Kernel Granger Causality Mapping Effective Connectivity on fMRI Data

Although it is accepted that linear Granger causality can reveal effective connectivity in functional magnetic resonance imaging (fMRI), the issue of detecting nonlinear connectivity has hitherto not been considered. In this paper, we address kernel Granger causality (KGC) to describe effective connectivity in simulation studies and real fMRI data of a motor imagery task. Based on the theory of reproducing kernel Hilbert spaces, KGC performs linear Granger causality in the feature space of suitable kernel functions, assuming an arbitrary degree of nonlinearity. Our results demonstrate that KGC captures effective couplings not revealed by the linear case. In addition, effective connectivity networks between the supplementary motor area (SMA) as the seed and other brain areas are obtained from KGC.      

Probabilistic framework for brain connectivity from functional MR images

This paper unifies our earlier work on detection of brain activation (Rajapakse and Piyaratna, 2001) and connectivity (Rajapakse and Zhou, 2007) in a probabilistic framework for analyzing effective connectivity among activated brain regions from functional magnetic resonance imaging (fMRI) data. Interactions among brain regions are expressed by a dynamic Bayesian network (DBN) while contextual dependencies within functional images are formulated by a Markov random field. The approach simultaneously considers both the detection of brain activation and the estimation of effective connectivity and does not require a priori model of connectivity. Experimental results show that the present approach outperforms earlier fMRI analysis techniques on synthetic functional images and robustly derives brain connectivity from real fMRI data.     

具有Hammerstein模型特征的非线性远程预报辨识

为提高内河船舶远程通信预警功能的精度和可靠性,提出了具有非线性预测控制模型特征的远程复杂目标预报辨识算法。通过将远程复杂目标的辨识分解为一个静态非线性环节和动态线性环节的串联,利用稳态信息获取稳态模型的一致性估计,并通过动态模型获得非线性静态环节的增益,再利用奇异值分解法和动态信息辨识获取非线性系统未知参数的估计。仿真结果验证了该方法的有效性。     

Automatic Parameters Selection for SVM Based on PSO

Motivated by the fact that automatic parameters selection for Support Vector Machine （SVM） is an important issue to make SVM practically useful and the common used Leave - One - Out （LO0） method is complex calculation and time consuming,an effective strategy for automatic parameters selection for SVM is proposed by using the Particle Swarm Optimization （PSO） in this paper. Simulation results of practice data model demonstrate the effectiveness and high efficiency of the proposed approach.     

Two-Stage Mixed Discrete–Continuous Identification of Radial Basis Function (RBF) Neural Models for Nonlinear Systems

The identification of nonlinear dynamic systems using radial basis function (RBF) neural models is studied in this paper. Given a model selection criterion, the main objective is to effectively and efficiently build a parsimonious compact neural model that generalizes well over unseen data. This is achieved by simultaneous model structure selection and optimization of the parameters over the continuous parameter space. It is a mixed-integer hard problem, and a unified analytic framework is proposed to enable an effective and efficient two-stage mixed discrete–continuous identification procedure. This novel framework combines the advantages of an iterative discrete two-stage subset selection technique for model structure determination and the calculus-based continuous optimization of the model parameters. Computational complexity analysis and simulation studies confirm the efficacy of the proposed algorithm.      

HRF estimation in fMRI data with an unknown drift matrix by iterative minimization of the Kullback-Leibler divergence

Hemodynamic response function (HRF) estimation in noisy functional magnetic resonance imaging (fMRI) plays an important role when investigating the temporal dynamic of a brain region response during activations. Nonparametric methods which allow more flexibility in the estimation by inferring the HRF at each time sample have provided improved performance in comparison to the parametric methods. In this paper, the mixed-effects model is used to derive a new algorithm for nonparametric maximum likelihood HRF estimation. In this model, the random effect is used to better account for the variability of the drift. Contrary to the usual approaches, the proposed algorithm has the benefit of considering an unknown and therefore flexible drift matrix. This allows the effective representation of a broader class of drift signals and therefore the reduction of the error in approximating the drift component. Estimates of the HRF and the hyperparameters are derived by iterative minimization of the Kullback-Leibler divergence between a model family of probability distributions defined using the mixed-effects model and a desired family of probability distributions constrained to be concentrated on the observed data. The performance of proposed method is demonstrated on simulated and real fMRI data, the latter originating from both event-related and block design fMRI experiments.     

