We propose a time-domain approach to detect frequencies, frequency couplings, and phases using no... more We propose a time-domain approach to detect frequencies, frequency couplings, and phases using nonlinear correlation functions. For frequency analysis, this approach is a multivariate extension of discrete Fourier transform, and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short and sparse time series and can be extended to cross-trial and cross-channel spectra (CTS) for electroencephalography data where multiple short data segments from multiple trials of the same experiment are available. There are two versions of CTS. The first one assumes some phase coherency across the trials, while the second one is independent of phase coherency. We demonstrate that the phase-dependent version is more consistent with event-related spectral perturbation analysis and traditional Morlet wavelet analysis. We show that CTS can be applied to short data windows and yields higher temporal resolution than traditional Morlet wavelet analysis. Furthermore, the CTS can be used to reconstruct the event-related potential using all linear components of the CTS.
The pathophysiology of Parkinson’s disease (PD) is known to involve altered patterns of neuronal ... more The pathophysiology of Parkinson’s disease (PD) is known to involve altered patterns of neuronal firing and synchronization in cortical-basal ganglia circuits. One window into the nature of the aberrant temporal dynamics in the cerebral cortex of PD patients can come from analysis of the patients electroencephalography (EEG). Rather than using spectral-based methods, we used data models based on delay differential equations (DDE) as non-linear time-domain classification tools to analyze EEG recordings from PD patients on and off dopaminergic therapy and healthy individuals. Two sets of 50 1-s segments of 64-channel EEG activity were recorded from nine PD patients on and off medication and nine age-matched controls. The 64 EEG channels were grouped into 10 clusters covering frontal, central, parietal, and occipital brain regions for analysis. DDE models were fitted to individual trials, and model coefficients and error were used as features for classification. The best models were selected using repeated random sub-sampling validation and classification performance was measured using the area under the ROC curve A′. In a companion paper, we show that DDEs can uncover hidden dynamical structure from short segments of simulated time series of known dynamical systems in high noise regimes. Using the same method for finding the best models, we found here that even short segments of EEG data in PD patients and controls contained dynamical structure, and moreover, that PD patients exhibited a greater dynamic range than controls. DDE model output on the means from one set of 50 trials provided nearly complete separation of PD patients off medication from controls: across brain regions, the area under the receiver-operating characteristic curves, A′, varied from 0.95 to 1.0. For distinguishing PD patients on vs. off medication, classification performance A′ ranged from 0.86 to 1.0 across brain regions. Moreover, the generalizability of the model to the second set of 50 trials was excellent, with A′ ranging from 0.81 to 0.94 across brain regions for controls vs. PD off medication, and from 0.62 to 0.82 for PD on medication vs. off. Finally, model features significantly predicted individual patients’ motor severity, as assessed with standard clinical rating scales.
Parkinson's disease (PD) is known to lead to marked alterations in cortical-basal ganglia activit... more Parkinson's disease (PD) is known to lead to marked alterations in cortical-basal ganglia activity that may be amenable to serve as a biomarker for PD diagnosis. Using non-linear delay differential equations (DDE) for classification of PD patients on and off dopaminergic therapy (PD-on, PD-off, respectively) from healthy age-matched controls (CO), we show that 1 second of quasi-resting state clean and raw electroencephalogram (EEG) data can be used to classify CO from PD-on/off based on the area under the receiver operating characteristic curve (AROC). Raw EEG is shown to classify more robustly (AROC=0.59-0.86) than clean EEG data (AROC=0.57-0.72). Decomposition of the raw data into stereotypical and non-stereotypical artifacts provides evidence that increased classification of raw EEG time series originates from muscle artifacts. Thus, non-linear feature extraction and classification of raw EEG data in a low dimensional feature space is a potential biomarker for Parkinson's disease.
Time series analysis with delay differential equations (DDEs) reveals non-linear properties of th... more Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson’s disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to −30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A′ under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2011
Starting from an observed single time series, it is shown how to reconstruct a global model in th... more Starting from an observed single time series, it is shown how to reconstruct a global model in the original phase space by using the ansatz library approach. This model is then compared to the underlying dynamical system that describes the initial time series, and the nonuniqueness of the reconstructed model is discussed. This framework is extended by taking an additional time scaling factor in the reconstructed model class under consideration.
Time series analysis with nonlinear delay differential equations (DDEs) is a very powerful tool s... more Time series analysis with nonlinear delay differential equations (DDEs) is a very powerful tool since it reveals spectral as well as topological properties of the underlying dynamical system and is robust against noise. Here we apply nonlinear DDEs to examine the nature ...
