Variability, regularity, and complexity of time series generated by schizophrenic patients and control subjects

We analyzed time series generated by 20 schizophrenic patients and 20 sex- and age-matched control subjects using three nonlinear methods of time series analysis as test statistics: central tendency measure (CTM) from the scatter plots of first differences of data, approximate entropy (ApEn), and Lempel-Ziv (LZ) complexity. We divided our data into a training set (10 patients and 10 control subjects) and a test set (10 patients and 10 control subjects). The training set was used for algorithm development and optimum threshold selection. Each method was assessed prospectively using the test dataset. We obtained 80% sensitivity and 90% specificity with LZ complexity, 90% sensitivity, and 60% specificity with ApEn, and 70% sensitivity and 70% specificity with CTM. Our results indicate that there exist differences in the ability to generate random time series between schizophrenic subjects and controls, as estimated by the CTM, ApEn, and LZ. This finding agrees with most previous results showing that schizophrenic patients are characterized by less complex neurobehavioral and neuropsychologic measurements.     

Comparison of entropy-based regularity estimators: application to the fetal heart rate signal for the identification of fetal distress

This paper considers the multiscale entropy (MSE) approach for estimating the regularity of time series at different scales. Sample entropy (SampEn) and approximate entropy (ApEn) are evaluated in MSE analysis on simulated data to enhance the main features of both estimators. We applied the approximate entropy and the sample entropy estimators to fetal heart rate signals on both single and multiple scales for an early identification of fetal sufferance antepartum. Our results show that the ApEn index significantly distinguishes suffering from normal fetuses between the 30th and the 35th week of gestation. Furthermore, our data shows that the MSE entropy values are reliable indicators of the fetal distress associated with the presence of a pathological condition at birth.     

Monotonicity of approximate entropy during transition from awareness to unresponsiveness due to propofol anesthetic induction

The ability to monitor the physiological effects of sedative medication accurately is of interest in clinical practice. During the anesthetic agent driven transition to unresponsiveness, nonstationary changes such as signal amplitude variations appear in electroencephalography. In this paper, it is studied whether the application of the approximate entropy (ApEn) method to electroencephalographic (EEG) signal produces a monotonic response curve during the transition from awareness to unresponsiveness. Data from fourteen patients, undergoing propofol anesthetic induction were studied. To optimize the ApEn performance, different parameter choices were carefully evaluated. It was assumed with our protocol, that the level of anesthesia changes monotonically with the elapsed induction time. The monotonicity of the ApEn change was assessed with the prediction probability statistic (PK). The monotonicity of the ApEn time-series depends on the parameters employed in the algorithm and the varying signal amplitude. Depending on the parameter values, the median PK value ranged from 0.886 to 0.527. Thus, a good directionality and concordance was observed, but the nonstationarity of the signal affected the results. In conclusion, EEG-based ApEn measure shows a nonlinear response during propofol induction. With a judicious choice of parameters, a monotonic response is confirmed using PK statistic.     

Utility of approximate entropy from overnight pulse oximetry data in the diagnosis of the obstructive sleep apnea syndrome

Approximate entropy (ApEn) is a family of statistics introduced as a quantification of regularity in time series without any a priori knowledge about the system generating them. The aim of this preliminary study was to assess whether a time series analysis of arterial oxygen saturation (SaO2) signals from overnight pulse oximetry by means of ApEn could yield essential information on the diagnosis of obstructive sleep apnea (OSA) syndrome. We analyzed SaO2 signals from 187 subjects: 111 with a positive diagnosis of OSA and 76 with a negative diagnosis of OSA. We divided our data in a training set (44 patients with OSA Positive and 30 patients with OSA Negative) and a test set (67 patients with OSA Positive and 46 patients with OSA Negative). The training set was used for algorithm development and optimum threshold selection. Results showed that recurrence of apnea events in patients with OSA determined a significant increase in ApEn values. This method was assessed prospectively using the test dataset, where we obtained 82.09% sensitivity and 86.96% specificity. We conclude that ApEn analysis of SaO2 from pulse oximetric recording could be useful in the study of OSA.     

Approximate entropy-based epileptic EEG detection using artificial neural networks.

The electroencephalogram (EEG) signal plays an important role in the diagnosis of epilepsy. The EEG recordings of the ambulatory recording systems generate very lengthy data and the detection of the epileptic activity requires a time-consuming analysis of the entire length of the EEG data by an expert. The traditional methods of analysis being tedious, many automated diagnostic systems for epilepsy have emerged in recent years. This paper proposes a neural-network-based automated epileptic EEG detection system that uses approximate entropy (ApEn) as the input feature. ApEn is a statistical parameter that measures the predictability of the current amplitude values of a physiological signal based on its previous amplitude values. It is known that the value of the ApEn drops sharply during an epileptic seizure and this fact is used in the proposed system. Two different types of neural networks, namely, Elman and probabilistic neural networks, are considered in this paper. ApEn is used for the first time in the proposed system for the detection of epilepsy using neural networks. It is shown that the overall accuracy values as high as 100% can be achieved by using the proposed system.     