Estimation of the hemodynamic response of fMRI Data using RBF neural network

Functional magnetic resonance imaging (fMRI) is an important technique for neuroimaging. The conventional system identification methods used in fMRI data analysis assume a linear time-invariant system with the impulse response described by the hemodynamic responses (HDR). However, the measured blood oxygenation level-dependent (BOLD) signals to a particular processing task (for example, rapid event-related fMRI design) show nonlinear properties and vary with different brain regions and subjects. In this paper, radial basis function (RBF) neural network (a powerful technique for modelling nonlinearities) is proposed to model the dynamics underlying the fMRI data. The equivalence of the proposed method to the existing Volterra series method has been demonstrated. It is shown that the first- and second-order Volterra kernels could be deduced from the parameters of the RBF neural network. Studies on both simulated (using Balloon model) as well as real event-related fMRI data show that the proposed method can accurately estimate the HDR of the brain and capture the variations of the HDRs as a function of the brain regions and subjects.     

A sparse and spatially constrained generative regression model for fMRI data analysis

In this study, we present an advanced Bayesian framework for the analysis of functional magnetic resonance imaging (fMRI) data that simultaneously employs both spatial and sparse properties. The basic building block of our method is the general linear regression model that constitutes a well-known probabilistic approach. By treating regression coefficients as random variables, we can apply an enhanced Gibbs distribution function that captures spatial constrains and at the same time allows sparse representation of fMRI time series. The proposed scheme is described as a maximum a posteriori approach, where the known expectation maximization algorithm is applied offering closed-form update equations for the model parameters. We have demonstrated that our method produces improved performance and functional activation detection capabilities in both simulated data and real applications.     

Selection criteria for the analysis of data-driven clusters in cerebral FMRI

Functional MRI (fMRI) may be possible without a priori models of the cerebral hemodynamic response. First, such data-driven fMRI requires that all cerebral territories with distinct patterns be identified. Second, a systematic selection method is necessary to prevent the subjective interpretation of the identified territories. This paper addresses the second point by proposing a novel method for the automated interpretation of identified territories in data-driven fMRI. Selection criteria are formulated using: 1) the temporal cross-correlation between each identified territory and the paradigm and 2) the spatial contiguity of the corresponding voxel map. Ten event-design fMRI data sets are analyzed with one prominent algorithm, fuzzy c-means clustering, before applying the selection criteria. For comparison, these data are also analyzed with an established, model-based method: statistical parametric mapping. Both methods produced similar results and identified potential activation in the expected territory of the sensorimotor cortex in all ten data sets. Moreover, the proposed method classified distinct territories in separate clusters. Selected clusters have a mean temporal correlation coefficient of 0.39+/-0.07 (n=19) with a mean 2.7+/-1.4 second response delay. At most, four separate contiguous territories were observed in 87% of these clusters. These results suggest that the proposed method may be effective for exploratory fMRI studies where the hemodynamic response is perturbed during cerebrovascular disease.     

Model selection through a statistical analysis of the globalminimum of a weighted nonlinear least squares cost function

This paper presents a model selection algorithm for the identification of parametric models that are linear in the measurements. It is based on the mean and variance expressions of the global minimum of a weighted nonlinear least squares cost function. The method requires the knowledge of the noise covariance matrix but does not assume that the true model belongs to the model set. Unlike the traditional order estimation methods available in literature, the presented technique allows to detect undermodeling. The theory is illustrated by simulations on signal modeling and system identification problems and by one real measurement example     

Decomposition Based Newton Iterative Identification Method for a Hammerstein Nonlinear FIR System with ARMA Noise

This paper derives a Newton iterative algorithm for identifying a Hammerstein nonlinear FIR system with ARMA noise (i.e., Hammerstein nonlinear controlled autoregressive moving average system). This method decomposes a Hammerstein nonlinear system into two subsystems using the hierarchical identification principle, estimating the parameters of the system directly without using the over-parameterization method. The simulation results show that the proposed algorithm is effective.     

