Estimate Of Magnitude Squared Coherence Research Articles

Feature and channel selection for designing a regression-based continuous-variable emotion recognition system with two EEG channels

Objective:With deepened interactions between human and computer, the need for a reliable and practical system for emotion recognition has become significant. The aim of this study is to propose a practical system for estimation of a continuous measure of valence based on a few number of EEG channels. Methods:A vast spectrum of time, frequency and coherence features were implemented with linear Regression (LR), Support Vector Regression (SVR) and Multi-Layer Perceptron (MLP) models and then ranked for the performance on DEAP database using a regression-based Relief filter. Regression outcomes were also classified to compare the performance of the proposed method with the literature. Finally, a video-based emotion recognition experiment was designed and conducted on 12 subjects using F7, F8, FC2 and T7 electrodes. Results:Magnitude Squared Coherence Estimate(MSCE) on F7–F8 with SVR model provided the highest performance on DEAP dataset. Classification of the output led to an average accuracy of 67.5%. For the gathered data, combination of MSCE and Hilbert–Huang Spectrum provided the best performance with 0.22 root mean square error and 0.67 correlation with self-reported valence in the scale of 1–9. Conclusion:MSCE could provide a good accuracy in estimation of Valence using 2 EEG channels on Deep dataset, and with addition of Hilbert–Huang Spectrum, it also demonstrated good accuracy and correlation with self-reported valence, in a completely different experiment. Significance:Continuous-value estimation of the valence can be achieved with only 2 EEG channels for practical applications out of the lab.

Approximation of statistical distribution of magnitude squared coherence estimated with segment overlapping

This paper suggests an approximation to the statistical distribution of a magnitude squared coherence (MSC) function estimated with segment overlapping. So far, the statistical distribution is known for an MSC computed without segment overlapping only. However, as the overlapped segmentation provides a more accurate MSC estimate, its statistical distribution is desired to allow its evaluation. This paper provides an approximation of the cumulative density function, probability density function, confidence limit formula, confidence interval computation and a procedure for the comparison of two MSC estimates, all for an MSC accurately estimated with the segment overlapping. Additionally, the benefits of the knowledge of the approximated statistics are illustrated on EEG–EMG (i.e. cortico-muscular) MSC estimates.

Experimental approach for testing the uncoupling between cardiovascular variability series.

In cardiovascular variability analysis, the significance of the coupling between two series is commonly assessed by defining a zero level on the magnitude-squared coherence (MSC). Although the use of the conventional value of 0.5 does not consider the dependence of MSC estimates on the analysis parameters, a theoretical threshold Tt is available only for the weighted covariance (WC) estimator. In this study, an experimental threshold for zero coherence Te was derived by a statistical test from the sampling distribution of MSC estimated on completely uncoupled time series. MSC was estimated by the WC method (Parzen window, spectral bandwidth B = 0.015, 0.02, 0.025, 0.03 Hz) and by the parametric autoregressive (AR) method (model order M= 4, 8, 12, 16), on time series with length L = 180, 300, 420, 540 s. Te decreased with increasing B and L and with decreasing M (range: 0.11-0.54 for WC estimator, 0.06-0.46 for AR estimator). Values for the typical parameter settings of WC and AR estimation (B = 0.025 Hz; M = 8; L = 300 s) were, respectively, 0.24 and 0.17. Moreover, Tt was always higher (range: 0.12-0.65) and the results were less dependable than those for Te in defining the zero level of MSC. Thus, with the proposed method, the hypothesis of uncoupling is rejected by accounting for the parameters that affect the confidence of spectral and cross-spectral estimates. The broad applicability of this approach should favour its introduction for assessing the significance of the coupling between cardiovascular variability series.

