Liangyue Cao

Bio: Liangyue Cao is an academic researcher from University of Western Australia. The author has contributed to research in topics: Series (mathematics) & Embedding. The author has an hindex of 6, co-authored 6 publications receiving 1643 citations.

Determining the Minimum Embedding Dimensions of Input–Output Time Series Data

Abstract: Input–output dynamical systems are in many ways quite different from the autonomous systems that are usually modeled in dynamical system reconstruction. In this paper we investigate the problem of determining the embedding dimension of such systems from input and output data. A successful embedding is essential if one wishes to model the system, or to design a control law. We propose a variant of the well-known false nearest neighbors method, which we call the method of averaged false nearest neighbors. Our method has a simple interpretation and is easy to implement on a computer. We provide several numerical examples.

Modeling and Predicting Non-Stationary Time Series

Abstract: Many experimental time series are non-stationary. Modeling and predicting them is generally considered to be difficult. In this paper we introduce time-dependent regressive (TDR) models, which depend not only on system states but also on time. We test artificial time series which come from parameter-changing systems and are therefore non-stationary, and a simulated experimental time series from a model of a non-stationary industrial system. The TDR models work well on those time series, not only in prediction but also in extraction of the underlying bifurcations.

Transfer entropy--a model-free measure of effective connectivity for the neurosciences

Abstract: Understanding causal relationships, or effective connectivity, between parts of the brain is of utmost importance because a large part of the brain's activity is thought to be internally generated and, hence, quantifying stimulus response relationships alone does not fully describe brain dynamics. Past efforts to determine effective connectivity mostly relied on model based approaches such as Granger causality or dynamic causal modeling. Transfer entropy (TE) is an alternative measure of effective connectivity based on information theory. TE does not require a model of the interaction and is inherently non-linear. We investigated the applicability of TE as a metric in a test for effective connectivity to electrophysiological data based on simulations and magnetoencephalography (MEG) recordings in a simple motor task. In particular, we demonstrate that TE improved the detectability of effective connectivity for non-linear interactions, and for sensor level MEG signals where linear methods are hampered by signal-cross-talk due to volume conduction.

A Wavelet-Chaos Methodology for Analysis of EEGs and EEG Subbands to Detect Seizure and Epilepsy

Abstract: A wavelet-chaos methodology is presented for analysis of EEGs and delta, theta, alpha, beta, and gamma subbands of EEGs for detection of seizure and epilepsy. The nonlinear dynamics of the original EEGs are quantified in the form of the correlation dimension (CD, representing system complexity) and the largest Lyapunov exponent (LLE, representing system chaoticity). The new wavelet-based methodology isolates the changes in CD and LLE in specific subbands of the EEG. The methodology is applied to three different groups of EEG signals: 1) healthy subjects; 2) epileptic subjects during a seizure-free interval (interictal EEG); 3) epileptic subjects during a seizure (ictal EEG). The effectiveness of CD and LLE in differentiating between the three groups is investigated based on statistical significance of the differences. It is observed that while there may not be significant differences in the values of the parameters obtained from the original EEG, differences may be identified when the parameters are employed in conjunction with specific EEG subbands. Moreover, it is concluded that for the higher frequency beta and gamma subbands, the CD differentiates between the three groups, whereas for the lower frequency alpha subband, the LLE differentiates between the three groups

Multivariate multiscale entropy: a tool for complexity analysis of multichannel data.

Abstract: This work generalizes the recently introduced univariate multiscale entropy (MSE) analysis to the multivariate case. This is achieved by introducing multivariate sample entropy (MSampEn) in a rigorous way, in order to account for both within- and cross-channel dependencies in multiple data channels, and by evaluating it over multiple temporal scales. The multivariate MSE (MMSE) method is shown to provide an assessment of the underlying dynamical richness of multichannel observations, and more degrees of freedom in the analysis than standard MSE. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate stochastic processes and on real-world multichannel physiological and environmental data.