Comparison of entropy and complexity measures for the assessment of depth of sedation

Entropy and complexity of the electroencephalogram (EEG) have recently been proposed as measures of depth of anesthesia and sedation. Using surrogate data of predefined spectrum and probability distribution we show that the various algorithms used for the calculation of entropy and complexity actually measure different properties of the signal. The tested methods, Shannon entropy (ShEn), spectral entropy, approximate entropy (ApEn), Lempel-Ziv complexity (LZC), and Higuchi fractal dimension (HFD) are then applied to the EEG signal recorded during sedation in the intensive care unit (ICU). It is shown that the applied measures behave in a different manner when compared to clinical depth of sedation score--the Ramsay score. ShEn tends to increase while the other tested measures decrease with deepening sedation. ApEn, LZC, and HFD are highly sensitive to the presence of high-frequency components in the EEG signal.     

近似熵、互近似熵的性质、快速算法及其在脑电与认知研究中的初步应用

本文从信号处理的角度介绍了近似嫡、互近似熵的概念、性质与应用,并给出了一种计算近似熵、互近似熵的实用快速算法．本文还通过实际算例说明了近似烟在表征信号的复杂性、互近似熵在表征信号的模式相似性方面的能力及其在脑电与认知研究中的初步应用。     

Influence of the vagus nerve on respiratory patterns during early maturation

Nonlinear dynamical analysis was performed on the phrenic neurogram before and after vagotomy in order to study the influence of the vagus nerve on the complexity of the phrenic neurogram in piglets in three age groups: 3-7 days (n = 7); 11-19 days (n = 6); and 29-34 days (n = 8). The phrenic neurogram, generated by the respiratory neural networks in the medulla, projects on the diaphragm muscles and initiate the respiratory movement. On the other hand, the vagus nerves carry the information from mechanoreceptors, located at the lower airway and lungs, to the medulla. The data was recorded during normal breathing (eupnea) before and after vagotomy while piglets were ventilated with 40% O2 in N2 and analyzed using the approximate entropy (ApEn) method. The mean values of the approximate entropy before and after vagotomy during the first 7 days of the postnatal age were 1.32 +/- 0.1 (standard deviation) and 1.34 +/- 0.07, respectively. These values before and after vagotomy during the 11-19 days age group were 1.15 +/- 0.09 and 1.12 +/- 0.05, respectively. For the 29-34 days age group, they were 1.14 +/- 0.05 before vagotomy and 1.19 +/- 0.08 after vagotomy. These differences in the ApEn (complexity) values of the phrenic neurogram before and after vagotomy are not statistically different at each age group. However, the mean mean approximate entropy (complexity) values between the 3-7 days age group and the other two groups were significantly different both before and after vagotomy (p < 0.05) using an analysis off variance test. These results suggest that the vagus nerve may not be mature during early maturation in piglets.     

Characterizing the Complexity of Spontaneous Electrical Signals in Cultured Neuronal Networks Using Approximate Entropy

In this paper, neurons were cultured on a substrate above a multielectrode array, so the changes of electrophysiological activity patterns during development of the neuronal network or in response to environmental perturbations were monitored. But the complexity of these spontaneous activity patterns is not well understood. In order to solve the problem, a comprehensive method (approximate entropy (ApEn) in combination with a ldquosliding windowrdquo over the data) is introduced to quantify the complexity of four spontaneous activity patterns (sporadic spikes, tonic spikes, pseudobursts, and typical bursts) in cultured hippocampal neuronal networks. The results show that the dynamic curves of ApEn illustrate vivid differences between the four patterns and the values of ApEn fall into different ranges. Among these patterns, the complexity of tonic spikes is the highest while that of pseudobursts is the lowest. This suggests that the proposed method is a valid procedure for tracking the dynamic variation in neuronal signals and can distinguish the different firing patterns of neuronal networks in terms of their complexity.     

高频地波雷达多目标跟踪系统

为实现高频地波雷达中的多目标跟踪,有效利用多普勒量测改善系统性能,采用多假设数据关联算法的多目标跟踪系统,提出了多普勒速度优先的二重波门设置和基于扩展卡尔曼滤波(EKF)的多假设算法。基于EKF的多假设算法,直接利用EKF过程中得到的参数更新观测向量方差,计算假设的概率,实现多假设数据关联。建立仿真场景,验证了二重波门设置能有效减少杂波干扰,并将基于EKF的多假设算法与独立假设下引入多普勒速度的关联算法比较,结果表明基于EKF的多假设算法在高频地波雷达这种较高杂波密度条件下效率更高,捕捉航迹和滤除虚假点迹的能力更强。     

Epileptic seizures detection in EEG using DWT-based ApEn and artificial neural network

There are numerous neurological disorders such as dementia, headache, traumatic brain injuries, stroke, and epilepsy. Out of these epilepsy is the most prevalent neurological disorder in the human after stroke. Electroencephalogram (EEG) contains valuable information related to different physiological state of the brain. A scheme is presented for detecting epileptic seizures from EEG data recorded from normal subjects and epileptic patients. The scheme is based on discrete wavelet transform (DWT) analysis and approximate entropy (ApEn) of EEG signals. Seizure detection is performed in two stages. In the first stage, EEG signals are decomposed by DWT to calculate approximation and detail coefficients. In the second stage, ApEn values of the approximation and detail coefficients are calculated. Significant differences have been found between the ApEn values of the epileptic and the normal EEG allowing us to detect seizures with 100 % classification accuracy using artificial neural network. The analysis results depicted that during seizure activity, EEG had lower ApEn values compared to normal EEG. This gives that epileptic EEG is more predictable or less complex than the normal EEG. In this study, feed-forward back-propagation neural network has been used for classification and training algorithm for this network that updates the weight and bias values according to Levenberg–Marquardt optimization technique.     

An information-theoretic criterion for intrasubject alignment of FMRI time series: motion corrected independent component analysis

A three-dimensional image registration method for motion correction of functional magnetic resonance imaging (fMRI) time-series, based on independent component analysis (ICA), is described. We argue that movement during fMRI data acquisition results in a simultaneous increase in the joint entropy of the observed time-series and a decrease in the joint entropy of a nonlinear function of the derived spatially independent components calculated by ICA. We propose this entropy difference as a reliable criterion for motion correction and refer to a method that maximizes this as motion-corrected ICA (MCICA). Specifically, a given motion-corrupted volume may be corrected by determining the linear combination of spatial transformations of the motion-corrupted volume that maximizes the proposed criterion. In essence, MCICA consists of designing an adaptive spatial resampling filter which maintains maximum temporal independence among the recovered components. In contrast with conventional registration methods, MCICA does not require registration of motion-corrupted volumes to a single reference volume which can introduce artifacts because corrections are applied without accounting for variability due to the task-related activation. Simulations demonstrate that MCICA is robust to activation level, additive noise, random motion in the reference volumes and the exact number of independent components extracted. When the method was applied to real data with minimal estimated motion, the method had little effect and, hence, did not introduce spurious changes in the data. However, in a data series from a motor fMRI experiment with larger motion, preprocessing the data with the proposed method resulted in the emergence of activation in primary motor and supplementary motor cortices. Although mutual information (MI) was not explicitly optimized, the MI between all subsequent volumes and the first one was consistently increased for all volumes after preprocessing the data with MCICA. We suggest MCICA represents a robust and reliable method for preprocessing of fMRI time-series corrupted with motion.     

Independent Component Analysis Applied to fMRI Data: A Generative Model for Validating Results

Methods for testing and validating independent component analysis (ICA) results in fMRI are growing in importance as the popularity of this model for studying brain function increases. We introduce and apply a synthesis/analysis model for analyzing functional Magnetic Resonance Imaging (fMRI) data using ICA. Classes of signal types relevant to fMRI are described and a statistical approach for validation of simulation results is developed. Additionally, we propose an empirical version of our validation approach to test the performance of various ICA approaches in “hybrid” fMRI data, a mixture of real fMRI data and known (validatable) sources. The synthesis portion of the model assumes statistically independent spatial sources in the brain. We also assume that the fMRI scanner acquires overdetermined data such that there are more time points than hemodynamic brain sources. We propose several signal classes relevant to fMRI and discuss the properties of each. The analysis portion of the model includes several candidates for spatial smoothing, ICA algorithm, and data reduction. We use the Kullback-Leibler divergence between the estimated source distributions and the “true” distributions as a measure of the optimality of the final ICA decomposition. Using this model, we generate fMRI-like data and optimize the analysis stage as a function of ICA algorithm, data reduction scheme, and spatial smoothing. An example of how our synthesis/analysis model can be used in validating an fMRI experiment is demonstrated using simulations and “hybrid” fMRI data.     