Unified Framework for Robust Estimation of Brain Networks From fMRI Using Temporal and Spatial Correlation Analyses

There is a rapidly growing interest in the neuroimaging field to use functional magnetic resonance imaging (fMRI) to explore brain networks, i.e., how regions of the brain communicate with one another. This paper presents a general and novel statistical framework for robust and more complete estimation of brain functional connectivity from fMRI based on correlation analyses and hypothesis testing. In addition to the ability of examining the correlations with each individual seed as in the standard and existing methods, the proposed framework can detect functional interactions by simultaneously examining multiseed correlations via multiple correlation coefficients. Spatially structured noise in fMRI is also taken into account during the identification of functional interconnection networks through noncentral $F$ hypothesis tests. The associated issues for the multiple testing and the effective degrees-of-freedom are considered as well. Furthermore, partial multiple correlations are introduced and formulated to measure any additional task-induced but not stimulus-locked relation over brain regions so that we can take the analysis of functional connectivity closer to the characterization of direct functional interactions of the brain. Evaluation for accuracy and advantages, and comparisons of the new approaches in the presented general framework are performed using both realistic synthetic data and in vivo fMRI data.      

Nonlinear identification and optimal feedforward friction compensation for a motion platform

In this study, we present a method of nonlinear identification and optimal feedforward friction compensation for an industrial single degree of freedom motion platform. The platform has precise reference tracking requirements while suffering from nonlinear dynamic effects, such as friction and backlash in the driveline. To eliminate nonlinear dynamic effects and achieve precise reference tracking, we first identified the nonlinear dynamics of the platform using Higher Order Sinusoidal Input Describing Function (HOSIDF) based system identification. Next, we present optimal feedforward compensation design to improve reference tracking performance. We modeled the friction using the Stribeck model and identified its parameters through a procedure including a special reference signal and the Nelder–Mead algorithm. Our results show that the RMS trajectory tracking error decreased from 0.0431 deg/s to 0.0117 deg/s when the proposed nonlinear identification and friction compensation method is utilized.     

Acoustic Echo Cancellation Using a Pseudocoherence Function in the Presence of Memoryless Nonlinearity

Acoustic echo cancellation (AEC) is critical for telecommunication applications involving two or more locations such as teleconferencing. It is also challenging because of loudspeaker's nonlinearity, real-time implementation requirement, and multipath effects of indoor environments. This paper addresses the nonlinear AEC problem. We use a Hammerstein model to describe the memoryless nonlinearity of loudspeaker concatenated with a linear room impulse response. We propose a method using a pseudo magnitude squared coherence (MSC) function to identify the nonlinearity in the Hammerstein system and develop an on-line AEC algorithm. Our method identifies nonlinearity without knowing the linear block in the Hammerstein system, which guarantees the stability of the algorithm and leads to a faster convergence rate. Moreover, several alternative criteria based on the MSC function are also proposed for nonlinearity identification. Effectiveness of the proposed algorithms is demonstrated through computer simulations.      

