Higuchi fractal dimension: An efficient approach to detection of brain entrainment to theta binaural beats

Shamsi, Elham; Ahmadi-Pajouh, Mohammad Ali; Seifi, Tirdad

doi:10.1016/j.bspc.2021.102580

Cited by 30 publications

(14 citation statements)

References 115 publications

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“…Higuchi’s fractal dimension (HFD) [ 51 ] can provide a better measure of signal complexity when there are few data points available [ 52 ]. Therefore, HFD has been widely used in biomedical signal and image processing [ 53 – 55 ]. HFD can be calculated as follows.…”

Section: Methodsmentioning

confidence: 99%

FFP: joint Fast Fourier transform and fractal dimension in amino acid property-aware phylogenetic analysis

Yang

Qiu

et al. 2022

BMC Bioinformatics

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Background Amino acid property-aware phylogenetic analysis (APPA) refers to the phylogenetic analysis method based on amino acid property encoding, which is used for understanding and inferring evolutionary relationships between species from the molecular perspective. Fast Fourier transform (FFT) and Higuchi’s fractal dimension (HFD) have excellent performance in describing sequences’ structural and complexity information for APPA. However, with the exponential growth of protein sequence data, it is very important to develop a reliable APPA method for protein sequence analysis. Results Consequently, we propose a new method named FFP, it joints FFT and HFD. Firstly, FFP is used to encode protein sequences on the basis of the important physicochemical properties of amino acids, the dissociation constant, which determines acidity and basicity of protein molecules. Secondly, FFT and HFD are used to generate the feature vectors of encoded sequences, whereafter, the distance matrix is calculated from the cosine function, which describes the degree of similarity between species. The smaller the distance between them, the more similar they are. Finally, the phylogenetic tree is constructed. When FFP is tested for phylogenetic analysis on four groups of protein sequences, the results are obviously better than other comparisons, with the highest accuracy up to more than 97%. Conclusion FFP has higher accuracy in APPA and multi-sequence alignment. It also can measure the protein sequence similarity effectively. And it is hoped to play a role in APPA’s related research.

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Section: Methodsmentioning

confidence: 99%

FFP: joint Fast Fourier transform and fractal dimension in amino acid property-aware phylogenetic analysis

Yang

Qiu

et al. 2022

BMC Bioinformatics

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“…A structure's Fractal Dimension is a measure of its complexity. The same concept can be applied to the EEG signal to measure the magnitude of its complexity [85], which is the amount of non-linear information transmitted over time. In other words, FD represents the signal's dimension in the temporal domain.…”

Section: Feature Extractionmentioning

confidence: 99%

Fractal Dimensions and Machine Learning for Detection of Parkinson’s Disease in Resting-State EEG

Lal,

Chikkankod,

Longo

2023

Preprint

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Parkinson's Disease (PD) is an incurable neurological disorder that degenerates the cerebrospinal nervous system and hinders motor functions. Electroencephalography (EEG) signal analysis can provide reliable information regarding PD conditions. However, EEG is a complex, multi-channel, and non-linear signal with noise that problematizes identifying PD symptoms. A few studies have employed Fractal Dimension (FD) to extract distinguishing PD features from EEG signals. However, no exploratory study exists, as per our knowledge, on the efficiency of the different FD measures. We aim to conduct a comparative analysis of the various FDs that, as feature extraction measures, can discriminate PD patients who are ON and OFF medication from healthy controls using ML architecture. This study has implemented and analyzed several techniques for segmentation, feature extraction, and ML models. The results show that K-Nearest Neighbors (KNN) classifier with Higuchi FD and 90% overlap for segmented window delivers the highest accuracies, yielding a mean accuracy of 99.65% for PD patients ON medication and 99.45% for PD patients OFF medication, respectively. The model accurately identifies the signs of the disease in resting-state EEG with almost equivalent accuracy in both OFF and ON medication patients. To enhance the interpretability in our study, we leveraged XGB's feature importance to generate brain topographic plots. This integration of Explainable AI (XAI) enhanced the transparency and comprehensibility of our model's classifications. Additionally, a comparison between the performance of FD and a few Entropy measures has also been drawn to validate the significance of FD as a superior feature extraction measure. This study contributes to the body of knowledge with an architectural pipeline for detecting PD in resting-state EEG while emphasizing Fractal Dimension as an effective way of extracting salient features from EEG signals.

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“…The HFD value of smooth signals (e.g., linear signals) is determined to be 1. The HFD of random white noise signals or complex signals is determined to be ≈ 2 [30]. Given that the fractal dimension is approximated numerically, the computed HFD values may be slightly higher than 2 [31].…”

Section: Fractal Dimensionmentioning

confidence: 99%

Chaotic Dynamics in the 2D System of Nonsmooth Ordinary Differential Equations

Rahman

Jasim

Al‐Yasir

2022

ijcsm

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Over the last decade, the chaotic behaviors of dynamical systems have been extensively explored. Recently, discovering or developing a 2D system of ordinary differential equations (ODEs) capable of exhibiting chaotic dynamical behaviors is an attractive research topic. In this study, a chaotic system with a 2D system of nonsmooth ODEs has been developed. This system is can exhibit chaotic dynamical behaviors. Its main dynamical behaviors, including time-series trajectories, phase portraits of attractors, and equilibria and their stability, have been investigated. The developed system has been verified by an excessive variety of fascinating chaotic behaviors, such as chaotic attractor, symmetry, sensitivity to initial conditions (ICs), fractal dimension, autocorrelation, power spectrum, Lyapunov exponent, and bifurcation diagram. Analytical and numerical simulations are used to study the dynamical behaviors of such a system. The developed system has extreme sensitivity to ICs, a fractal dimension of more than 1.8 and less than 2.05, an autocorrelation fluctuating randomly about an average of zero, a broadband power spectrum, and one positive Lyapunov exponent. The obtained numerical simulation results have proven the capability of the developed 2D system for exciting chaotic dynamical behaviors

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Higuchi fractal dimension: An efficient approach to detection of brain entrainment to theta binaural beats

Cited by 30 publications

References 115 publications

FFP: joint Fast Fourier transform and fractal dimension in amino acid property-aware phylogenetic analysis

FFP: joint Fast Fourier transform and fractal dimension in amino acid property-aware phylogenetic analysis

Fractal Dimensions and Machine Learning for Detection of Parkinson’s Disease in Resting-State EEG

Chaotic Dynamics in the 2D System of Nonsmooth Ordinary Differential Equations

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