Normative modeling of neuroimaging data using generalized additive models of location scale and shape

Normative modeling aims to quantify the degree to which an individual's brain deviates from a reference sample with respect to one or more variables, which can be used as a potential biomarker of a healthy brain and as a tool to study heterogeneity of psychiatric disorders. The application of normative models is hindered by methodological challenges and lacks standards for the usage and evaluation of normative models. In this paper, we present generalized additive models for location scale and shape (GAMLSS) for normative modeling of neuroimaging data, a flexible modeling framework that can model heteroskedasticity, non-linear effects of variables, and hierarchical structure of the data. It can model non-Gaussian distributions, and it allows for an automatic model order selection, thus improving the accuracy of normative models while mitigating problems of overfitting. Furthermore, we describe measures and diagnostic tools suitable for evaluating normative models and step-by-step examples of normative modeling, including fitting several candidate models, selecting the best models, and transferring them to new scan sites.

Tensor analysis of electroencephalogram signal for localization of event-related potentials

Electroencephalogram (EEG) is widely used for monitoring, diagnosis purposes and also for study of brains physiological, mental and functional abnormalities. EEG is known to be a high-dimensional signal in which processing of information by the brain is reected in dynamical changes of the electrical activity in time, frequency, and space. EEG signal processing tends to describe and quantify these variations into functions with known spatio-temporal-spectral properties or at least easier to characterize. Multi-channel EEG recordings naturally include multiple modes. Matrix analysis, via stacking or concatenating other modes with the retained two modes, has been extensively used to represent and analyze the EEG data. On the other hand, Multi-way (tensor) analysis techniques keep the structure of the data, and by analyzing more dimensions simultaneously, summarize the data into more interpretable components. This work presents a generalized multi-way array analysis methodology in pattern classification systems as related to source separation and discriminant feature selection in EEG signal processing problems. Analysis of ERPs, as one of the main categories of EEG signals, requires systems that can exploit the variation of the signals in different contextual domains in order to reveal the hidden structures in the data. Temporal, spectral, spatial, and subjects/experimental conditions of multi-channel ERP signals are exploited here to generate three-way and four-way ERP tensors. Two key elements of this framework are the Time-Frequency representation (TFR) and CANDECOMP/PARAFAC model order selection techniques we incorporate for analysis. Here, we propose a fully data-driven TFR scheme, via combining the Empirical Mode Decomposition and Reassignment method, which yields a high resolution and cross-term free TFR. Furthermore, we develop a robust and effective model order selection scheme that outperforms conventional techniques in mid and low SNRs (i.e. 0􀀀10 dB) with a better Probability of Detection (PoD) and almost no extra computational overhead after the CANDECOMP/PARAFAC decomposition. ERP tensor can be regarded as a mixture that includes different kinds of brain activity, artifacts, interference, and noise. Using this framework, the desired brain activity could be extracted out from the mixture. The extracted signatures are then translated for different applications in brain-computer interface and cognitive neuroscience.

Tensor analysis of electroencephalogram signal for localization of event-related potentials

