A comparison of methods for ERP assessment in a P300-based GKT

International Journal of Psychophysiology 62 (2006) 309–320www.elsevier.com/locate/ijpsychoA comparison of methods for ERP assessment in a P300-based GKTVahid Abootalebi a , Mohammad Hassan Moradi a, ⁎ , Mohammad Ali Khalilzadehb,ca Biomedical Engineering Faculty, Amirkabir University of Technology, Tehran, Iranb Islamic Azad University, Mashhad Branch, Iranc Research Center of Intelligent Signal Processing, Tehran, IranReceived 16 January 2006; received in revised form 25 May 2006; accepted 26 May 2006Available online 24 July 2006AbstractP300-based GKT (guilty knowledge test) has been suggested as an alternative approach for conventional polygraphy. The purpose of this studyis to evaluate three classifying methods for this approach and compare their performances in a lab analogue. Several subjects went through thedesigned GKT paradigm and their respective brain signals were recorded. For the analysis of signals, BAD (bootstrapped amplitude difference)and BCD (bootstrapped correlation difference) methods as two predefined methods alongside a new approach consisting of wavelet features and astatistical classifier were implemented. The rates of correct detection in guilty and innocent subjects were 74–80%. The results indicate thepotential of P300-based GKT for detecting concealed information, although further research is required to increase its accuracy and precision andevaluating its vulnerability to countermeasures.© 2006 Elsevier B.V. All rights reserved.Keywords: Psychophysiological detection of deception; Event-related potential (ERP); P300; Guilty knowledge test (GKT); Lie detection; Wavelet1. IntroductionIn recent years, various approaches to psychophysiologicaldetection of deception have been developed (National ResearchCouncil [NRC], 2002). The polygraphic tests are the mosttraditional methods for this approach. Most commonly usedphysiological measures in polygraph systems are respiration,cardiovascular measures and electrodermal response (EDR).These measures are derived principally from structures innervatedby the autonomic nervous system. Emotional effects ofdeception are presumed to be reflected in such autonomic measures.A polygraph system records these measures during a specifiedtest in which the examiner asks some questions of thesubject. By analyzing these physiological signs during relevantand irrelevant questions, the polygraph examiner can detect guiltor innocence. Hence the polygraph and other measure of autonomicactivity reflect the peripheral manifestations of very complexcognitive and affective operations that occur when peoplegive deceptive or nondeceptive answers to questions.⁎ Corresponding author. Fax: +98 21 66495655.E-mail address: mhmoradi@aut.ac.ir (M.H. Moradi).By their very nature, polygraph measurements provide anextremely limited and indirect view of complex underlying brainprocesses. A researchable hypothesis is that by looking at brainfunction more directly, it might be possible to understand andultimately detect deception. There are mainly two techniques forstudying on brain functions: (1) functional brain imaging and (2)recording of brain potentials. In the former, imaging methods suchas positron emission tomography (PET) or functional magneticresonance imaging (fMRI) are used to measure local brain activity.The latter technique measures event-related changes in theEEG that are known as event-related potentials (ERP). The mainadvantage of the imaging methods is their good spatial resolutionand their main disadvantage is their low time resolution. On theother hand, ERPs have better time resolution and lower spatialresolution. Besides that, functional imaging methods are moreexpensive and time consuming than ERP recording.Both of the techniques described above have been used asmeans for lie detection. There are few recent studies that use fMRIto identify association between deception and specific brainactivity (Ganis et al., 2003; Kozel et al., 2004a,b; Langleben et al.,2005; Lee et al., 2002; Nunez et al., 2005; Phan et al., 2005).These investigations seek to identify signatures of deception0167-8760/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.ijpsycho.2006.05.009