Measuring the coherence of intracranial electroencephalograms

Objective: Previous coherence studies of human intracranial electroencephalograms (EEGs) can be faulted on two methodological issues: (1) coherence estimates in a majority were formed from a very small number of independent sample spectra, and (2) the statistical significance of coherence estimates was either not reported or was poorly evaluated. Coherence estimator performance may be poor when a small number of independent sample spectra are employed, and the coupling of poor estimation and statistical testing can result in inaccuracy in the measurement of coherence. The performance characteristics of the coherence estimator and statistical testing of coherence estimates are described in this manuscript.Methods: The bias, variance, probability density functions, and confidence intervals of the estimate of magnitude squared coherence (MSC); and power analysis for the test of zero MSC were developed from the exact analytic form of the probability density function of the estimate of MSC for Gaussian random processes. The coherence of a single epoch of background EEG, recorded from a patient with intractable seizures, was evaluated with different parameter values to aid in the exposition of the concepts developed here.Results: The statistical characteristics of WOSA coherence estimates are a function of a single estimator parameter, the number of independent sample spectra employed in the estimation. Bias and variance are high, confidence intervals may be large, and the probability of Type II errors is high if a small number of independent sample spectra are employed. A considerable improvement in measurement accuracy is possible with careful selection of estimator parameter values.Conclusions: Coherence measurement accuracy can be improved over previous applications by attention to estimator performance and accurate statistical testing of coherence estimates.

Invariance of the magnitude-squared coherence estimate with respect to second-channel statistics

Properties of the magnitude-squared coherence (MSC) estimate in the presence of spherically symmetric noise are examined from a geometric point of view. Invariance to second-channel statistics is shown and the distribution function of the estimate is derived. A relationship between spherically symmetric and Gaussian sequences is also given.

Estimation of coherence and time delay with ARMA models

Magnitude squared coherence (MSC) and time delay are two important quantities needed for passive detection and localization of a radiating source using several sensors. This paper presents a novel approach to estimating the MSC and time delay from the outputs of two sensors. It first models the MSC as the product of the transfer functions of two autoregressive moving-average (ARMA) filters. The ARMA coefficients are then determined by a least squares, matrix pseudoinverse solution to the estimation equation. Time delay estimation follows as a byproduct, since both phase and MSC estimates are now available. Simulation results obtained from this modeling approach are compared against those estimated from the traditional periodograms. In the majority of cases studied, the ARMA approach appears to be superior, giving smaller bias and variances in both MSC and time delay estimations.

An approximation to the cumulative distribution function of the magnitude-squared coherence estimate

We investigate a nonlinear distortion that converts the magnitude-squared coherence estimate to a near-Gaussian random variable. In particular, we present simple approximations for the mean and variance of this nonlinearly distorted magnitude-squared coherence estimate and fit a Gaussian cumulative distribution function over a wide range of parameters.

Confidence bounds for signal-to-noise ratios from magnitude-squared coherence estimates

Coherence is used frequently to determine the degree to which one observed voltage is related to another observed voltage. Typically, in practice, these observables are degraded by system noise that is often independent, white, and Gaussian. Often, in measuring coherence, the interest is to determine the fraction of the observed power that is due to coherent signals and the fraction that is due to the uncorrelated noise floor. The term "signal" as used here describes a component of voltage of interest to an observer. With accurate coherence estimates, uncorrelated noise power can be separated from coherent signal power. Therefore, the concern in this article is with the accuracy of signal-to-noise ratio (SNR) calculations made from magnitude-squared coherence (MSC) estimates. Use is made of work by Carter and Scannel [1] in which they determine confidence bounds of MSC estimates for stationary Gaussian processes. Their results are used in this article to derive corresponding confidence bounds for SNR calculations without recourse to the complicated details of the underlying SNR statistics.

Bias of the estimate of magnitude-squared coherence

A simple accurate approximation for the bias of the estimate of magnitude-squared coherence (MSC) is derived from exact theoretical expressions. Simulation results corroborate the exact and approximate expressions, all of which differ from a previously published simulation result on this topic. A method for reducing the bias is suggested and investigated.

Statistics of the estimate of coherence

Expressions for the moments of the estimate of magnitude-squared coherence are presented. The expression presented are in convenient and accurate forms for digital computer evaluation. Simple approximations are given for the bias and variance.