alzheimer s disease ( ad ) is the most common neurodegenerative disorder in the western world and the number of patients is expected to double approximately every 20 years because of the aging population . ad is characterized by the accumulation of amyloid plaques and neurofibrillary tangles in the patient s brain and loss of cortical neurons and synapses . these pathological changes cause memory loss and other cognitive and behavioral impairments that progressively affect the patient s ability to live independently . the guidelines for clinical diagnosis of ad   are based on the exclusion of other causes for the symptoms . however , a definite diagnosis of ad can only be made by necropsy   and ad pathology is hypothesized to start years before the first symptoms appear . the patient s quality of life already affected by the time clinical diagnosis is made . thus , there is a need for objective , non - invasive and affordable means to support clinicians in the detection and monitoring of ad . the analysis of eeg time series has been explored previously for its diagnostic potential in ad , based on the notion that the eeg signals represent fluctuations of aggregate brain activity in the respective brain regions and , therefore , may be able to reveal differences in brain function under different clinical conditions , . many previous studies have explored this question through the computation of diverse signal features from eeg recordings , . spectral features , including both spectral indices such as median frequency and relative power values , have revealed a spectral slowdown of the brain activity in ad . the results indicate that ad affects the nonlinear characteristics of the eeg signals , making them more regular and predictable , . therefore , there is increasing interest in the inspection of the connectivity of eeg recordings , , , , . this is often evaluated by measuring the ( linear or nonlinear ) dependencies between two signals in different spectral bands , , . this is particularly important in ad as the disease may cause opposing changes in different frequency ranges , , . traditional approaches to measure the connectivity between eeg signals are limited by a number of factors . to start with , spurious results could appear due to the volume conduction effects , , , because nearby channels are likely to record activity from identical sources . ideally , the connectivity evaluation should also inform about the causality of the interactions between signals . while some techniques have been recently developed to address these issues ( e.g. , phase lag index in ) , their use is limited perhaps due to a less straightforward interpretation than other techniques . as an alternative , the present study focuses on the modeling and analysis of the possible causal relationship between occipital recordings ( viewed as the  input  signal ) and frontal recordings ( viewed as the  output  signal ) in order to generate model - based indices to characterize the eegs of ad patients . to this purpose , we apply the volterra modeling approach using laguerre expansions of the kernels and employ the concept of principal dynamic modes ( pdm ) , which our group has pioneered . this reduces significantly the required number of free parameters in the model and enables estimation of reliable linear or nonlinear dynamic models under conditions of low snr . this modeling methodology has been recently applied to many different physiological domains , including the cerebral hemodynamics in ad patients . the proposed diagnostic indices in this study are generated through the use of the associated nonlinear functions ( anfs ) that correspond to each pdm of each subject . our aim is to examine whether the estimated pdms exhibit spectral characteristics in line with the neural rhythms naturally occurring in the brain ( delta , theta , alpha , beta , and gamma ) and whether the anfs obtained for each subject can be used as descriptors of disease . features  for the classification and differentiation of overall cognitive function in ad patients versus controls . this study involves 24 control subjects ( 42% male ; average age : 69.411.5years , meanstandard deviation , sd ) and 17 ad patients ( 53% male ; average age : 77.610.0 years ) who voluntarily participated and signed the informed consent form according to institutional guidelines . the eeg recordings were obtained for patients at rest and with their eyes closed using the traditional 1020 system in a common reference montage using a sampling rate of 256 hz . the data were obtained under a strict protocol from derriford hospital , plymouth , uk , and had been collected using normal hospital practices . the patients were referred to the hospital eeg department from a specialist memory clinic where all patients undergo a battery of psychometric tests before referral . each patient was given a diagnosis at the memory clinic on the basis of the clinical and psychometric findings and discussions held by a multidisciplinary team . all age - matched controls were healthy volunteers and had normal eegs ( confirmed by a consultant clinical neurophysiologist ) . for each subject , continuous epochs of 60 seconds were simultaneously extracted from the left frontal ( f3 ) , right frontal ( f4 ) , left occipital ( o1 ) and right occipital ( o2 ) channels . the selection of these electrodes is supported by the fact that ad is hypothesized to affect long - range connectivity as a result of the loss of long cortico - cortical association fibers , which may play an important role in functional interactions . moreover , selecting nearby channels would probably result in all of them picking up identical sources , which may lead to spurious connectivity levels reflecting simple volume conduction rather than true functional connectivity . they were then band - pass filtered in the range of 1 to 40 hz with a band - pass hamming window fir filter with order 200 . the data were then demeaned and scaled by a factor of 1/100 for computational / numerical convenience . 