Electroencephalogram (EEG) is widely used for monitoring, diagnosis purposes and also for study of brains physiological, mental and functional abnormalities. EEG is known to be a high-dimensional signal in which processing of information by the brain is reected in dynamical changes of the electrical activity in time, frequency, and space. EEG signal processing tends to describe and quantify these variations into functions with known spatio-temporal-spectral properties or at least easier to characterize. Multi-channel EEG recordings naturally include multiple modes. Matrix analysis, via stacking or concatenating other modes with the retained two modes, has been extensively used to represent and analyze the EEG data. On the other hand, Multi-way (tensor) analysis techniques keep the structure of the data, and by analyzing more dimensions simultaneously, summarize the data into more interpretable components. This work presents a generalized multi-way array analysis methodology in pattern classification systems as related to source separation and discriminant feature selection in EEG signal processing problems. Analysis of ERPs, as one of the main categories of EEG signals, requires systems that can exploit the variation of the signals in different contextual domains in order to reveal the hidden structures in the data. Temporal, spectral, spatial, and subjects/experimental conditions of multi-channel ERP signals are exploited here to generate three-way and four-way ERP tensors. Two key elements of this framework are the Time-Frequency representation (TFR) and CANDECOMP/PARAFAC model order selection techniques we incorporate for analysis. Here, we propose a fully data-driven TFR scheme, via combining the Empirical Mode Decomposition and Reassignment method, which yields a high resolution and cross-term free TFR. Furthermore, we develop a robust and effective model order selection scheme that outperforms conventional techniques in mid and low SNRs (i.e. 0􀀀10 dB) with a better Probability of Detection (PoD) and almost no extra computational overhead after the CANDECOMP/PARAFAC decomposition. ERP tensor can be regarded as a mixture that includes different kinds of brain activity, artifacts, interference, and noise. Using this framework, the desired brain activity could be extracted out from the mixture. The extracted signatures are then translated for different applications in brain-computer interface and cognitive neuroscience.

Online LTI system identification and time delay estimation

Model order selection for linear time-invariant (LTI) systems is an important system modeling concern and has been widely investigated through past decades. Different approaches of order selection such as Akaike information criterion (AIC), Bayesian information criterion (BIC), minimum description length (MDL) and reconstruction error LTI system identification (RE-LTI) propose different criteria to select the optimum order of a system. In many real life applications of model order selection the size of an observed data set is increasing. Thus, order selection methods need to adopt the best fit of a model as the data set size is increasing. This is our motivation to extend RE-LTI order selection for online application of order selection with lower computational cost and complexity. It has been shown previously that AIC, BIC, two-stage MDL and many existing order selection criteria are special cases of RE-LTI method. Our online order selection approach reduces the computational complexity of the offline approach from O(N3) to O(N2). It should be noted that RE-LTI and MNDL order selection methods have same fundamentals and consequently extending RE-LTI to online RE-LTI also extends MNDL to online MNDL. Another crucial issue in system identification and modeling is estimating the time delay of a system’s impulse response (or determining the start of its non-zero part). This problem is addressed in various areas including radar, sonar, acoustic source tracking, multipath channel identification, as well as many automatic control applications. Utilizing fundamentals of RE-LTI approach, here we introduce a new time-delay estimator. Simulation results show advantages of the proposed method and its superiority to existing approaches in accuracy and robustness in terms of the FIT index.

Online LTI system identification and time delay estimation

Model order selection for linear time-invariant (LTI) systems is an important system modeling concern and has been widely investigated through past decades. Different approaches of order selection such as Akaike information criterion (AIC), Bayesian information criterion (BIC), minimum description length (MDL) and reconstruction error LTI system identification (RE-LTI) propose different criteria to select the optimum order of a system. In many real life applications of model order selection the size of an observed data set is increasing. Thus, order selection methods need to adopt the best fit of a model as the data set size is increasing. This is our motivation to extend RE-LTI order selection for online application of order selection with lower computational cost and complexity. It has been shown previously that AIC, BIC, two-stage MDL and many existing order selection criteria are special cases of RE-LTI method. Our online order selection approach reduces the computational complexity of the offline approach from O(N3) to O(N2). It should be noted that RE-LTI and MNDL order selection methods have same fundamentals and consequently extending RE-LTI to online RE-LTI also extends MNDL to online MNDL. Another crucial issue in system identification and modeling is estimating the time delay of a system’s impulse response (or determining the start of its non-zero part). This problem is addressed in various areas including radar, sonar, acoustic source tracking, multipath channel identification, as well as many automatic control applications. Utilizing fundamentals of RE-LTI approach, here we introduce a new time-delay estimator. Simulation results show advantages of the proposed method and its superiority to existing approaches in accuracy and robustness in terms of the FIT index.