ABSTRACT We present a systematic comparison of machine learning methods applied to the problem of... more ABSTRACT We present a systematic comparison of machine learning methods applied to the problem of fully automatic recognition of facial expressions. We explored recognition of facial actions from the Facial Action Coding System (FACS), as well as recognition of full facial expressions. Each video-frame is first scanned in real-time to detect approximately upright-frontal faces. The faces found are scaled into image patches of equal size, convolved with a bank of Gabor energy filters, and then passed to a recognition engine that codes facial expressions into 7 dimensions in real time: neutral, anger, disgust, fear, joy, sadness, surprise. We report results on a series of experiments comparing recognition engines, including AdaBoost, support vector machines, linear discriminant analysis, as well as feature selection techniques. Best results were obtained by selecting a subset of Gabor filters using AdaBoost and then training Support Vector Machines on the outputs of the filters selected by AdaBoost. The generalization performance to new subjects for recognition of full facial expressions in a 7-way forced choice was 93% correct, the best performance reported so far on the Cohn-Kanade FACS-coded expression dataset. We also applied the system to fully automated facial action coding. The present system classifies 18 action units, whether they occur singly or in combination with other actions, with a mean agreement rate of 94.5% with human FACS codes in the Cohn-Kanade dataset. The outputs of the classifiers change smoothly as a function of time and thus can be used to measure facial expression dynamics.
We present a systematic comparison of machine learning methods applied to the problem of fully au... more We present a systematic comparison of machine learning methods applied to the problem of fully automatic recognition of facial expressions. We explored recognition of facial actions from the Facial Action Coding System (FACS), as well as recognition of full facial expressions. Each videoframe is first scanned in real-time to detect approximately upright-frontal faces. The faces found are scaled into image patches of equal size, convolved with a bank of Gabor energy filters, and then passed to a recognition engine that codes facial expressions into 7 dimensions in real time: neutral, anger, disgust, fear, joy, sadness, surprise. We report results on a series of experiments comparing recognition engines, including AdaBoost, support vector machines, linear discriminant analysis, as well as feature selection techniques. Best results were obtained by selecting a subset of Gabor filters using AdaBoost and then training Support Vector Machines on the outputs of the filters selected by AdaB...
We propose a time-domain approach to detect frequencies, frequency couplings, and phases using no... more We propose a time-domain approach to detect frequencies, frequency couplings, and phases using nonlinear correlation functions. For frequency analysis, this approach is a multivariate extension of discrete Fourier transform, and for higher-order spectra, it is a linear and multivariate alternative to multidimensional fast Fourier transform of multidimensional correlations. This method can be applied to short and sparse time series and can be extended to cross-trial and cross-channel spectra (CTS) for electroencephalography data where multiple short data segments from multiple trials of the same experiment are available. There are two versions of CTS. The first one assumes some phase coherency across the trials, while the second one is independent of phase coherency. We demonstrate that the phase-dependent version is more consistent with event-related spectral perturbation analysis and traditional Morlet wavelet analysis. We show that CTS can be applied to short data windows and yields higher temporal resolution than traditional Morlet wavelet analysis. Furthermore, the CTS can be used to reconstruct the event-related potential using all linear components of the CTS.
The pathophysiology of Parkinson’s disease (PD) is known to involve altered patterns of neuronal ... more The pathophysiology of Parkinson’s disease (PD) is known to involve altered patterns of neuronal firing and synchronization in cortical-basal ganglia circuits. One window into the nature of the aberrant temporal dynamics in the cerebral cortex of PD patients can come from analysis of the patients electroencephalography (EEG). Rather than using spectral-based methods, we used data models based on delay differential equations (DDE) as non-linear time-domain classification tools to analyze EEG recordings from PD patients on and off dopaminergic therapy and healthy individuals. Two sets of 50 1-s segments of 64-channel EEG activity were recorded from nine PD patients on and off medication and nine age-matched controls. The 64 EEG channels were grouped into 10 clusters covering frontal, central, parietal, and occipital brain regions for analysis. DDE models were fitted to individual trials, and model coefficients and error were used as features for classification. The best models were selected using repeated random sub-sampling validation and classification performance was measured using the area under the ROC curve A′. In a companion paper, we show that DDEs can uncover hidden dynamical structure from short segments of simulated time series of known dynamical systems in high noise regimes. Using the same method for finding the best models, we found here that even short segments of EEG data in PD patients and controls contained dynamical structure, and moreover, that PD patients exhibited a greater dynamic range than controls. DDE model output on the means from one set of 50 trials provided nearly complete separation of PD patients off medication from controls: across brain regions, the area under the receiver-operating characteristic curves, A′, varied from 0.95 to 1.0. For distinguishing PD patients on vs. off medication, classification performance A′ ranged from 0.86 to 1.0 across brain regions. Moreover, the generalizability of the model to the second set of 50 trials was excellent, with A′ ranging from 0.81 to 0.94 across brain regions for controls vs. PD off medication, and from 0.62 to 0.82 for PD on medication vs. off. Finally, model features significantly predicted individual patients’ motor severity, as assessed with standard clinical rating scales.