1 shows illustrative pre - processed time - series data over 3 sec and the respective spectrogram for the o1 eeg signal of an ad patient . figure 1.top panel : illustrative time - series data over 3 sec from the o1 eeg signal of ad patient # 1 . bottom panel : the spectrogram over 60 sec of the time - series data up to 40hz for this patient . top panel : illustrative time - series data over 3 sec from the o1 eeg signal of ad patient # 1 . bottom panel : the spectrogram over 60 sec of the time - series data up to 40hz for this patient . the proposed modeling approach utilizes the concept of principal dynamic modes ( pdm ) that has been pioneered by our group and applied successfully over the last 10 years to various physiological systems . in this approach , we seek to determine from input - output data a set of basis functions ( the pdms ) that represent an efficient  coordinate system  for the representation of the volterra kernels of a given class of systems . static nonlinear functions associated with each pdm ( termed anf : associated nonlinear functions ) describe the ( possible ) nonlinearities of the system . the pdm modeling approach relies on an efficient methodology for the estimation of volterra kernels using laguerre expansions . to reduce the complexity of the obtained pdm - based models and facilitate comparisons between different cohorts , we seek to determine the  global  pdms of a given system from the estimated kernels of a cohort this is accomplished through singular value decomposition ( svd ) of a rectangular matrix containing all estimated volterra kernels in the cohort . we note that the computation of the global pdms must be based on all subjects because they represent a common frame of reference for all subjects who are subsequently classified according to their respective anfs . the global pdms correspond to the selected  significant  singular vectors by applying a selection criterion on the respective singular values . in this study , we analyze the causal relationship between two eeg signals , in which the frontal signal is taken as the  output  and the occipital signal is taken as the  input  . using the laguerre expansion technique , we start with linear modeling ( 1st order volterra kernel only ) and proceed with nonlinear modeling estimating the 2nd - order volterra kernels as well . these kernel estimates are used to compute the global pdms of these cohorts via svd of a rectangular matrix that contains either all the 1st order kernels ( method 1 ) or the 1st and 2nd order kernels ( method 2 ) for all subjects ( patients and controls ) . the key to the model estimation problem is the use of the laguerre expansion technique that keeps the number of free parameters manageable for all models . we summarize below the methodology of pdm - based modeling . the 1st order ( linear ) volterra model is:\documentclass[12pt]{minimal } 
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 } { } \begin{equation * } y(n)=k_{o}+\sum \nolimits _ { m = o}^{m-1}k_{1}(m)x(n - m ) \end{equation*}\end{document } where 
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 } { } $ \{{b}_{\,j}\}~(\,j=1,2\ldots l)$ 
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 } { } $ \mathrm { l=7 , \alpha = 0.6)}$ 
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 } { } \begin{equation * } v_{j}(n)=\sum \nolimits ^{m=1}_{m=0}b_{j}(m)x(n - m ) \end{equation*}\end{document } the 8 expansion coefficients ( \documentclass[12pt]{minimal } 
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 } { } $ c_{0 } , c_{1})$ 
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 } { } \begin{equation * } k_{1}(m)=\sum \nolimits ^{l}_{j_{1}=1}c_{1}(j_{1})b_{{j}_{1}}(m ) \end{equation*}\end{document } this model has 8 free parameters , as compared to 71 free parameters for the original linear volterra model . the second - order volterra model is given by:\documentclass[12pt]{minimal } 
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 } { } \begin{align } y(n)=&k_{0}+\sum \nolimits _ { m=0}^{m-1}k_{1}(m)x(n - m)\notag \\&+\sum \nolimits _ { m_{1}=0}^{m-1}\sum \nolimits _ { m_{2}=0}^{m_{1}}k_{2}(m_{1},m_{2})x({n - m_{1}})x({n - m_{2}})\notag \\ { } \end{align } 
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 } { } $ k_{2}$ 
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 } { } \begin{align } y(n)=&c_{0}+\sum \nolimits _ { j=1}^{l}c_{1}(j)v_{j}(n)\notag \\&+\sum \nolimits _ { j_{1}=1}^{l}\sum \nolimits _ { j_{2}=1}^{j_{1}}c_{2}(j_{1},j_{2})v_{j_{1}}(n)v_{j_{2}}(n ) \end{align } 