310 V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320in brain processes. In spite of some good results, which werereported from these studies, the number of subjects studied is notsufficient enough and they also have some limitation as a soundmethod for detection of deception (NRC, 2002). In contrast tofMRI approaches to lie detection, ERP-based methods havebeen more widely studied and have achieved more satisfyingresults (Rosenfeld, 2002; Farwell and Donchin, 1991; Allen etal., 1992).ERPs are recorded from the central nervous system and areconsidered to be affected by the recognition of important events,which is more cognitively determined activity than autonomicresponses. An endogenous ERP, which has been extensivelystudied, is the P300 (P3) wave. It is seen in response to rare,meaningful stimuli often called “oddball” stimuli (Polich, 2000).For example, if a subject is viewing a Bernoulli (random) series ofnames, one every three seconds, and occasionally, one of these isthe subject's name, a P3 wave is evoked in response to this rarelypresented, recognized, meaningful (autobiographical) stimulus.P3 is a positive-going wave with a scalp amplitude distribution inwhich it is largest parietally (at Pz) and smallest frontally (Fz),taking intermediate values centrally (Cz). (Fz, Cz, and Pz are scalpsites along the midline of the head.) Its peak has a typical latencyof 300–1000 ms from stimulus onset. The size or amplitude of P3at a given recording site is inversely proportional to the rareness ofpresentation; in practice, probabilities I while in innocents Pis another I and so no P−I difference is expected. Based on thistheory, the BAD method (bootstrapped amplitude difference)was introduced which will be described in the following section.The second approach, introduced by Farwell and Donchin(1991), is based on the expectation that in a guilty person, the Pand T stimuli should evoke similar P300 responses, whereas inan innocent subject, P responses will look more like I responses.Thus, in this method we called here bootstrapped correlationdifference (BCD), the cross correlation of P and T waveforms iscompared with that of P and I. In guilty subjects, the P–Tcorrelation is expected to exceed the P–I correlation and theopposite is expected in innocents.Despite introduction of P300-based lie detectors in 1985–1990 by some research groups, its efficacy is yet controversial.There are different results reported from independent laboratorieson the accuracy of this method. Farwell and Donchinreported a detection rate of 87.5% using BCD method (Farwelland Donchin, 1991). But in recent years, Farwell claims that hisupdated method – named BrainFingerPrinting – has reached toa detection rate of 100% (see www.brainwavescience.com),although these results have not been published in any peerreviewedpaper and are highly controversial (Rosenfeld, 2005).Rosenfeld lab has reported a typically 80–95% detection rateusing BAD and BCD methods and found the former to be moreaccurate (Rosenfeld et al., 2004). Allen and his coworkers hadreported 90% and above hit rate in detection concealed thoughtover-learned information (Allen et al., 1992). But in their recentpaper, they report poor detection (27–47%) of mock crimedetails (Mertens et al., 2003). Apart from these lab analogues,there has been only one independent field study of P300-basedlie detection, which has reported only 48% detection of guiltysubjects (Miyake et al., 1993).The purpose of the present study was to examine the P300-based GKT in a lab analogue and also to compare three differentclassifiers for this approach. Similar to all lie detection systems,this method included a paradigm for conducting the test andrecording brain signals and also a method for analyzing therecords to detect the guilty/innocent subjects. Our scenario in

V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320311the test was a mock crime (stealing a jewel), which was similarto paradigms used in other studies on GKT. In the analysis of thesignal, BAD and BCD methods – with some modifications –were implemented. In addition to these methods, a new approachbased on some wavelet features and a statistic classifierwas designed and applied on the data. The results of thesemethods will be reported and compared.2. Methods of ERP assessment2.1. Bootstrapped amplitude difference (BAD)In the BAD method, we want to determine whether theamplitude of the P300 evoked by P stimuli, are significantlygreater than that evoked by irrelevants within an individual ornot? Answering this statistical question requires knowing thedistributions of average P300 waves for each set or at leastenough samples of the averages. However for each subject, onehas available only one average P300 from each set of stimuli(Ts, Ps, and Is). The statistical technique of bootstrapping(Wasserman and Bockenholt, 1989) provides a solution to thisproblem. The bootstrap variation used here is as follows: acomputer program goes through the probe set (all singlesweeps) and selects at random, with replacement, a set of N 1single sweeps. It averages these waveforms and calculates P300amplitude from this average as described later. Similarly a set ofN 2 single sweeps is selected from the irrelevant set and theaverage P300 amplitude is calculated from them. The numbersN 1 and N 2 are the actual number of accepted probe sweeps andirrelevant sweeps for that subject, respectively. The calculatedirrelevant mean P300 is subtracted from the comparable probevalue, and one thus obtains a difference value between P andI (D 1 =P−I). Then a set of N 3 single sweeps is selected similarlyfrom the target set and an average P300 amplitude iscalculated for this >set. Next a difference value between P andT (D 2 =T−P) is calculated. In the present study, the main BADparameter used for decision about guilt/innocence of subject isD=D 1 −D 2 . 100 iterations of this algorithm will yield 100values for the D parameter. The number of D-values in whichD>0 is then counted (N D_0 ). The larger this number (N D_0 )is, the more different P is from I and the more similar is to T andthus the subject is more likely to be guilty. One can use athreshold (N th )onN D_0 and make a decision on the guilt of thesubject if N D_0 >N th . It must be noted that, the greater N th is, themore certain the guilty decisions will be; however, some reallyguilty subjects – with poor P300 in their P stimuli – may be undetectedand appear to be innocent.2.2. Bootstrapped correlation difference (BCD)BCD answers this question: “Are the cross correlation coefficientsbetween ERP responses to probe and target stimulisignificantly greater than the corresponding cross correlation ofresponses to probe and irrelevant stimuli?” if so, the subject isfound to be guilty. To answer this question, for each subject, theprogram first averages all single sweeps of P, T and I stimuli, anddetermines the within-subject ERP average over all stimuli. Thisoverall average is saved in a vector called M. Thenbythebootstrapping method, one value for the average of each stimulustype is obtained. M is subtracted from each P, T and I averagevalues. This enlarges the difference between the waveforms. Thecross correlation coefficients of the P and T (r(P,T)) and of the Pand I (r(P,I)) are now computed. The difference between thesetwo r-values (D=r(P,T)−r(P,I)) is computed next. The D is ascale for the existence or absence of P300 in the probe stimuli. Theabove process is iterated 100 times yielding 100 values for Dparameter. Using the method of Farwell and Donchin (1991),thenumber of D-values in which D>0 is counted (N D_0 ). If thisnumber is greater than a predefined threshold (N th ), a guiltydecision will be made. Similar to the BAD method, the greater N this, the more accurate the guilty decision will be, but the efficiencyof the method in detection of all guilties is lost.2.3. Wavelet classifier methodThe new approach considered in this study, is a patternrecognition method based on wavelet features and a statisticalclassifier. In such methods, first some suitable features areextracted from the raw data. These selected features will bethose, which contain suitable information about the inspectedphenomena.Typically, ERP analysis is performed in the time domain,whereby the amplitudes and latencies of prominent peaks in theaveraged potentials are measured and correlated to informationprocessing mechanisms. This Conventional approach has twomajor drawbacks: (i) ERPs are time-varying signals reflectingthe sum of underlying neural events during stimulus processingoperating on different time scales ranging from milliseconds toseconds. Various procedures have been employed to separatefunctionally meaningful events that partly or completely overlapin time, however, the reliable identification of these componentsin ERP waveform still remains as a problem. (ii) Analysisin the frequency domain has revealed that EEG/ERP frequencycomponents in different frequency ranges (delta, theta, alpha,beta, gamma) are functionally related to information processingand behavior (Basar et al., 2001a,b; Herrmann and Knight,2001; Basar and Schurmann, 2001). However, the Fouriertransform (FT) of ERP lacks the information about the timelocalization of transient neural events. Therefore, efficient algorithmsfor analyzing a signal in a time–frequency plane areextremely important in extraction and analysis of these functionalcomponents.The wavelet transform is one such algorithm, which can beused to represent the EEG/ERP signal in both time and frequency(Akay, 1997; Mallat, 1999; Unser and Aldroubi, 1996;Yordanova et al., 2002). The wavelet representations provideprecise measurements of when and to what degree transientevents occur in a neuroelectric waveform and of when and howthe frequency content of a neuroelectric waveform changesover time (Samar et al., 1999). This is achieved by usingfamilies of functions (wavelets) that are generated from a singlefunction (basic wavelet, which can be a smooth and quicklyvanishing oscillation) by operations of scaling (stretching orshrinking the basic wavelet) and translation (moving the basic

312 V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320wavelet to different time positions at any scale withoutchanging its shape).In this way, as shown in Fig. 1 and described in Samar et al.(1999), the WT performs a time-frequency decomposition of thesignal, i.e. at each resolution level (corresponding roughly to agiven frequency band) and each time interval, the waveletfunction is correlated with the shape of the neuroelectric waveformat that position. This correlation, known as a waveletcoefficient, measures how much of the wavelet at that resolutionlevel and position is included in the neuroelectric waveform. Thisprocess produces a sequence of wavelet coefficients at each level.The sequences from different levels of decomposition can bearranged in a hierarchical scheme called multi-resolution decomposition(Mallat, 1999). Signals corresponding to different levelscan be reconstructed by applying an inverse transform. The mainalgorithms and equations for the calculation of wavelet coefficientsare explained in Appendix A.In summary, the wavelet transform gives a time-frequencyrepresentation of a signal that has three main advantages overprevious methods: (a) retaining both time and frequency information,(b) optimal resolution even in the time and frequencydomains, (c) does not require the signal to be stationarity.In the present study, a multi-resolution decomposition(Mallat, 1999) was performed by applying a decimated discreteWT. In the discrete WT, the parameters of scaling and translationhave discrete values, which can also be taken at logarithmic(dyadic) scales. Quadratic B-Spline functions wereused here as mother wavelets due to their similarity with theevoked response. This function had been used in similar studies,and its efficiency for ERP decomposition and detection hasbeen reported (Quiroga, 2000; Ademoglu et al., 1997; Quirogaet al., 2001; Abootalebi et al., 2004). The filter coefficientsassociated with quadratic B-Splines are shown in Table 1. Thefirst column corresponds to the high-pass filter G used to obtainthe details and second column the ones of low-pass filter H usedto obtain the successive approximations. The third and fourthcolumns are the inverse filter coefficients used for reconstructingthe signal.Extracted wavelet coefficients can be used as features ofsingle trial ERPs. These features has more information thansimple features such as amplitude, latency and correlationwhich are used in BAD and BCD analysis and also moreinformation than frequency features which are derived fromspectral analysis.After the feature extraction step, a statistical classifier can beused for the separation of ERPs from Guilty subjects and thosefrom innocents. In the present study, linear discriminant analysiswas used for classification (Fukunaga, 1990). This proceduregenerates a discriminant function based on linearcombinations of the features that provide the best discriminationbetween two different groups (guilties and innocents). Thefunctions are generated based on some cases for which groupmembership is known (the train set); the functions can then beapplied to new cases with known features but unknown groupmembership (the test set). In this method a normal densitydistribution is fitted to each group, with group means andpooled covariance estimated from the training set. Hence, anyother subject who does not pertain to the training set can beFig. 1. Wavelet decomposition of a single trial ERP: (a) the wavelet coefficients in the A (0.3–4 Hz), B (4–8 Hz), C (8–16 Hz) and D (16–30 Hz) bands; (b) thereconstructed signal in these bands.

V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320313Table 1Filter coefficients corresponding to quadratic B-Spline waveletsk G(k) H (k) G′ (k) H′ (k)−10 0.0016 −0.0039−9 0.0191 −0.0342−8 −0.0050 0.0342−7 −0.0444 0.0793−6 0.0117 −0.0210−5 0.1033 −0.1840−4 −0.0259 0.0498 −0.0021−3 −0.2437 0.4239 0.0604−2 0.0340 −0.1403 −0.3063 0.25−1 0.6552 −0.9004 0.6312 0.750 0.6552 0.9004 −0.6312 0.751 0.0340 0.1403 0.3063 0.252 −0.2437 −0.4239 0.06043 −0.0259 −0.0498 0.00214 0.1033 0.18415 0.0117 0.02106 −0.0444 −0.07937 −0.0050 −0.00908 0.0191 0.03429 0.0016 0.0039G and H are the high-pass and low-pass filters, respectively. H′ and G′ are theinverse filters used for the reconstruction [23].evaluated based on the distribution with higher density at thecorresponding point in feature space.3. Methods3.1. SubjectsSixty-two subjects (59 male, 3 female) participated in thestudy. They were generally undergraduate or postgraduate studentsand all had normal or corrected vision.3.2. Data acquisitionThe electroencephalogram (EEG) was recorded using Ag/AgClelectrodes placed at the Fz (Frontal), Cz (Central) and Pz (Parietal)sites (10–20 international system). All sites were referenced tolinked mastoids. Only the results from Pz will be reported here.Electrooculogram (EOG) was recorded from sub- and supraorbitalelectrodes (above and below the right eye). The subjects weregrounded at the forehead. Brain electrical activities were amplifiedand digitized at a rate of 256 samples per second. Digitized datawere subsequently analyzed offline using MATLAB software.Prior to data analysis, all data were digitally filtered in the 0.3–30 Hz range. This is the frequency range which is used typically inP300-based GKT studies (Rosenfeld et al., 2004).3.3. ProcedureAll subjects were trained and then performed a mock crimescenario. After a training phase about the protocol, a box –containing a jewel – was given to the subject. The examiner leftthe room and permitted the subject to perform his role in thescenario. In this step the subject could choose and implement oneof two possible roles (Guilty/Innocent). The guilty subject openedthe box, saw the jewel precisely and imagined that he/she hasstolen the jewel. The subject was asked to memorize the jeweldetails, so he/she can act as the actual robber. For reassurance, thesubject was asked to write the detail of the object on a piece ofpaper and deliver it after the test. The innocent subject has neveropened the box and thus has no information about the object. Thisprotocol is a single-probe protocol similar to the protocols whichwere usually used by Rosenfeld et al. (2004).Then the examiner returned to the room and executed theP300-based GKT for the knowledge of the scenario. After theattachment of electrodes and starting the recording, stimuliconsisting of single pictures of five pieces of jewelry, werepresented randomly and successively on a monitor to thesubject. Each item remained 1.1 s on the screen, of which 1 swere used for processing. The inter-stimulus interval was 2 s.During the test, pictures of five items (for example: ring,wristwatch, necklace, earring and hairpin) were randomlypresented one at a time (each with 30 iterations). These objectscontained one target, one probe and three irrelevants. The probewas the object in the box. The target was another object, whichhad been previously presented to the subject in the trainingphase at the start of the protocol.One push button was given to each hand of the subject, rightclick as “YES” and left click as “NO”. The subjects were askedto reply to the items by pressing one of the two buttons; “YES”for familiar items and “NO” for unknowns. This task hadalready been practiced during training phase. The subjects alsowere instructed to try to hide their information about the probeitem in the guilty condition and to behave mentally as innocent.Any covert action was permitted, providing that it did notdisarrange the totality of the test and was not observable to theexaminer either by visual inspection of the subject or from therecorded signal. Hence, actions such as voluntary blinking orbody movement detected by the examiner were not permitted.Indeed, all subjects were supposed to press “YES” for targetsand “NO” for probes and irrelevants. Thus, guilties andinnocents, both replied honestly to targets and irrelevants; butfor probes, the guilty subjects replied falsely while the innocentsanswered honestly. Subjects with more than 10% error incorrect clicking for all stimuli were removed from analysis.Each subject participated in two experiments in which theboxes and all displayed jewels were different. The jewel in the boxwas a gold coin in the first experiment and a hairpin in the secondexperiment. Subjects were instructed to select a guilty role in oneexperiment and an innocent role in the other, by their choice.Signals from these two experiments were analyzed independently.Therefore with 62 subjects, a total number of 124 tests wereperformed. 32 subjects chose the innocent role and 30 subjectschose the guilty role in their first experiment. A few test resultswere removed due to misdoing of protocol or inappropriatelyrecorded signals. Finally, 59 guilty cases and 51 innocent caseswere chosen to be used in the following investigations.3.4. Data analysisAfter the filtering of signals, each continuous record wasseparated to single sweeps according to the known times of