二阶Volterra变数据块长LMS算法

二阶Volterra数据块LMS算法利用当前时刻及其以前时刻更多输入信号和误差信号的信息提高了算法的收敛速度,但由于其固定数据块长取值的不同导致了算法的收敛速度和稳态误差此消彼长。针对这个问题,本文提出一种二阶Volterra变数据块长LMS算法,通过时刻改变输入信号数据块长度提高算法性能。本算法首先采用两个并行的二阶Volterra滤波器,其输入信号数据块长差值始终保持一个单位;然后将其各自的输出误差信号同时输入到数据块长判决器,通过判决器得到下一时刻各个滤波器输入信号的数据块长度;最后以第1个二阶Volterra滤波器的输出作为整个滤波系统的输出,从而改善了算法性能。将本算法应用于非线性系统辨识,计算机仿真结果表明,高斯噪声背景下本算法的收敛速度和稳态性能都得到了明显的提高。      

Penalized least squares estimation of Volterra filters and higherorder statistics

Volterra filters (VFs) and higher order statistics (HOS) are important tools for nonlinear analysis, processing, and modeling. Despite their highly desirable properties, the transfer of VFs and HOS to real-world signal processing problems has been hindered by the requirement of very large data records needed to obtain reliable estimates. The identification of VFs and the estimation of HOS both fall into the category of ill-posed estimation problems. We develop penalized least squares (PLS) estimation methods for VFs and HOS. It is shown that PLS is a very effective way to incorporate prior information of the problem at hand without directly constraining the estimation procedure. Hence, PLS produces much more reliable estimates. The main contributions of this paper are the development of appropriate penalizing functionals and cross-validation procedures for PLS based VF identification and HOS estimation     

Parameter identification and position control for helical hydraulic rotary actuators based on particle swarm optimization

It is difficult to obtain an accurate mathematical model in electro-hydraulic servo control system, due to the nonlinear factors such as dead zone, saturation, flow coefficient, and friction. Hence, a parameter identification algorithm, combining recursive least squares (RLS) with modified nonlinear particle swarm optimization (NPSO) algorithm, is proposed. On this basis, another improved NPSO algorithm is also put forward, aiming at searching for the optimal proportional–integral (PI) controller gain of the nonlinear hydraulic system while giving comprehensive consideration to the system performance indexes. The system identification experiments and position tracking control are conducted, respectively. As indicated by the comparison with the least squares (LS), RLS, PSO, and RLS–LPSO results, the proposed method shows higher identification and control accuracy.     

Identification of pneumatic artificial muscle manipulators by a MGA-based nonlinear NARX fuzzy model

This study investigates the technique of modeling and identification of a new dynamic NARX fuzzy model by means of genetic algorithms. In conventional identification techniques, there are difficulties such as poor knowledge of the process, inaccurate process or complexity of the resulting mathematical model. All these factors deteriorate the identification performance when dealing with dynamic nonlinear industrial processes. To overcome these difficulties, this paper proposes a novel approach by using a modified genetic algorithm (MGA) combined with the predictive capability of nonlinear ARX (NARX) model for generating the dynamic NARX Takagi–Sugeno (TS) fuzzy model. The MGA algorithm processes the experimental input–output training data from the real system and optimizes the NARX fuzzy model parameters. This is referred to as fuzzy identification, which automatically generates the appropriate fuzzy if-then rules to characterize the dynamic nonlinear features of the real plant. The prototype pneumatic artificial muscle (PAM) manipulator, being a typical nonlinear and time-varying system, is used as a test system for this novel approach. This result shows that, with this MGA-based modeling and identification, the novel NARX fuzzy model identification approach to the PAM manipulator achieved highly outstanding performance and high precision as well. The accuracy of the proposed MGA-based NARX fuzzy model proves excellent in comparison with the MGA-based TS fuzzy model and the conventional GA-based TS fuzzy model.     

改进量子遗传算法辨识超混沌系统

混沌系统的参数辨识是非线性科学中混沌控制与同步的关键问题。提出改进量子遗传算法,该算法具有良好的全局搜索能力,将其应用在混沌系统参数辨识问题。通过尽量减小实际系统与数学模型的状态同步误差来构造适应度函数,将参数辨识问题转化为一个多维优化问题。对超混沌Chen系统进行研究,并与基本量子遗传算法比较。实验仿真结果表明,改进量子遗传算法的有效和可行性,为混沌系统辨识开拓了一种新方法。