 \end{document } the number of free parameters in this model is 36 , as compared to 2556 free parameter for the original 2nd order volterra model . the 2nd order volterra kernel is expressed in terms of the expansion coefficients as:\documentclass[12pt]{minimal } 
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 } { } \begin{equation * } k_{2}({m_{1}},{m_{2}})=\sum \nolimits _ { j_{1}=1}^{l}\sum \nolimits _ { j_{2}}^{j_{1}}c_{2}(j_{1},j_{2})b_{j_{1}}(m_{1})b_{j_{2}}(m_{2 } ) \end{equation*}\end{document } the pdm - based modeling approach seeks to find the minimum set  of basis functions ( the  global  pdms ) that are able to represent the input - output dynamics adequately for each particular system . this is achieved via svd of a rectangular matrix composed of the estimated volterra kernels of the respective cohort using either of two methods : method 1 : the kernel - based matrix is composed of the 1st order kernel estimates for all subjects ; method 2 : the kernel - based matrix is composed of the 1st and 2nd order kernel estimates for all subjects . in both methods , the global pdms are determined as the significant singular vectors of the kernel - based matrix that correspond to singular values satisfying a specified selection criterion ( e.g. at least 10% of the maximum singular value ) . in this study , 5 to 6 global pdms were selected . the global pdms are used to describe the dynamics of this system ( via expansions of the system kernels ) for all subjects . the possible nonlinearities of the system are described by the respective anfs , which are subject - specific and can be used for diagnostic purposes . the case of linear models is included in this representation , when the anfs are linear functions . the output equation for the pdm - based model is:\documentclass[12pt]{minimal } 
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 } { } \begin{equation * } f_{i}=a_{1,\,j}u_{j}+a_{2.,\,j}u_{j}^{2}+a_{3,\,j}u_{j}^{3}+\cdots \end{equation*}\end{document } the polynomial anf can be replaced by its best linear fit ( in a least - squares sense ) if reduction of model complexity is desirable . in that case , the linear coefficient is an  effective gain constant  for the respective pdm and can be used as an index for delineating ad patients from control subjects . \documentclass[12pt]{minimal } 
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 } { } $ z_{j}=a_{1,j}u_{j}+a_{2,j}u_{j}^{2}+a_{3,j}u_{j}^{3}+a_{j,4}u_{j}^{4}+a_{j,5}u_{j}^{5}$ 
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 } { } $ c(\,f)$ 
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 , . the assessment of spectral characteristics of the eeg activity is based on the power spectral density ( psd ) of each eeg epoch , which is computed as the fourier transform of its autocorrelation function . the psds obtained from segments of 10s of each channel and subject are averaged to compute the mean psd corresponding to that channel and subject . then , the psd is normalized by the total power in the considered broadband ( 1hz to 40hz ) to obtain a normalized psd ( \documentclass[12pt]{minimal } 
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 } { } $ psd_{n})$ 
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 } { } \begin{equation * } psd_{n}(\,f)=\frac { psd ( \,f)}{\sum \limits _ { f=1\mathrm { hz}}^{40\mathrm { hz}}{psd ( \,f ) } } \end{equation*}\end{document } so that:\documentclass[12pt]{minimal } 
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 } { } $ f_{low}$ 
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 } { } $ f_{high}$ 
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 } { } \begin{equation * } c(\,f)=\frac { |\langle x(\,f)y^{\ast } ( \,f)\rangle |^{2}}{|\langle x(\,f)\rangle ||\langle y(\,f)\rangle | } \end{equation*}\end{document } where \documentclass[12pt]{minimal } 
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 } { } $ \langle \ , \rangle $ 
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 } { } $ b$ 
 \end{document } blocks , respectively , . the concept of phase synchrony may also be used to measure dependencies between eeg signals by examining the interdependence between the corresponding phases , which may be strongly synchronized even if the amplitudes of the signals are statistically independent . a causal relationship between two signals at a certain time we will use the psi to estimate such direction of information flow robustly even in the presence of independent background activity . the predictive capability of the obtained pdm - based model is assessed by the normalized mean square error ( nmse ) of the respective model prediction . the minimum nmse among the four combinations of occipital - to - frontal input - output systems was obtained for the nonlinear model of the o1-to - f3 system ( nmse=89.7% ) , only slightly better than its linear counterpart ( nmse=91.2% ) . it is evident that the model prediction only accounts for a small portion of the output signal , but this should be expected in a system of such low signal - to - noise ratio . 5 pdms for the o1-to - f3 model were obtained using method 2 . for the sake of clarity , only 4 pdms are shown in fig . 3 and fig . 4 for the frequency - domain and time - domain respectively . 3 ) , the global pdms exhibit spectral characteristics that correspond to the following neural rhythm bands : 
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 } { } $ \sim 20 $ 
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 } { } $ \sim 12 $ 
