A study on the best order for autoregressive EEG modelling

The autoregressive (AR) model is a widely used tool in electroencephalogram (EEG) analysis. The dependence of the AR model on both the segment length and several characteristic EEG patterns is addressed. The best AR model order is computed with three different criteria. The results show that the Rissanen criteria provides the more consistent order estimate for the EEG patterns considered. This study shows that for our data set, a 5th order AR model represents adequately 1- or 2-s EEG segments with the exception of featureless background, where higher order models are necessary.     

Measuring the dissimilarity between EEG recordings through a non-linear dynamical system approach

A new measure of dissimilarity between two EEG segments is proposed. It is derived from the application of the mathematical concept of distance between series of one-step predictions according to the estimated non-linear autoregressive functions. The non-linear autoregressive estimation is performed by non-parametric regression using kernel estimators. The possibility of applying this measure for automatic classification of EEG segments is explored. For this purpose multidimensional scaling and cluster analyses are applied on the basis of the calculated dissimilarity measures. In particular, its application to different EEG segments with delta activity and also with alpha waves reveals high agreement with visual classification by EEG specialists.     

Selection of relevant features for EEG signal classification of schizophrenic patients

In this paper, EEG signals of 20 schizophrenic patients and 20 age-matched control participants are analyzed with the objective of determining the more informative channels and finally distinguishing the two groups. For each case, 22 channels of EEG were recorded. A two-stage feature selection algorithm is designed, such that, the more informative channels are first selected to enhance the discriminative information. Two methods, bidirectional search and plus-L minus-R (LRS) techniques are employed to select these informative channels. The interesting point is that most of selected channels are located in the temporal lobes (containing the limbic system) that confirm the neuro-phychological differences in these areas between the schizophrenic and normal participants. After channel selection, genetic algorithm (GA) is employed to select the best features from the selected channels. In this case, in addition to elimination of the less informative channels, the redundant and less discriminant features are also eliminated. A computationally fast algorithm with excellent classification results is obtained. Implementation of this efficient approach involves several features including autoregressive (AR) model parameters, band power, fractal dimension and wavelet energy. To test the performance of the final subset of features, classifiers including linear discriminant analysis (LDA) and support vector machine (SVM) are employed to classify the reduced feature set of the two groups. Using the bidirectional search for channel selection, a classification accuracy of 84.62% and 99.38% is obtained for LDA and SVM, respectively. Using the LRS technique for channel selection, a classification accuracy of 88.23% and 99.54% is also obtained for LDA and SVM, respectively. Finally, the results are compared and contrasted with two well-known methods namely, the single-stage feature selection (evolutionary feature selection) and principal component analysis (PCA)-based feature selection. The results show improved accuracy of classification in relatively low computational time with the two-stage feature selection.     

Non-linear and linear forecasting of the EEG time series

The method of non-linear forecasting of time series was applied to different simulated signals and EEG in order to check its ability of distinguishing chaotic from noisy time series. The goodness of prediction was estimated, in terms of the correlation coefficient between forecasted and real time series, for non-linear and autoregressive (AR) methods. For the EEG signal both methods gave similar results. It seems that the EEG signal, in spite of its chaotic character, is well described by the AR model.     

Simulation of nonstationary EEG

In this paper we present a systematic method for generating simulations of nonstationary EEG. Such simulations are needed, for example, in the evaluation of tracking algorithms. First a state evolution process is simulated. The states are initially represented as segments of stationary autoregressive processes which are described with the corresponding predictor coefficients and prediction error variances. These parameters are then concatenated to give a piecewise time-invariant parameter evolution. The evolution is projected onto an appropriately selected set of smoothly time-varying functions. This projection is used to generate the final EEG simulation. As an example we use this method to simulate the EEG of a drowsy rat. This EEG can be described as toggling between two states that differ in the degree of synchronization of the activity-inducing neuron clusters. Received: 22 June 1994 / Accepted in revised form: 18 February 1997     

The use of a multi-channel kalman filter algorithm in structural analysis of the epileptic EEG

An extension of the Kalman filter algorithm to the multi-channel case is presented and its application as a segmenting procedure in the analysis of the epileptic EEG is discussed. An analytical example of structural analysis, using the segments extracted by the proposed filter, is presented for a particular set of 4-channel EEG recordings. This analysis is shown to be especially fruitful if the autoregressive coefficients - a by product of the filtering procedure - are used to estimate the information flow between the channels by the calculation of partial as well as directed coherences for the representative segments.     

Comparison of different methods of time shift measurement in EEG

Digital signal processing techniques are often used for measurement of small time shifts between EEG signals. In our work we tested properties of linear cross-correlation and phase/coherence method. The last mentioned method was used in two versions. The first version used fast Fourier transform (FFT) algorithm and the second was based on autoregressive modeling with fixed or adaptive model order. Methods were compared on several testing signals mimicking real EEG signals. The accuracy index for each method was computed. Results showed that for long signal segments all methods bring comparably good results. Accuracy of FFT phase/coherence method significantly decreased when very short segments were used and also decreased with an increasing level of the additive noise. The best results were obtained with autoregressive version of phase/coherence. This method is more reliable and may be used with high accuracy even in very short signals segments and it is also resistant to additive noise.     

Segmentation of EEG during sleep using time-varying autoregressive modeling

Time-varying AR modeling is applied to sleep EEG signal, in order to perform parameter estimation and detect changes in the signal characteristics (segmentation). Several types of basis functions have been analyzed to determine how closely they can approximate parameter changes characteristics of the EEG signal. The TV-AR model was applied to a large number of simulated signal segments, in order to examine the behaviour of the estimation under various conditions such as variations in the EEG parameters and in the location of segment boundaries, and different orders of the basis functions. The set of functions that is the basis for the Discrete Cosine Transform (DCT), and the Walsh functions were found to be the most efficient in the estimation of the model parameters. A segmentation algorithm based on an “Identification function” calculated from the estimated model parameters is suggested.     

A method of neuronal spike train study based on autoregressive analysis

The method of autoregressive (AR) analysis for neuronal spike trains (NST) is proposed in the paper. The AR model and the Green's function as well as the power spectral density function are used to process and analyse the neuronal interspike interval (ISI) sequences of cat's first somatosensory area of cortex (SI area) under various situations. With these methods the characteristics of the ISI sequence such as the AR order and parameters, memory property, correlativity and periodicity etc. can be extracted.     

Single evoked potential reconstruction by means of wavelet transform

We would like to propose a method of single evoked potential (EP) extraction free from assumptions and based on a novel approach — the wavelet representation of the signal. Wavelets were introduced by Grossman and Morlet in 1984. The method is based on the multiresolution signal decomposition. Wavelets are already used for speech recognition, geophysics investigations and fractal analysis. This method seems to be a useful improvement upon Fourier Transform analysis, since it provides simultaneous information on frequency and time localization of the signal. We would like to introduce wavelet formalism for the first time to brain signal analysis. One of the most important problems in this field is the analysis of evoked potentials. This signal has an amplitude several times smaller than EEG, therefore stimulus-synchronized averaging is commonly used. This method is based on several assumptions. Namely it is postulated that: 1) EP are characterized by a deterministic repeatable pattern, 2) EEG has purely stochastic character, 3) EEG and EP are independent. These assumptions have been challenged e.g. the variability of the EP pattern was demonstrated by John (1973) by means of factor analysis. In view of the works of Sayers et al. (1974) and Baar (1988) EP reflects the reorganization of the spontaneous activity under the influence of a stimulus and it is connected with the redistribution of EEG phases. Several attempts to overcome the limitation of the averaging method have been made. Heintze and Künkel (1984) used an autoregressive moving average (ARMA) model to extract evoked potentials from 2 segments. This was possible under two condiitons: high signal to noise ratio and clear separation of the EEG and EP spectra. These assumptions are not easy to fulfill, though. Cerutti et al. (1987) modeled background EEG activity by means of an AR process and event related brain activity by ARMA. In this way they were able to find a filter extracting single EP. Nevertheless, their method was not quite free of assumptions, since they since they used averaged EP to define their ARMA filter. In the following we shall briefly describe the method of the multiresolution decomposition and we will apply it to the analysis and reconstruction of single evoked potentials.     