314 V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320stimulus presentation. EOG data were checked for blink artifactby visual inspection and sweeps with blink artifacts wereremoved. Then BAD, BCD and wavelet analyses were appliedon the signals and the detection rates of them were assessed.3.4.1. BAD analysisIn BAD, P300 amplitude was measured by the Peak–Peak(P–P) method. The algorithm searches within a window from400 to 900 ms after-stimulus for the maximally positivesegment average of 100 ms. The midpoint of the maximumpositivity defines P300 latency. Then the algorithm searchesfrom P300 latency to the end of sweep for the maximum 100 msnegativity. The difference between the maximum positivity andnegativity defines the P–P measure. In some researches theBaseline–Peak (B–P) amplitude of P300 has been used, but it isrepeatedly shown that using the BAD method, P–P is betterindex than B–P for diagnosis of guilt vs. innocence in detectionof deception (Soskins et al., 2001).3.4.2. BCD analysisIn BCD, before computing the cross correlation coefficients,a time window was applied on single sweeps between 300 and900 ms after-stimulus, and the correlation of sweeps were onlynoticed in this time limits, because we expected that the P300appeared only in this region. In this study, only the correlationcoefficient at lag=0 was considered.3.4.3. Wavelet analysis3.4.3.1. Signal decomposition. The data were decomposedinto five-octaves using the wavelet transform. Six sets ofcoefficients (including residual scale) within the followingfrequency bands were obtained; 0–4 Hz,4–8 Hz,8–16 Hz,16–32 Hz, 32–64 Hz and 64–128 Hz. The coefficients in each setare concerned with sequential time bands between 0 and 1000 ms.Because of previous filtering of the signal, coefficients within 30–128 Hz and 0–0.3 Hz ranges had not any useful information. Butother coefficients represent the signal information in fourfrequency bands: A, 0.3–4 Hz;B,4–8 Hz; C, 8–16 Hz; and D,16–30 Hz. Fig. 1 shows the decomposition and reconstruction ofa single trial ERP into five octaves, using the quadratic B-Splinewavelet. As shown in Fig. 1(a), each octave contained the numberof coefficients necessary to provide the relevant time resolutionfor that frequency range. The interpolation of coefficients byquadratic spline functions was used to reconstruct the analyzedsignal within the particular band in Fig 1(b). In the present study,8 coefficients of band A, 8 coefficients of band B and 16coefficients of band C were obtained for the post-stimulus epoch.The wavelet coefficients are designated with a lettercorresponding to each frequency band (A for 0.3–4 Hz,Bfor4–8Hz,andCfor8–16 Hz) together with the coefficient numberand two other numbers in brackets representing the approximatetime window in millisecond (for example, A5 (450–580)).3.4.3.2. Statistical analysis. For statistical analysis, theselected wavelet coefficients (8 A-band, 8 B-band and 16 C-band coefficients) for all sweeps of all subjects were saved in afile and fed into the SPSS program. There were totally 2508Target, 7651 Irrelevant, and 2552 Probe (1371 guilty+1181innocent) single sweeps. To determine the most relevant timefrequency components differing between probes from guiltysubjects (G-probes) and probes from innocents (I-probes), thewavelet coefficients of probe sweeps were subjected to independent-samplet-test, with the subject type (Guilty/Innocent) asgrouping variable.3.4.3.3. Classification. Coefficients of probe stimuli weresubjected to discriminant analysis. This method was used tofind a linear combination of coefficients provides the bestdiscrimination between G-probes and I-probes. Performance ofthis algorithm was estimated using a leave-one-out jackknifingmethod. For each subject, the probe sweeps of other subjectswith their real labels (G-probe/I-probe) were used as trainingdata, and then the trained classifier applied on the probe sweepsof the given subject. Then the number of sweeps labeled as G-probe were counted and saved as N G . N G is an index of guiltfor each subject. Similar to BAD and BCD, if the N G wasgreater than a predefined threshold (N th ), a guilty decision wasmade.4. Results4.1. Time domain analysisIn all descriptions of P300 to follow, only the results at sitePz was noted, since Pz is the site where P300 is usually reportedto be maximal and since the analytic procedures (below) wereperformed on Pz data only.Fig. 2 below shows grand averages in guilty group for superimposedprobe, target and irrelevant responses. Also, Fig. 3shows superimposed ERPs to P, T, and I items in the innocentgroup. The responses were as predicted. As can be seen in thefigures, a large P300 was elicited by the target stimuli but not bythe irrelevant stimuli. The probes elicited a P300 when theywere relevant to subject's “crime”, i.e. in guilty condition. Avery small P300, if any, was elicited by probes when the subjectwas “innocent”.Fig. 2. Superimposed grand averaged P, T and I responses in guilty group.

