Non uniform Embedding based on Relevance Analysis with reduced computational complexity: Application to the detection of pathologies from biosignal recordings

Multi-Frequency Entropy for Quantifying Complex Dynamics and Its Application on EEG Data

Multivariate entropy algorithms have proven effective in the complexity dynamic analysis of electroencephalography (EEG) signals, with researchers commonly configuring the variables as multi-channel time series. However, the complex quantification of brain dynamics from a multi-frequency perspective has not been extensively explored, despite existing evidence suggesting interactions among brain rhythms at different frequencies. In this study, we proposed a novel algorithm, termed multi-frequency entropy (mFreEn), enhancing the capabilities of existing multivariate entropy algorithms and facilitating the complexity study of interactions among brain rhythms of different frequency bands. Firstly, utilizing simulated data, we evaluated the mFreEn's sensitivity to various noise signals, frequencies, and amplitudes, investigated the effects of parameters such as the embedding dimension and data length, and analyzed its anti-noise performance. The results indicated that mFreEn demonstrated enhanced sensitivity and reduced parameter dependence compared to traditional multivariate entropy algorithms. Subsequently, the mFreEn algorithm was applied to the analysis of real EEG data. We found that mFreEn exhibited a good diagnostic performance in analyzing resting-state EEG data from various brain disorders. Furthermore, mFreEn showed a good classification performance for EEG activity induced by diverse task stimuli. Consequently, mFreEn provides another important perspective to quantify complex dynamics.

Color Recurrence Plots for Bearing Fault Diagnosis

This paper presents bearing fault diagnosis using the image classification of different fault patterns. Feature extraction for image classification is carried out using a novel approach of Color recurrence plots, which is presented for the first time. Color recurrence plots are created using non-linear embedding of the vibration signals into delay coordinate space with variable time lags. Deep learning-based image classification is then performed by building the database of the extracted features of the bearing vibration signals in the form of Color recurrence plots. A Series of computational experiments are performed to compare the accuracy of bearing fault classification using Color recurrence plots. The standard bearing vibration dataset of Case Western Reserve University is used for those purposes. The paper demonstrates the efficacy and the accuracy of a new and unique approach of scalar time series extraction into two-dimensional Color recurrence plots for bearing fault diagnosis.

Refined nonuniform embedding for coupling detection in multivariate time series

State-space reconstruction is essential to analyze the dynamics and internal interactions of complex systems. However, it is difficult to estimate high-dimensional conditional mutual information and select the optimal time delays in most existing nonuniform state-space reconstruction methods. Therefore, we propose a nonuniform embedding method framed in information theory for state-space reconstruction. We use a low-dimensional approximation of conditional mutual information criterion for time delay selection, which is effectively solved by the particle swarm optimization algorithm. The obtained embedded vector has relatively strong independence and low redundancy, which better characterizes multivariable complex systems and detects coupling within complex systems. In addition, the proposed nonuniform embedding method exhibits good performance in coupling detection of linear stochastic, nonlinear stochastic, chaotic systems. In the actual application, the importance of small airports that cause delay propagation has been demonstrated by constructing the delay propagation network.

Quantitative coordination evaluation for screening children with Duchenne muscular dystrophy

As the potential for a treatment of Duchenne muscular dystrophy (DMD) grows, the need for methods for the early diagnosis of DMD becomes more and more important. Clinical experiences suggest that children with DMD will show some lack of motor ability in the early stage when compared with children at the same age, especially in balance and coordination abilities. Is it possible to quantify the coordination differences between DMD and typically developing (TD) children to achieve the goal of screening for DMD diseases? In this study, we introduced a Local Manifold Structure Mapping approach in phase space and extracted a novel index, relative coupling coefficient (RCC), from gait pattern signals, which were acquired by wearable accelerometers to evaluate the coordination of children with DMD during a walking task. Furthermore, we compared the RCC of 100 children with DMD and 100 TD children in four different age groups and verified the feasibility and reliability of the proposed indices to distinguish children with TD from DMD. T-test results show that, for all age groups, children of the same age with DMD and TD show significant differences in RCC (p < 0.001). Moreover, RCC comprehensively reflects that the coordination ability of DMD patients under walking tasks gradually decreases with age, which is consistent with clinical experience. As a functional biomarker extracted in the phase space of the gait data, the proposed coupling degree index RCC could sensitively distinguish between DMD and TD children at the same age and provide alternative insights and potentially valuable tools for the screening of DMD.

Nonuniform State Space Reconstruction for Multivariate Chaotic Time Series

State space reconstruction is the foundation of chaotic system modeling. Selection of reconstructed variables is essential to the analysis and prediction of multivariate chaotic time series. As most existing state space reconstruction theorems deal with univariate time series, we have presented a novel nonuniform state space reconstruction method using information criterion for multivariate chaotic time series. We derived a new criterion based on low dimensional approximation of joint mutual information for time delay selection, which can be solved efficiently through the use of an intelligent optimization algorithm with low computation complexity. The embedding dimension is determined by conditional entropy, after which the reconstructed variables have relatively strong independence and low redundancy. The scheme, which integrates nonuniform embedding and feature selection, results in better reconstructions for multivariate chaotic systems. Moreover, the proposed nonuniform state space reconstruction method shows good performance in forecasting benchmark and actual multivariate chaotic time series.