Scaling vs. nonscaling methods of assessing autonomic tone in streptozotocin-induced diabetic rats

We studied heart rate variability in rats by power scaling spectral analysis (PSSA), autoregressive modeling (AR), and detrended fluctuation analysis (DFA), assessed stability by coefficient of variation between consecutive 6-h epochs, and then compared cross-correlation among techniques. These same parameters were checked from baseline conditions through acute and chronic disease states (streptozotocin-induced diabetes) followed by therapeutic intervention (insulin). Cross-correlation between methods over the entire time period was r = 0.94 (DFA and PSSA), r = 0.81 (DFA and AR), and r = 0.77 (AR and PSSA). Under baseline conditions the scaling parameter measured by DFA and PSSA and the high-frequency (HF) component measured by AR fluctuated around an average value, but these fluctuations were different for the three methods. After diabetes induction, a strong correlation was found between the HF power and the short-term scaling parameter. Despite their differences in methodology, DFA and PSSA assess changes in parasympathetic tone as detected by autoregressive modeling.     

Nonrandom variability in respiratory cycle parameters of humans during stage 2 sleep

We analyzed breath-to-breath inspiratory time (TI), expiratory time (TE), inspiratory volume (VI), and minute ventilation (Vm) from 11 normal subjects during stage 2 sleep. The analysis consisted of 1) fitting first- and second-order autoregressive models (AR1 and AR2) and 2) obtaining the power spectra of the data by fast-Fourier transform. For the AR2 model, the only coefficients that were statistically different from zero were the average alpha 1 (a1) for TI, VI, and Vm (a1 = 0.19, 0.29, and 0.15, respectively). However, the power spectra of all parameters often exhibited peaks at low frequency (less than 0.2 cycles/breath) and/or at high frequency (greater than 0.2 cycles/breath), indicative of periodic oscillations. After accounting for the corrupting effects of added oscillations on the a1 estimates, we conclude that 1) breath-to-breath fluctuations of VI, and to a lesser extent TI and Vm, exhibit a first-order autoregressive structure such that fluctuations of each breath are positively correlated with those of immediately preceding breaths and 2) the correlated components of variability in TE are mostly due to discrete high- and/or low-frequency oscillations with no underlying autoregressive structure. We propose that the autoregressive structure of VI, TI, and Vm during spontaneous breathing in stage 2 sleep may reflect either a central neural mechanism or the effects of noise in respiratory chemical feedback loops; the presence of low-frequency oscillations, seen more often in Vm, suggests possible instability in the chemical feedback loops. Mechanisms of high-frequency periodicities, seen more often in TE, are unknown.     

Investigation of the modulation between EEG alpha waves and slow/fast delta waves in children in different depths of Desflurane anesthesia

ObjectivesInvestigation of the amplitude modulation of alpha-band EEG oscillations (i.e., grouping of alpha-band activities) by delta-band EEG activities in various depths of anesthesia (DOA).MethodsThis modulation, which is a sort of phase dependent amplitude modulation, is studied in 10 children in various depths of Desflurane anesthesia. Two parameters are defined to quantify the modulation: strength of modulation (SOM) and phase of modulation (POM). SOM indicates to what extent delta and alpha activities are related to each other, and POM is the delta phase in which the alpha amplitude is maximal. These parameters are analyzed in different DOA for various formations of delta sub-bands.ResultsThe ability of POM and SOM were explored to characterize mechanisms contributing to delta activities and their correlation with the level of anesthesia. These parameters are influenced by DOA and frequency intervals of delta sub-bands. SOM takes higher values around certain frequency ranges of delta band. According to this, delta band comprises three main sub-bands in various unconsciousness levels. Although boundaries of these sub-bands change with DOA, they are almost in [0.1–0.5] Hz (very slow delta), [0.7–1.7] Hz (slow delta) and [2–4] Hz (fast delta) intervals. POMs relating to slow and fast delta bands increase with consciousness level. This is an indication that delta waves differently modulate alpha EEG activities (in terms of phase lag) in different DOA. In deep anesthesia, POM relating to fast delta correlates with DOA better than POM relating to slow delta does. In light anesthesia this correlation is inversed. Investigation regarding to different formations of delta sub-bands shows that POM relating to [1.8–4] Hz is a proper choice for distinguishing deep, moderate and light anesthesia.ConclusionSOM allows separating mechanisms underlying delta band activities, and POM can be seen as a complementary neurophysiologic-based parameter for quantifying DOA.     