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 } { } $ \sim 1 $ 
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 } { } $ \sim 8 $ 
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 } { } $ \sim 4 $ 
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 } { } $ \sim 12 $ 
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 } { } $ \sim 4 $ 
 \end{document } hz ) . frequency - domain representations of the global pdms of the input - output model for the o1-to - f3 system ( four out of five pdms are plotted for the sake of clarity , see text ) . time - domain representations of the global pdms of the input - output model for the o1-to - f3 system ( four out of five pdms are plotted for the sake of clarity , see text ) . the average associated nonlinear functions ( anfs ) for the nonlinear models of the o1-to - f3 system ( defined as 5th degree polynomials in this application ) are shown in fig . 5 with dark line for the 17 ad patients ( bottom row ) and the 24 control subjects ( top row ) , along with the best ( in mean - square sense ) linear fits shown in gray . 5 that the slope of the 4th anf changes sign for the patients ( i.e. becomes positive for the ad patients from negative for the controls ) , and the negative slopes of the 3rd and 5th anfs decrease ( in absolute value ) for the patients . this suggests that these three pdms are more likely to provide the means for differentiation between patients and controls . however , the difference between the average values of anf slopes may not portray correctly the separation between the two groups which relies on the distribution of the individual values . figure 5.average anfs ( dark line ) for the 5 pdms of the 17 ad patients ( bottom row ) and 24 control subjects ( top row ) , along with the best linear fits ( gray line ) for the o1-to - f3 system . average anfs ( dark line ) for the 5 pdms of the 17 ad patients ( bottom row ) and 24 control subjects ( top row ) , along with the best linear fits ( gray line ) for the o1-to - f3 system . after examining the differentiating capability of all pair combinations of pdms / anfs 8 , and their respective linear trends ) are the most differentiating between patients and controls for o2-f3 system , as shown in the scatter - plot of fig . 6 . they result in one false - positive ( # 40 ) and two false - negatives ( # 3 and # 17 ) . the sensitivity of 88.2% and specificity of 95.8% are marked on the corresponding roc curve shown in fig . figure 6.scatter-plot of computed anf linear trends ( slopes ) for 2nd and 4th pdms of the o2-to - f3 system , corresponding to the alpha - delta and theta - delta bands . the classification line has been obtained by nonlinear regression algorithm ( with 150 000 iterations ) . . 6 ( 2nd versus 4th anf / pdms ) of the o2-to - f3 system . figure 8.frequency-domain representations of global pdms of the input - output model for the o2-to - f3 system ( four out of six pdms are plotted for the sake of clarity , see text ) . scatter - plot of computed anf linear trends ( slopes ) for 2nd and 4th pdms of the o2-to - f3 system , corresponding to the alpha - delta and theta - delta bands . the classification line has been obtained by nonlinear regression algorithm ( with 150 000 iterations ) . roc curve for the scatter - plot of fig . 6 ( 2nd versus 4th anf / pdms ) of the o2-to - f3 system . frequency - domain representations of global pdms of the input - output model for the o2-to - f3 system ( four out of six pdms are plotted for the sake of clarity , see text ) . we note that satisfactory delineation between the two groups is also achieved in the o1-f3 system ( see scatter - plot in fig . 9 ) using the pair of 2nd and 4th pdms / anfs that correspond to the alpha - delta and theta - delta bands respectively , as shown in fig . sensitivity of 88.2% ) and two false - positives ( # 29 , # 40 . specificity of 91.7% ) result in this case . this suggests that the use of more than two pdms / anfs ought to be explored for differentiation of patients from controls . figure 9.scatter-plot of computed anf linear trends ( slopes ) for 2nd and 4th pdms of the o1-to - f3 system , corresponding to the alpha - delta and theta - delta bands . scatter - plot of computed anf linear trends ( slopes ) for 2nd and 4th pdms of the o1-to - f3 system , corresponding to the alpha - delta and theta - delta bands . a number of features were computed from the same eeg signals , including the rps in five spectral bands , mf and se . however , they have been reported to discriminate between the electromagnetic brain activity of ad and control subjects . hence , they are used here as benchmark for comparison purposes . 10 shows the boxplots of the rps for each eeg electrode for ad patients and controls subjects . the bottom and top of the boxplot show the first and third quartiles respectively , with the middle band representing the median ( second quartile ) . outliers are shown as crosses , with the maximum and minimum values of the data after exclusion of outliers shown as black bars above and below the boxplot . similarly , fig . figure 10.boxplots with the distributions of rp in \documentclass[12pt]{minimal } 
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 } { } $ \gamma $ 
