Time-varying system identification using an ultra-orthogonal forward regression and multiwavelet basis functions with applications to EEG

A new parametric approach is proposed for nonlinear and non-stationary system identification based on a time-varying nonlinear autoregressive with exogenous input (TV-NARX) model. The time-varying coefficients of the TV-NARX model are expanded using multi- wavelet basis functions and the model is thus transformed into a time-invariant regression problem. An ultra-orthogonal forward regression (UOFR) algorithm aided by mutual information (MI) is designed to identify a parsimonious model structure and estimate the associated model parameters. The UOFR-MI algorithm which uses not only the observed data themselves but also weak derivatives of the signals is more powerful in model structure detection. The proposed approach combining the advantages of both the basis function expansion method and the UOFR-MI algorithm is proved to be capable of tracking the change of time-varying parameters effectively in both numerical simulations and the real EEG data

A parametric time frequency-conditional Granger causality method using ultra-regularized orthogonal least squares and multiwavelets for dynamic connectivity analysis in EEGs

Objective: This study proposes a new para-metric TF-CGC (time-frequency conditional Granger causality) method for high-precision connectivity analysis over time and frequency domain in multivariate coupling nonstationary systems, and applies it to source EEG signals to reveal dynamic interaction patterns in oscillatory neo-cortical sensorimotor networks. Methods: The Geweke's spectral measure is combined with the TVARX (time-varying autoregressive with exogenous input) model-ling approach, which uses multiwavelet-based ul-tra-regularized orthogonal least squares (UROLS) algo-rithm aided by APRESS (adjustable prediction error sum of squares), to obtain high-resolution time-varying CGC representations. The UROLS-APRESS algorithm, which adopts both the regularization technique and the ultra-least squares criterion to measure not only the signal themselves but also the weak derivatives of them, is a novel powerful method in constructing time-varying models with good generalization performance, and can accurately track smooth and fast changing causalities. The generalized measurement based on CGC decomposition is able to eliminate indirect influences in multivariate systems. Re-sults: The proposed method is validated on two simulations and then applied to source level motor imagery (MI) EEGs, where the predicted distributions are well recovered with high TF precision, and the detected connectivity patterns of MI-EEGs are physiologically interpretable and yield new insights into the dynamical organization of oscillatory cor-tical networks. Conclusion: Experimental results confirm the effectiveness of the TF-CGC method in tracking rapidly varying causalities of EEG-based oscillatory networks. Significance: The novel TF-CGC method is expected to provide important information of neural mechanisms of perception and cognition

Neural activity inspired asymmetric basis function TV-NARX model for the identification of time-varying dynamic systems

Inspired by the unique neuronal activities, a new time-varying nonlinear autoregressive with exogenous input (TV-NARX) model is proposed for modelling nonstationary processes. The NARX nonlinear process mimics the action potential initiation and the time-varying parameters are approximated with a series of postsynaptic current like asymmetric basis functions to mimic the ion channels of the inter-neuron propagation. In the model, the time-varying parameters of the process terms are sparsely represented as the superposition of a series of asymmetric alpha basis functions in an over-complete frame. Combining the alpha basis functions with the model process terms, the system identification of the TV-NARX model from observed input and output can equivalently be treated as the system identification of a corresponding time-invariant system. The locally regularised orthogonal forward regression (LROFR) algorithm is then employed to detect the sparse model structure and estimate the associated coefficients. The excellent performance in both numerical studies and modelling of real physiological signals showed that the TV-NARX model with asymmetric basis function is more powerful and efficient in tracking both smooth trends and capturing the abrupt changes in the time-varying parameters than its symmetric counterparts

A multiple beta wavelet-based locally regularized ultraorthogonal forward regression algorithm for time-varying system identification with applications to EEG

Time-varying (TV) nonlinear systems widely exist in various fields of engineering and science. Effective identification and modeling of TV systems is a challenging problem due to the nonstationarity and nonlinearity of the associated processes. In this paper, a novel parametric modeling algorithm is proposed to deal with this problem based on a TV nonlinear autoregressive with exogenous input (TV-NARX) model. A new class of multiple beta wavelet (MBW) basis functions is introduced to represent the TV coefficients of the TV-NARX model to enable the tracking of both smooth trends and sharp changes of the system behavior. To produce a parsimonious model structure, a locally regularized ultraorthogonal forward regression (LRUOFR) algorithm aided by the adjustable prediction error sum of squares (APRESS) criterion is investigated for sparse model term selection and parameter estimation. Simulation studies and a real application to EEG data show that the proposed MBW-LRUOFR algorithm can effectively capture the global and local features of nonstationary systems and obtain an optimal model, even for signals contaminated with severe colored noise

Boosting wavelet neural networks using evolutionary algorithms for short-term wind speed time series forecasting

This paper addresses nonlinear time series modelling and prediction problem using a type of wavelet neural networks. The basic building block of the neural network models is a ridge type function. The training of such a network is a nonlinear optimization problem. Evolutionary algorithms (EAs), including genetic algorithm (GA) and particle swarm optimization (PSO), together with a new gradient-free algorithm (called coordinate dictionary search optimization – CDSO), are used to train network models. An example for real speed wind data modelling and prediction is provided to show the performance of the proposed networks trained by these three optimization algorithms

Time-varying nonlinear causality detection using regularized orthogonal least squares and multi-wavelets with applications to EEG

A new transient Granger causality detection method is proposed based on a time-varying parametric modelling framework, and is applied to real EEG signals to reveal the causal information flow during motor imagery (MI) tasks. The time-varying parametric modelling approach employs a nonlinear autoregressive with external input (NARX) model, whose parameters are approximated by a set of multiwavelet basis functions. A regularized orthogonal least squares (ROLS) algorithm is then used to produce a parsimonious or sparse regression model and estimate the associated model parameters. The time-varying Granger causality between nonstationary signals can be detected accurately by making use of both the good approximation properties of multi-wavelets and the good generalization performance of the ROLS in the presence of high-level noise. Two simulation examples are presented to demonstrate the effectiveness of the proposed method for both linear and nonlinear causal detection respectively. The proposed method is then applied to real EEG signals of MI tasks. It follows that transient causal information flow over the time course between various sensorimotor related channels can be successfully revealed during the whole reaction processes. Experiment results from these case studies confirm the applicability of the proposed scheme and show its utility for the understanding of the associated neural mechanism and the potential significance for developing MI tasks based brain-computer interface (BCI) systems

Sparse, interpretable and transparent predictive model identification for healthcare data analysis

Data-driven modelling approaches play an indispensable role in analyzing and understanding complex processes. This study proposes a type of sparse, interpretable and transparent (SIT) machine learning model, which can be used to understand the dependent relationship of a response variable on a set of potential explanatory variables. An ideal candidate for such a SIT representation is the well-known NARMAX (nonlinear autoregressive moving average with exogenous inputs) model, which can be established from measured input and output data of the system of interest, and the final refined model is usually simple, parsimonious and easy to interpret. The performance of the proposed SIT models is evaluated through two real healthcare datasets

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a small amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention