Asymptotic Distribution of Certain Types of Entropy under the Multinomial Law

Rey, Andrea; Frery, Alejandro C.; Lucini, María Magdalena; Gambini, Juliana; Chagas, Eduarda T. C.; Ramos, Heitor S.

doi:10.3390/e25050734

Cited by 5 publications

(2 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The mathematical expression of accuracy, sensitivity, specificity, F1-score, and MCC is given from Eqs. ( 23)- (27).…”

Section: Results and Performance Analysismentioning

confidence: 99%

Classification of Epileptic Seizures Using LSTM Based Zebra Optimization Algorithm with Hyperparameter Tunin

2024

IJIES

View full text Add to dashboard Cite

Electroencephalogram (EEG) are the neuro-electrophysiology signals, which are commonly used as a diagnostic tool to measure the seizure activity of the brain. The accurate detection and classification of seizures help to provide an optimal solution to diagnose the patient. In this research, a hyperparameter tuning with Zebra Optimization Algorithm (ZOA) is proposed for the fine tuning of features from EEG signals. The EEG signals are taken from the three standard datasets such as Temple University Hospital (TUH) at a rate of sampling signal of 250Hz, Bonn University (BU) at a 173.61 Hz sampling rate, and Bern Barcelona (BB) alongside the sampling frequency of 512 Hz. The EEG signals are pre-processed using Butterworth 8th order filtering method to remove the unwanted noise, and de-noised signals are decomposed by the swarm decomposition method. Features like statistic-based features, frequency-dependent features, multi-scale wavelet transformation, entropy features, and power spectral features are extracted from the decomposition of signals. The extracted features then undergo hyperparameter tuning using ZOA followed by feature selection using Enhanced Spatial bound Whale Optimization Algorithm (WOA) with the combination of Salp Swarm Algorithm (SSA) hybridized with Lens Opposition-based Learning (LOBL) mechanism. The features obtained from the selection algorithm are then fed to hyper parameter optimized Long Short-Term Memory (LSTM) classifier to classify the normality and abnormality of seizures. The attained outcomes of the suggested approach exhibit a better classification rate with 98.43% accuracy on BU dataset, 99.71% accuracy on BB dataset, and 98.43% accuracy on TUH dataset.

show abstract

“…The mathematical expression of accuracy, sensitivity, specificity, F1-score, and MCC is given from Eqs. ( 23)- (27).…”

Section: Results and Performance Analysismentioning

confidence: 99%

Classification of Epileptic Seizures Using LSTM Based Zebra Optimization Algorithm with Hyperparameter Tunin

2024

IJIES

View full text Add to dashboard Cite

show abstract

“…The findings were derived from simulations, and to extend the same approach to different time series, users need to generate additional simulations under the underlying model. Rey et al 11 obtained the asymptotic distribution of certain types of entropies of histograms under the Multinomial law and developed a hypothesis test for comparing histograms of different numbers of bins. In order to use these results with the Permutation Entropy, the authors introduced a simplification: the patterns in π are independent.…”

Section: Introductionmentioning

confidence: 99%

The asymptotic distribution of the permutation entropy

Rey,

Frery,

Gambini

et al. 2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

Ordinal patterns serve as a robust symbolic transformation technique, enabling the unveiling of latent dynamics within time series data. This methodology involves constructing histograms of patterns, followed by the calculation of both entropy and statistical complexity—an avenue yet to be fully understood in terms of its statistical properties. While asymptotic results can be derived by assuming a multinomial distribution for histogram proportions, the challenge emerges from the non-independence present in the sequence of ordinal patterns. Consequently, the direct application of the multinomial assumption is questionable. This study focuses on the computation of the asymptotic distribution of permutation entropy, considering the inherent patterns’ correlation structure. Furthermore, the research delves into a comparative analysis, pitting this distribution against the entropy derived from a multinomial law. We present simulation algorithms for sampling time series with prescribed histograms of patterns and transition probabilities between them. Through this analysis, we better understand the intricacies of ordinal patterns and their statistical attributes.

show abstract