 \end{document } (  g  ) bands for ad patients and control subjects (  cn  ) . among the features with significant differences , the highest areas under the roc curve for the separation between ad and control subjects were achieved at o1 and o2 with the feature rp\documentclass[12pt]{minimal } 
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 } { } $ \alpha $ 
 \end{document } ( areas of 0.983 and 0.990 , respectively ) . we explored combining the best classification features of the two approaches ( i.e. those with most differentiating capability from pdm modeling and from relative power measurement ) and achieved complete separation of patients from controls by using the 4th pdm of the o1-f3 system and the relative power in the alpha band measured at o1 ( fig . 14 ) , or the 4th pdm of the o2-f3 system and the relative power in the alpha band measured at o2 ( fig . figure 14.scatter-plot of computed anf linear trends ( slopes ) for 4th pdms of the o1-to - f3 system , corresponding to the theta - delta band , versus the relative power in o1 corresponding to the alpha band . figure 15.scatter-plot of computed anf linear trends ( slopes ) for 4th pdms of the o2-to - f3 system , corresponding to the theta - delta band , versus the relative power in o2 corresponding to the alpha band . scatter - plot of computed anf linear trends ( slopes ) for 4th pdms of the o1-to - f3 system , corresponding to the theta - delta band , versus the relative power in o1 corresponding to the alpha band . scatter - plot of computed anf linear trends ( slopes ) for 4th pdms of the o2-to - f3 system , corresponding to the theta - delta band , versus the relative power in o2 corresponding to the alpha band . we have presented a methodology for input - output modeling of the dynamic relationships between eeg recordings in ad patients and control subjects that can be used for diagnostic delineation of the two groups . the methodology is based on the concept of principal dynamic modes ( pdms ) and their associated nonlinear functions ( anfs ) that has been recently developed and applied successfully to various physiological systems . preliminary results of the application of this methodology to data collected from 17 ad patients and 24 control subjects offer considerable promise . specifically , when the effective gain coefficients of the 2nd and 4th pdms ( i.e. the slopes of the linear trends in their respective anfs ) are used as classifiers for the o2-f3 system , we have one false - positive and two false - negatives ( see fig . when the effective gain coefficients of the 2nd and 4th pdms are used as classifiers for the o1-f3 system , we have two false - negatives and two false - positves ( see fig . 9 , i.e. 82.3% sensitivity and 91.7% specificity ) . this suggests that the use of more than two pdms / anfs ought to be explored for differentiation of patients from controls . the roc curve also demonstrates promising performance of these classifiers ( see fig . 7 ) . the best classifiers for both o1-f3 and o2-f3 systems corresponded to the pdms with theta - delta spectral characteristics , consistent with previously reported observations of increased theta and delta activity in the left hemispheric frontal region in ad patients compared to control subjects , as well as decreased alpha activity in ad patients 
 . if these results become confirmed in larger numbers of subjects , then the proposed approach will offer a valuable non - invasive diagnostic tool for ad . these initial results are consistent with the current view that elevated theta activity in the awake adult may indicate abnormal neurological conditions , and reduced alpha activity may reflect ( in part ) a state of heightened anxiety in ad patients . we note , however , that our pdm - based analysis yields classification features that concern the causal relation between two eeg signals ( e.g. o1 as a putative  input  and f3 as a putative  output  ) , while activity within a neural - rhythm band concerns simply the spectral characteristics of the signals themselves . even though the coherence \documentclass[12pt]{minimal } 
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 } { } $ c(\,f)$ 
 \end{document } only captures linear interactions between signals , previous research has suggested that it is strongly correlated with other commonly used synchronization measures . however , there have been differences in the findings of previous studies about how ad affects brain connectivity . this might be due to differences in the analyzed populations , the heterogeneity of the disease and small differences in the connectivity metrics . the use of pdm - based connectivity models addresses some of these issues by extending the analysis of the data into the nonlinear domain and , more importantly , by focusing on the dynamic relation between two eeg signals ( measured at the frontal and occipital lobes in this case ) and not the temporal or spectral structure of the signals themselves . this distinction may prove useful because it removes part of the potential ambiguity in differentiating patients from controls by virtue of the fact that the employed  classification feature  ( i.e. the slope of the anfs in this case ) is independent of the particular neural activity that defines the spectro - temporal signal structure at the time of data collection . in other words , the pdm - based approach focuses on the system between the two signals and not on the signals themselves . we examined the correlation between the pdm gain that yielded the best classification result ( pdm4 in the o2-to - f3 ) and the relative power in o2 corresponding to theta band ( rp\documentclass[12pt]{minimal } 