Analysis of EEG signals during epileptic and alcoholic states using AR modeling techniques

Electroencephalogram (EEG) analysis remains problematic due to limited understanding of the signal origin, which leads to the difficulty of designing evaluation methods. In spite of these shortcomings, the EEG is a valuable tool in the evaluation of some neurological disorders as well as in the evaluation of overall cerebral activity. In most studies, which use quantitative EEG analysis, the properties of measured EEG are computed by applying power spectral density (PSD) estimation for selected representative EEG samples. The sample for which the PSD is calculated is assumed to be stationary. This work deals with a comparative study of the PSD obtained from normal, epileptic and alcoholic EEG signals. The power density spectra were calculated using fast Fourier transform (FFT) by Welch's method, auto regressive (AR) method by Yule–Walker and Burg's method. The results are tabulated for these different classes of EEG signals.     

Hidden Markov models used for the offline classification of EEG data.

Hidden Markov models (HMM) are introduced for the offline classification of single-trail EEG data in a brain-computer-interface (BCI). The HMMs are used to classify Hjorth parameters calculated from bipolar EEG data, recorded during the imagination of a left or right hand movement. The effects of different types of HMMs on the recognition rate are discussed. Furthermore a comparison of the results achieved with the linear discriminant (LD) and the HMM, is presented.     

脑电监测SD大鼠异氟醚全身麻醉模型的建立及脑电分析

目的建立脑电监测SD大鼠异氟醚全身麻醉模型并分析脑电监测结果。方法：随机选取SD大鼠20只,先行脑电电极置入术,术后使用密闭吸入麻醉动物行为学观察圆筒,观察异氟醚引起的麻醉诱导、维持、觉醒状态并记录诱导、觉醒时间。将记录的行为学结果对照典型脑电图波形改变判断麻醉深度。结果：实验SD大鼠均检测出脑电图,通过对照行为学观察发现动态脑电监、}测结果同异氟醚麻醉过程进展一致。在麻醉过程中SD大鼠出现典型的全身麻醉脑电循环。结论：动态脑电监测和SD大鼠行为学观察可以准确反应全身麻醉深度。     

Bag-of-words representation for biomedical time series classification

Automatic analysis of biomedical time series such as electroencephalogram (EEG) and electrocardiographic (ECG) signals has attracted great interest in the community of biomedical engineering due to its important applications in medicine. In this work, a simple yet effective bag-of-words representation that is originally developed for text document analysis is extended for biomedical time series representation. In particular, similar to the bag-of-words model used in text document domain, the proposed method treats a time series as a text document and extracts local segments from the time series as words. The biomedical time series is then represented as a histogram of codewords, each entry of which is the count of a codeword appeared in the time series. Although the temporal order of the local segments is ignored, the bag-of-words representation is able to capture high-level structural information because both local and global structural information are well utilized. The performance of the bag-of-words model is validated on three datasets extracted from real EEG and ECG signals. The experimental results demonstrate that the proposed method is not only insensitive to parameters of the bag-of-words model such as local segment length and codebook size, but also robust to noise.     

Autoregressive modeling of analytical sensor data can yield classifiers in the predictor coefficient parameter space

SUMMARY: The analysis of chromatographic data resulting from complex chemical mixtures is challenging. Components may co-elute, causing their signals to overlap. An algorithm that will increase the signal-to-noise ratio so compounds present in low abundance can be better distinguished from noise is useful in this type of analysis. The autoregressive (AR) filter offers the advantage of smoothing chromatograms to increase this ratio, while also offering data compression and increased resolution. Furthermore, this filter can be useful for classification, as the roots of the predictor coefficient vectors represent features present in the data and can therefore be used for pattern recognition. In this paper, we present a novel method for applying AR filtering to chromatogram data. We show that the AR filter outperforms the Savitzky-Golay filter for smoothing noise while retaining important information within chromatograms, and also that AR correlation coefficients have the potential to be used to classify chromatogram data into groups. CONTACT: cdavis@draper.com.