V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320315Fig. 3. Superimposed grand averaged P, T and I responses in innocent group.4.2. BAD methodFig. 4(a) displays the N D_0 parameter as the output of BADmethod for all observed subjects. Solid circles belong to guiltysubjects and empty circles to innocents. It was expected thatsolid circles would have large positive measures and in contrastempty circles would have small measures. If this happened, asuitable threshold could easily discriminate the groups. But inreal state, the groups have overlaps and each selected thresholdresults in some misclassification. For better inspection of theoverlaps, histograms of these measures in two groups are drawnin Fig. 4(b). Statistical analysis reveals that N D_0 is significantlygreater in the guilty group (t=7.3, p

316 V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320Fig. 5. BCD method: (a) N D_0 parameter for all subjects; (b) superimposed histograms of N D_0 measures in guilty and innocent groups; (c) superimposed cumulativehistograms of N D_0 measures in guilty and innocent groups.threshold that can give the best detection in all subjects is near46%, which results in 80% correct detection of two groups.4.4. Wavelet analysisAverages of 32 defined features corresponding to probe stimuliin all guilty and all innocent subjects are drawn in Fig. 6. Thisdiagram reveals the difference of each features' average in twogroups, But to determine the significance level of this difference,the t-test was applied on data. Table 2 displays the t-values andsignificance levels (p-values) measured for difference betweenguilties' and innocents' corresponding coefficients. According tothese parameters, 13 of 32 defined features have significant differencebetween two groups (p-value

V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320317Table 2Results of comparing probe response between guilty and innocent group usingstatistical t-test on wavelet featuresFeature no. Feature name t-value p-value1 A1 (0–125)⁎ 4.21 0.0002 A2 (125–250)⁎ 5.72 0.0003 A3 (250–375) −0.01 0.9934 A4 (375–500)⁎ −11.63 0.0005 A5 (500–625)⁎ −15.21 0.0006 A6 (625–750)⁎ −5.16 0.0007 A7 (750–875)⁎ 2.08 0.0378 A8 (875–1000)⁎ 2.56 0.0109 B1 (0–125) 0.59 0.55510 B2 (125–250) 1.02 0.31011 B3 (250–375) −1.42 0.15512 B4 (375–500)⁎ 3.32 0.00113 B5 (500–625) −0.12 0.90514 B6 (625–750) 0.27 0.78515 B7 (750–875) 1.07 0.28716 B8 (875–1000)⁎ 2.08 0.03817 C1 (0–62)⁎ 2.11 0.03418 C2 (63–125)⁎ −3.43 0.00119 C3 (125–187) 0.59 0.55520 C4 (188–250) 0.75 0.45621 C5 (250–312) 1.47 0.14122 C6 (313–375)⁎ −2.12 0.03423 C7 (375–437) 0.72 0.47224 C8 (438–500) 0.93 0.35025 C9 (500–562) −1.10 0.27326 C10 (563–625) −1.12 0.26127 C11 (625–687) 1.63 0.10228 C12 (688–750) −1.91 0.05629 C13 (750–812) −1.32 0.18630 C14 (813–875) 1.26 0.20831 C15 (875–937) 0.47 0.63932 C16 (938–1000)⁎ 3.80 0.000* p-value

318 V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320Fig. 7. Wavelet classifier: (a) N G parameter for all subjects; (b) superimposed histograms of N G measures in guilty and innocent groups; (c) superimposed cumulativehistograms of N G measures in guilty and innocent groups.obtain better performances using maximum correlation in all lags,instead of a correlation only at lag=0. This modification wasapplied to the BCD method and the results were computed again.The total accuracy of detection over all subjects was 80% and nosignificant change could be seen in the performance after thismodification. It is possible that this modification, in addition toour expected improvement, has improved probe–irrelevantcorrelation more than probe–target correlation and thus leadingto some false negatives.The detection accuracies of applied methods are lower thanwhat some other groups have reported. However, it must be notedthat the implemented methods were applied on different datasets.The obtained final accuracy depends on the subject type, usedprotocol, and the processing algorithm. So, the processing methodscan be compared fairly only when the subjects and protocols aresimilar. The main difference between this study and some previousstudies is the number of irrelevant questions used. There are threeirrelevant questions in this study, whereas previous studies usedtypically four irrelevant questions (Rosenfeld et al., 2004; Farwelland Donchin, 1991). Smaller number of irrelevant questionsincreases the probe probability and thus decreases the amplitude ofP300 peak in probe question and thus the detection rate.It should also be noted that like conventional polygraphy,P300-based GKT is potentially vulnerable to countermeasures.(Countermeasures are covert actions taken by the subjects so asFig. 8. Error-plots of the implemented methods.Table 3Results of two statistical comparisons between the implemented methodsCompared methodsPaired t-test (on thearea under error-plotcurve)McNemar's test (onthe detection rate)t-value p-value Z p-valueBAD – BCD 2.896 0.009 −1.04 0.15BAD – Wavelet analysis −0.134 0.448 −0.83 0.203BCD – Wavelet analysis \2.646 0.013 0.20 0.427

