviation (MSD) of the proposed algorithm are obtained. Simulation results confirm the theoretical predictions under both Gaussian and non- Gaussian noises, and demonstrate the excellent performance of the novel algorithm by comparing it with other conventional methods.

stat.ML↗

arXiv2016

Maximum Correntropy Unscented Filter

The unscented transformation (UT) is an efficient method to solve the state estimation problem for a non-linear dynamic system, utilizing a derivative-free higher-order approximation by approximating a Gaussian distribution rather than approximating a non-linear function. Applying the UT to a Kalman filter type estimator leads to the well-known unscented Kalman filter (UKF). Although the UKF works very well in Gaussian noises, its performance may deteriorate significantly when the noises are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises. To improve the robustness of the UKF against impulsive noises, a new filter for nonlinear systems is proposed in this work, namely the maximum correntropy unscented filter (MCUF). In MCUF, the UT is applied to obtain the prior estimates of the state and covariance matrix, and a robust statistical linearization regression based on the maximum correntropy criterion (MCC) is then used to obtain the posterior estimates of the state and covariance. The satisfying performance of the new algorithm is confirmed by two illustrative examples.

stat.ML↗

arXiv2016

Kernel Risk-Sensitive Loss: Definition, Properties and Application to Robust Adaptive Filtering

Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher-order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non-Gaussian signal processing and machine learning. In this work, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.

stat.ML↗

arXiv2016

Two improved normalized subband adaptive filter algorithms with good robustness against impulsive interferences

To improve the robustness of subband adaptive filter (SAF) against impulsive interferences, we propose two modified SAF algorithms with an individual scale function for each subband, which are derived by maximizing correntropy-based cost function and minimizing logarithm-based cost function, respectively, called MCC-SAF and LC-SAF. Whenever the impulsive interference happens, the subband scale functions can sharply drop the step size, which eliminate the influence of outliers on the tap-weight vector update. Therefore, the proposed algorithms are robust against impulsive interferences, and exhibit the faster convergence rate and better tracking capability than the sign SAF (SSAF) algorithm. Besides, in impulse-free interference environments, the proposed algorithms achieve similar convergence performance as the normalized SAF (NSAF) algorithm. Simulation results have demonstrated the performance of our proposed algorithms.

cs.OH↗

arXiv2016

Correntropy Maximization via ADMM - Application to Robust Hyperspectral Unmixing

In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writing the unmixing problem as the maximization of the correntropy criterion subject to the most commonly used constraints. Two unmixing problems are derived: the first problem considers the fully-constrained unmixing, with both the non-negativity and sum-to-one constraints, while the second one deals with the non-negativity and the sparsity-promoting of the abundances. The corresponding optimization problems are solved efficiently using an alternating direction method of multipliers (ADMM) approach. Experiments on synthetic and real hyperspectral images validate the performance of the proposed algorithms for different scenarios, demonstrating that the correntropy-based unmixing is robust to outlier bands.

stat.ML↗

arXiv2016

Diffusion Maximum Correntropy Criterion Algorithms for Robust Distributed Estimation

Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, such as the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power(DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean square convergence analysis of the new algorithms are also carried out.

stat.ML↗

arXiv2015

A novel normalized sign algorithm for system identification under impulsive noise interference

To overcome the performance degradation of adaptive filtering algorithms in the presence of impulsive noise, a novel normalized sign algorithm (NSA) based on a convex combination strategy, called NSA-NSA, is proposed in this paper. The proposed algorithm is capable of solving the conflicting requirement of fast convergence rate and low steady-state error for an individual NSA filter. To further improve the robustness to impulsive noises, a mixing parameter updating formula based on a sign cost function is derived. Moreover, a tracking weight transfer scheme of coefficients from a fast NSA filter to a slow NSA filter is proposed to speed up the convergence rate. The convergence behavior and performance of the new algorithm are verified by theoretical analysis and simulation studies.

eess.SY↗

arXiv2015

Maximum Correntropy Kalman Filter

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

stat.ML↗