Quality Map Thresholding for De-noising of Complex-Valued fMRI Data and Its Application to ICA of fMRI

Although functional magnetic resonance imaging (fMRI) data are acquired as complex-valued images, traditionally most fMRI studies only use the magnitude of the data. FMRI analysis in the complex domain promises to provide more statistically significant information; however, the noisy nature of the phase poses a challenge for successful study of fMRI by complex-valued signal processing algorithms. In this paper, we introduce a physiologically motivated de-noising method that uses phase quality maps to successfully identify and eliminate noisy areas in the fMRI data so they can be used in individual and group studies. Additionally, we show how the developed de-noising method improves the results of complex-valued independent component analysis of fMRI data, a very successful tool for blind source separation of biomedical data.     

Nonlinear Analysis of Clinical Epileptic EEG by Approximate Entropy

By the means of computing approximate entropy (ApEn) of video-EEG from some clinical epileptic, ApEn of EEG with epileptiform discharges is found significantly different from that of EEG without epileptiforrn discharges, (p=0.002). Meanwhile, dynamic ApEn shows consistent change of EEG signal with discharges of epileptic waves inside. These results suggest that ApEn may be a useful tool for automatic recognition and detection of epileptic activity and for understanding epileptogenic mechanism.     

Order Selection of the Linear Mixing Model for Complex-Valued FMRI Data

Functional magnetic resonance imaging (fMRI) data are originally acquired as complex-valued images, which motivates the use of complex-valued data analysis methods. Due to the high dimension and high noise level of fMRI data, order selection and dimension reduction are important procedures for multivariate analysis methods such as independent component analysis (ICA). In this work, we develop a complex-valued order selection method to estimate the dimension of signal subspace using information-theoretic criteria. To correct the effect of sample dependence to information-theoretic criteria, we develop a general entropy rate measure for complex Gaussian random process to calibrate the independent and identically distributed (i.i.d.) sampling scheme in the complex domain. We show the effectiveness of the approach for order selection on both simulated and actual fMRI data. A comparison between the results of order selection and ICA on real-valued and complex-valued fMRI data demonstrates that a fully complex analysis extracts more meaningful components about brain activation.     

基于熵特征的雷达辐射源信号识别

针对现有方法识别率低和没有考虑噪声影响的问题, 提出一种新的雷达辐射源信号识别方法. 将近似熵(ApEn)和范数熵(NoEn)构成特征向量, 用神经网络分类器实现自动分类识别. ApEn是定量描述信号复杂性和不规则性的有效测度, NoEn是定量表征信号能量分布的有效参数. 理论分析和实验结果表明, 熵特征类内聚集性强、类间分离度大, 在较大信噪比范围内均能获得非常满意的正确识别率, 证实了所提出方法的有效性.     

改进谱聚类算法在MCI患者检测中的应用研究

为了利用功能核磁影像（fMRI, functional magnetic resonance imaging）数据进行轻度认知障碍（MCI, mild cognitive impairment）自动检测,对患者的fMRI数据进行聚类分析,得到患者大脑血氧依赖水平(BOLD, blood oxygen level dependence)的变化模式,并将异常模式用于疾病检测中。由于传统谱聚类算法需要计算相似矩阵所有的特征值和特征向量、时间与空间复杂度较高。提出一种改进的谱聚类方法,在相似矩阵的构造以及σ与k值的确定等方面进行了改进,将其用于MCI fMRI数据的聚类与诊断研究中。与传统谱聚类及Nystr?m算法进行的对比实验结果表明,改进的谱聚类方法可以更准确得到患者异常BOLD模式,分类正确率较高,且时间和空间复杂度均小于传统算法。     

IMM/MHT fusing feature information in visual tracking

In multi-target tracking, Multiple Hypothesis Tracking (MHT) can effectively solve the data association problem. However, traditional MHT can not make full use of motion information. In this work, we combine MHT with Interactive Multiple Model (IMM) estimator and feature fusion. New algorithm greatly improves the tracking performance due to the fact that IMM estimator provides better estimation and feature information enhances the accuracy of data association. The new algorithm is tested by tracking tropical fish in fish container. Experimental result shows that this algorithm can significantly reduce tracking lost rate and restrain the noises with higher computational effectiveness when compares with traditional MHT.     

Errors in the Estimation of Approximate Entropy and Other Recurrence-Plot-Derived Indices Due to the Finite Resolution of RR Time Series

An analysis of the errors due to the finite resolution of RR time series in the estimation of the approximate entropy (ApEn) is described. The quantification errors in the discrete RR time series produce considerable errors in the ApEn estimation (bias and variance) when the signal variability or the sampling frequency is low. Similar errors can be found in indices related to the quantification of recurrence plots. An easy way to calculate a figure of merit [the signal to resolution of the neighborhood ratio (SRN)] is proposed in order to predict when the bias in the indices could be high. When SRN is close to an integer value n, the bias is higher than when near n-1/2 or n+1/2. Moreover, if SRN is close to an integer value, the lower this value, the greater the bias is.