EEG Preprocessing

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First of all, a preprocessing step is carried on the two EEG channels. They are both referenced to the right earlobe channel in order to cancel the common interference that can appear in all the channels. This is a common practice in EEG recordings. Since the earlobe is a position with no electrical activity, and it is very easy and unobtrusive

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18.3 Authentication Algorithm Based on EEG

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Figure 18.5. The owchart is identical to the enrollment one until the feature extraction module.

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One difference that is not shown in the scheme is that now we only record 1 min of data. The recognition module retrieves the claimed subjects EEG and ECG signature from their respective databases. At this point we have the probability that the 1-min EEG recorded belongs to the claimed subject. We also have the probability that the 1-min ECG recorded belongs to the claimed subject. The fusion module then takes care to fusion these probabilities to obtain a very con dent decision.

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to place an electrode there with the help of a clip, this site appeared the better one to reference the rest of electrodes. After referencing, a second-order pass band lter with cutoff frequencies 0.5 and 40 Hz is applied. Once the lters are applied, the whole signal is segmented in 4-s epochs. Artifacts are kept, in order to ensure that only 1 min of EEG data will be used for testing the system. We remind the reader that the subject is asked to close his/her eyes in order to minimize eye-related artifacts.

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Features Extracted from EEG

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We conducted an intensive preliminary analysis on the discrimination performance of a large initial set of features for example, Higuchi fractal dimension, entropy, skewness, kurtosis, mean, and standard deviation. We chose the ve ones that showed a higher discriminative power. These ve different features were extracted from each 4-s epoch and input into our classi er module. All the mentioned features are

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18 Multimodal Physiological Biometrics Authentication

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simultaneously computed in the biometry system presented herein. This is what we denote as the multifeature set. The features are detailed in the following. We can distinguish between two major types of features with respect to the number of EEG channels employed in their computation. Therefore we can group features in single-channel features and two-channels ones (the synchronicity features). 18.3.2.1 One Channel Features

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Autoregression (AR) and Fourier transform (FT) are the implemented single-channel features. They are calculated for each channel without taking into account the other channel. The usage of these features for EEG biometry is not novel [8,10 14,19 22]. However, we describe them for the sake of completeness.

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Autoregression. We use the standard methodology of making an autoregression on the EEG signal and the resulting coef cients as features. The employed autoregression is based on the Yule Walker method, which ts a pth-order AR model to the windowed input signal, X(t), by minimizing the forward prediction error in a least-square sense. The resulting Yule Walker equations are solved through the Levinson Durbin recursion. The AR model can be formulated as

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X(t) =

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a(i)X(t i) + e(t).

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(18.1)

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We take n = 100 based on the discrimination power obtained in some preliminary works. Fourier Transform. The well-known discrete Fourier transform (DFT) is expressed as

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X(k) =

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x(j) N

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N k=1

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(j 1)(k 1)

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(18.2)

x(j) = where

X(k) N

(j 1)(k 1)

(18.3)

N = e 18.3.2.2 Synchronicity Features

2 i N

(18.4)

Mutual information (MI), coherence (CO), and cross-correlation (CC) are examples of two-channel features related to synchronicity [23 25]. They represent some join characteristic of the two channels involved in the computation. This type of features is used for the rst time here.

18.3 Authentication Algorithm Based on EEG

Mutual Information. The mutual information [12,25] feature measures the dependency degree between two random variables given in bits, when logarithms of base 2 are used in its computation. The MI can be de ned as MIxy = E(x) + E(y) E(xy), (18.5)

where E is the entropy operator: E(x) is the entropy of signal x, and E(x, y) is the joint entropy of signals x and y. Coherence. The coherence measure quantizes the correlation between two time series at different frequencies [23,24]. The magnitude of the squared coherence estimate is a frequency function with values ranging from 0 to 1. The coherence Cxy (f ) is a function of the power spectral density (Pxx and Pyy ) of x and y and the cross-power spectral density (Pxy ) of x and y, as de ned in the following expression: Cxy (f ) = |Pxy (f )|2 . Pxx (f )Pyy (f ) (18.6)

In this case, the feature is represented by the set of points of the coherence function. Correlation Measures. The well-known correlation (CC) is a measure of the similarity of two signals, commonly used to nd occurrences of a known signal in an unknown one with applications in pattern recognition and cryptanalysis [27]. We calculate the autocorrelation of both channels, and the cross-correlation between them following: CCX,Y = cov(X, Y ) E((X X )(Y Y )) = , X Y X Y (18.7)

where E( ) is the expectation operator, cov( ) is the covariance one, and and are the corresponding mean and standard deviations values.