Parkinson's disease (PD) is known to lead to marked alterations in cortical-basal ganglia activit... more Parkinson's disease (PD) is known to lead to marked alterations in cortical-basal ganglia activity that may be amenable to serve as a biomarker for PD diagnosis. Using non-linear delay differential equations (DDE) for classification of PD patients on and off dopaminergic therapy (PD-on, PD-off, respectively) from healthy age-matched controls (CO), we show that 1 second of quasi-resting state clean and raw electroencephalogram (EEG) data can be used to classify CO from PD-on/off based on the area under the receiver operating characteristic curve (AROC). Raw EEG is shown to classify more robustly (AROC=0.59-0.86) than clean EEG data (AROC=0.57-0.72). Decomposition of the raw data into stereotypical and non-stereotypical artifacts provides evidence that increased classification of raw EEG time series originates from muscle artifacts. Thus, non-linear feature extraction and classification of raw EEG data in a low dimensional feature space is a potential biomarker for Parkinson's disease.
Time series analysis with delay differential equations (DDEs) reveals non-linear properties of th... more Time series analysis with delay differential equations (DDEs) reveals non-linear properties of the underlying dynamical system and can serve as a non-linear time-domain classification tool. Here global DDE models were used to analyze short segments of simulated time series from a known dynamical system, the Rössler system, in high noise regimes. In a companion paper, we apply the DDE model developed here to classify short segments of encephalographic (EEG) data recorded from patients with Parkinson’s disease and healthy subjects. Nine simulated subjects in each of two distinct classes were generated by varying the bifurcation parameter b and keeping the other two parameters (a and c) of the Rössler system fixed. All choices of b were in the chaotic parameter range. We diluted the simulated data using white noise ranging from 10 to −30 dB signal-to-noise ratios (SNR). Structure selection was supervised by selecting the number of terms, delays, and order of non-linearity of the model DDE model that best linearly separated the two classes of data. The distances d from the linear dividing hyperplane was then used to assess the classification performance by computing the area A′ under the ROC curve. The selected model was tested on untrained data using repeated random sub-sampling validation. DDEs were able to accurately distinguish the two dynamical conditions, and moreover, to quantify the changes in the dynamics. There was a significant correlation between the dynamical bifurcation parameter b of the simulated data and the classification parameter d from our analysis. This correlation still held for new simulated subjects with new dynamical parameters selected from each of the two dynamical regimes. Furthermore, the correlation was robust to added noise, being significant even when the noise was greater than the signal. We conclude that DDE models may be used as a generalizable and reliable classification tool for even small segments of noisy data.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2011
Starting from an observed single time series, it is shown how to reconstruct a global model in th... more Starting from an observed single time series, it is shown how to reconstruct a global model in the original phase space by using the ansatz library approach. This model is then compared to the underlying dynamical system that describes the initial time series, and the nonuniqueness of the reconstructed model is discussed. This framework is extended by taking an additional time scaling factor in the reconstructed model class under consideration.
Time series analysis with nonlinear delay differential equations (DDEs) is a very powerful tool s... more Time series analysis with nonlinear delay differential equations (DDEs) is a very powerful tool since it reveals spectral as well as topological properties of the underlying dynamical system and is robust against noise. Here we apply nonlinear DDEs to examine the nature ...
ABSTRACT We present a systematic comparison of machine learning methods applied to the problem of... more ABSTRACT We present a systematic comparison of machine learning methods applied to the problem of fully automatic recognition of facial expressions. We explored recognition of facial actions from the Facial Action Coding System (FACS), as well as recognition of full facial expressions. Each video-frame is first scanned in real-time to detect approximately upright-frontal faces. The faces found are scaled into image patches of equal size, convolved with a bank of Gabor energy filters, and then passed to a recognition engine that codes facial expressions into 7 dimensions in real time: neutral, anger, disgust, fear, joy, sadness, surprise. We report results on a series of experiments comparing recognition engines, including AdaBoost, support vector machines, linear discriminant analysis, as well as feature selection techniques. Best results were obtained by selecting a subset of Gabor filters using AdaBoost and then training Support Vector Machines on the outputs of the filters selected by AdaBoost. The generalization performance to new subjects for recognition of full facial expressions in a 7-way forced choice was 93% correct, the best performance reported so far on the Cohn-Kanade FACS-coded expression dataset. We also applied the system to fully automated facial action coding. The present system classifies 18 action units, whether they occur singly or in combination with other actions, with a mean agreement rate of 94.5% with human FACS codes in the Cohn-Kanade dataset. The outputs of the classifiers change smoothly as a function of time and thus can be used to measure facial expression dynamics.
We present a systematic comparison of machine learning methods applied to the problem of fully au... more We present a systematic comparison of machine learning methods applied to the problem of fully automatic recognition of facial expressions. We explored recognition of facial actions from the Facial Action Coding System (FACS), as well as recognition of full facial expressions. Each videoframe is first scanned in real-time to detect approximately upright-frontal faces. The faces found are scaled into image patches of equal size, convolved with a bank of Gabor energy filters, and then passed to a recognition engine that codes facial expressions into 7 dimensions in real time: neutral, anger, disgust, fear, joy, sadness, surprise. We report results on a series of experiments comparing recognition engines, including AdaBoost, support vector machines, linear discriminant analysis, as well as feature selection techniques. Best results were obtained by selecting a subset of Gabor filters using AdaBoost and then training Support Vector Machines on the outputs of the filters selected by AdaB...
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Papers by Claudia Lainscsek