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 } { } $ \theta ) $ 
 \end{document } that is dominant in pdm4 . this correlation is statistically significant with correlation coefficient of 0.81 and p - value less than 0.0001 . similar result was obtained between the pdm4 in the o1-to - f3 system ( delta - theta band ) and the rp\documentclass[12pt]{minimal } 
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 } { } $ \theta $ 
 \end{document } in o1 ( correlation coefficient equal to 0.82 and p - value < 0.0001 ) . similarly , the most delineating features in the benchmark study : rp\documentclass[12pt]{minimal } 
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 } { } $ \alpha $ 
 \end{document } in o1 and o2 , also correlate with their pdm counterparts ( gain of pdm2 corresponding to the alpha band ) with correlation coefficient equal to 0.3 and p - value < 0.05 . these findings suggest that the rp measurements in theta and alpha band achieve similar delineation between patients and controls as pdm analysis . it was shown that perfect delineation between patients and controls was achieved when the best pdm and rp features were combined ( see fig . the findings of the pdm analysis imply that ad patients may have slower neural connectivity than controls between the occipital and the frontal cortical regions , as suggested by the higher gains in theta band and lower gains in alpha band . this is consistent with current views of the progressive impairment of cortical connectivity in neurodegenerative diseases . although our sample size is insufficient to prove the clinical utility of the reported eeg analyses for ad diagnosis , it is beneficial to relate our research to the current framework for ad diagnosis in clinical practice and research , . current criteria distinguish between the pathological process of ad and the observable symptoms caused by that process , . whereas the clinical diagnosis of ad must be performed using only the patient s cognitive and behavioral symptoms , a few biomarkers ( magnetic resonance imaging , biochemical levels in the cerebrospinal fluid , specific genetic factors and positron emission tomography ) can increase or decrease the certainty that clinical symptoms are due to an underlying ad pathology , . although eeg is not currently included in such list of biomarkers , it provides a direct measure of the brain activity . . therefore , it holds promise to become , after suitable signal processing , a widely available method to support clinicians in the diagnosis of the disease . our preliminary results are promising but they are inevitably affected by various sources of errors , including the variability in physiological mechanisms and measurement instrumentation . we must emphasize that the sensitivity of parameter selection for model estimation is a critical issue for the reproducibility of results in a clinical context and , therefore , it should be examined in future studies with larger sample size and different clinical settings . another limitation of this study is that the average ages of the two subject groups were different . however , the ad patients were recruited following standard clinical procedures and the dataset have been used in a number of research studies . moreover , the probable ad subjects had not previously been diagnosed ( prior to the assessment at the memory clinic that led to their referral to the eeg department ) . thus , they were in the early stages of exhibiting clinical symptoms . finally , the subjects did not perform any task . hence , the classification performance might improve by analyzing signals acquired during specific experimental settings .
we examine whether modeling of the causal dynamic relationships between frontal and occipital electroencephalogram ( eeg ) time - series recordings reveal reliable differentiating characteristics of alzheimer s patients versus control subjects in a manner that may assist clinical diagnosis of alzheimer s disease ( ad ) . 
 the proposed modeling approach utilizes the concept of principal dynamic modes ( pdms ) and their associated nonlinear functions ( anf ) and hypothesizes that the anfs of some pdms for the ad patients will be distinct from their counterparts in control subjects . to this purpose , global pdms 
 are extracted from 1-min eeg signals of 17 ad patients and 24 control subjects at rest using volterra models estimated via laguerre expansions , whereby the o1 or o2 recording is viewed as the input signal and the f3 or f4 recording as the output signal . 
 subsequent singular value decomposition of the estimated volterra kernels yields the global pdms that represent an efficient basis of functions for the representation of the eeg dynamics in all subjects . 
 the respective anfs are computed for each subject and characterize the specific dynamics of each subject . for comparison , 
 signal features traditionally used in the analysis of eeg signals in ad are computed as benchmark . 
 the results indicate that the anfs of two specific pdms , corresponding to the delta  theta and alpha bands , can delineate the two groups well .