V. Abootalebi et al. / International Journal of Psychophysiology 62 (2006) 309–320319Fig. 9. Recursive implementation of the multiresolution decomposition and reconstruction. H and G are the low and high-pass filters, respectively, and H′ and G′ theinverse filters used for the reconstruction. Downward arrows mean decimation by 2 and upward arrows upsampling.prevent detection by the GKT (Honts and Amato, 2002).) Thisstudy did not focus on any specific countermeasure and thesubjects were permitted to use any covert action, providing that itdid not disarrange the totality of the test and was not observable tothe examiner. This matter is extensively investigated by someresearchers (Rosenfeld et al., 2004; Sasaki et al., 2001). The resultof such researches can help in the design of more reliableparadigms for P300-based lie detection.AcknowledgementThis research was supported by the research center ofintelligent signal processing (RCISP). The authors would like tothank them and also all those who took part in this study.Appendix A. Wavelet transformWavelet transform is defined as the convolution between thesignal x(t) and the wavelet function ψ a,b (t) W w X ða;bÞ ¼ xðtÞjw a;b ðtÞð1Þwhere ψ a,b (t) are dilated (contracted) and shifted versions of aunique wavelet function ψ(t)w a;b ðÞ¼jaj t−1=2 w t−b ð2Þa(a, b are the scale and translation parameters, respectively). Thewavelet transform gives a decomposition of x(t) in differentscales tending to be maximum at those scales and time locationswhere the wavelet best resembles x(t). Moreover, Eq. (1) can beinverted, thus giving the reconstruction of x(t).The wavelet transform maps a signal of one independentvariable t onto a function of two independent variables a, b. Thisprocedure is redundant and not efficient for algorithm implementations.In consequence, it is more practical to define the wavelettransform only at discrete scales a and discrete times b by choosingthe set of parameters {a j =2 −j ; b jk =2 −j k}, with integers j, k.Contracted versions of the wavelet function will match thehigh frequency components of the original signal and on the otherhand, the dilated versions will match low frequency oscillations.Then, by correlating the original signal with wavelet functions ofdifferent sizes we can obtain the details of the signal at differentscales. These correlations with the different wavelet functions canbe arranged in a hierarchical scheme called multiresolutiondecomposition (Mallat, 1999). The multiresolution decompositionseparates the signal into ‘details’ at different scales, theremaining part being a coarser representation of the signal called‘approximation’. Moreover, it was shown (Mallat, 1999)thateachdetail (D j ) and approximation signal (A j ) could be obtained fromthe previous approximation A j−1 via a convolution with high-passand low-pass filters, respectively (see Fig. 9).ReferencesAbootalebi, V., Moradi, M.H., Khalilzadeh, M.A., 2004. Detection of the cognitivecomponents of brain potentials using wavelet coefficients. Iranian Journal ofBiomedical Engineering 1 (1), 25–46 (Article in Persian).Ademoglu, A., Micheli-Tzanakou, E., Istefanopulos, Y., 1997. Analysis of patternreversal visual evoked potentials by spline wavelets. IEEE Transactions onBiomedical Engineering 44, 881–890.Akay, M. (Ed.), 1997. Time Frequency and Wavelets in Biomedical SignalProcessing. Wiley-IEEE Press. ISBN: 0-7803-1147-7.Allen, J., Iacono, W.G., Danielson, K.D., 1992. The identification of concealedmemories using the event-related potential and implicit behavioral measures:a methodology for prediction in the face of individual differences.Psychophysiology 29, 504–522.Basar, E., Schurmann, M., 2001. Toward new theories of brain function and braindynamics. International Journal of Psychophysiology 39, 87–89.Basar, E., Basar-Eroglu, C., Karakas, S., Schurmann, M., 2001a. Gamma, alpha,delta, and theta oscillations govern cognitive processes. International Journalof Psychophysiology 39, 241–248.Basar, E., Schurmann, M., Demiralp, T., Basar-Eroglu, C., Ademoglue, A.,2001b. Event-related oscillations are ‘real brain responses’: wavelet analysisand new strategies. International Journal of Psychophysiology 39, 91–127.Ben-Shakhar, G., Elaad, E., 2002. The guilty knowledge test (GKT) as anapplication of psychophysiology: future prospects and obstacles. In: Kleiner,M. (Ed.), Handbook of Polygraph Testing. Academic Press, N.Y., pp. 87–102.Farwell, L.A., Donchin, E., 1991. The truth will out: interrogative polygraphy(lie detection) with event-related potentials. Psychophysiology 28, 531–547.Fukunaga, J., 1990. Statistical Pattern Recognition, 2nd ed. Academic Press,New York.Ganis, G., Kosslyn, S.M., Stose, S., Thompson, W.L., Yurgelun-Todd, D.A., 2003.Neural correlates of different types of deception: an fMRI investigation.Cerebral Cortex 13, 830–836.

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