Abstract:In this letter, the authors propose a new entropy measure for analysis of time series. This measure is termed as the state space correlation entropy (SSCE). The state space reconstruction is used to evaluate the embedding vectors of a time series. The SSCE is computed from the probability of the correlations of the embedding vectors. The performance of SSCE measure is evaluated using both synthetic and real valued signals. The experimental results reveal that, the proposed SSCE measure along with SVM classifie… Show more
“…The limitation of this work is that we used multi-channel EEG recordings obtained from only 25 subjects. In future, we intend to consider other entropy-based measures such as slope entropy [ 50 ], distribution entropy [ 51 ], state space domain correlation entropy [ 52 , 53 ], and other entropy measures [ 31 ] to improve the classification performance of sleep stages using more subjects.…”
The categorization of sleep stages helps to diagnose different sleep-related ailments. In this paper, an entropy-based information–theoretic approach is introduced for the automated categorization of sleep stages using multi-channel electroencephalogram (EEG) signals. This approach comprises of three stages. First, the decomposition of multi-channel EEG signals into sub-band signals or modes is performed using a novel multivariate projection-based fixed boundary empirical wavelet transform (MPFBEWT) filter bank. Second, entropy features such as bubble and dispersion entropies are computed from the modes of multi-channel EEG signals. Third, a hybrid learning classifier based on class-specific residuals using sparse representation and distances from nearest neighbors is used to categorize sleep stages automatically using entropy-based features computed from MPFBEWT domain modes of multi-channel EEG signals. The proposed approach is evaluated using the multi-channel EEG signals obtained from the cyclic alternating pattern (CAP) sleep database. Our results reveal that the proposed sleep staging approach has obtained accuracies of 91.77%, 88.14%, 80.13%, and 73.88% for the automated categorization of wake vs. sleep, wake vs. rapid eye movement (REM) vs. Non-REM, wake vs. light sleep vs. deep sleep vs. REM sleep, and wake vs. S1-sleep vs. S2-sleep vs. S3-sleep vs. REM sleep schemes, respectively. The developed method has obtained the highest overall accuracy compared to the state-of-art approaches and is ready to be tested with more subjects before clinical application.
“…The limitation of this work is that we used multi-channel EEG recordings obtained from only 25 subjects. In future, we intend to consider other entropy-based measures such as slope entropy [ 50 ], distribution entropy [ 51 ], state space domain correlation entropy [ 52 , 53 ], and other entropy measures [ 31 ] to improve the classification performance of sleep stages using more subjects.…”
The categorization of sleep stages helps to diagnose different sleep-related ailments. In this paper, an entropy-based information–theoretic approach is introduced for the automated categorization of sleep stages using multi-channel electroencephalogram (EEG) signals. This approach comprises of three stages. First, the decomposition of multi-channel EEG signals into sub-band signals or modes is performed using a novel multivariate projection-based fixed boundary empirical wavelet transform (MPFBEWT) filter bank. Second, entropy features such as bubble and dispersion entropies are computed from the modes of multi-channel EEG signals. Third, a hybrid learning classifier based on class-specific residuals using sparse representation and distances from nearest neighbors is used to categorize sleep stages automatically using entropy-based features computed from MPFBEWT domain modes of multi-channel EEG signals. The proposed approach is evaluated using the multi-channel EEG signals obtained from the cyclic alternating pattern (CAP) sleep database. Our results reveal that the proposed sleep staging approach has obtained accuracies of 91.77%, 88.14%, 80.13%, and 73.88% for the automated categorization of wake vs. sleep, wake vs. rapid eye movement (REM) vs. Non-REM, wake vs. light sleep vs. deep sleep vs. REM sleep, and wake vs. S1-sleep vs. S2-sleep vs. S3-sleep vs. REM sleep schemes, respectively. The developed method has obtained the highest overall accuracy compared to the state-of-art approaches and is ready to be tested with more subjects before clinical application.
“…Among all these more advanced mathematical methods, those based on signal complexity, regularity, or predictability estimation are gaining momentum due to their ability of capturing the subtle differences among subjects. Approximate Entropy (ApEn) [8], Sample Entropy (SampEn) [9], Fuzzy Entropy (FuzzEn) [10], Dispersion Entropy [11], State-Space Correlation Entropy [12], Bubble Entropy [13], Lempel Ziv Complexity (LZC) [14], Detrended Fluctuation Analysis (DFA) [15], Distribution Entropy (DistEn) [16], and Permutation Entropy (PE) [17], are just a few of these methods that have been applied successfully in the context of biomedical records, including glucose time series in some cases [18,19,20,21,22,23]. Specifically, Permutation Entropy (PE) [17] is a complexity measure that is receiving a lot of attention in the last years.…”
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Highlights• First time Permutation Entropy is applied to glucose time series.• Test of different customizations for Permutation Entropy in order to address equal values and amplitude variations.• Prediction of evolution to diabetes based on a Permutation Entropy analysis of the glucose time series.
“…However, its use has some important limitations. For example, it should not be applied to long duration signals because more computations are required for real-time implementation (Tripathy et al, 2017 ).…”
Background: Beat-to-beat variability in action potential duration (APD) is an intrinsic property of cardiac tissue and is altered in pro-arrhythmic states. However, it has never been examined in mice.Methods: Left atrial or ventricular monophasic action potentials (MAPs) were recorded from Langendorff-perfused mouse hearts during regular 8 Hz pacing. Time-domain, frequency-domain and non-linear analyses were used to quantify APD variability.Results: Mean atrial APD (90% repolarization) was 23.5 ± 6.3 ms and standard deviation (SD) was 0.9 ± 0.5 ms (n = 6 hearts). Coefficient of variation (CoV) was 4.0 ± 1.9% and root mean square (RMS) of successive differences in APDs was 0.3 ± 0.2 ms. The peaks for low- and high-frequency were 0.7 ± 0.5 and 2.7 ± 0.9 Hz, respectively, with percentage powers of 39.0 ± 20.5 and 59.3 ± 22.9%. Poincaré plots of APDn+1 against APDn revealed ellipsoid shapes. The ratio of the SD along the line-of-identity (SD2) to the SD perpendicular to the line-of-identity (SD1) was 8.28 ± 4.78. Approximate and sample entropy were 0.57 ± 0.12 and 0.57 ± 0.15, respectively. Detrended fluctuation analysis revealed short- and long-term fluctuation slopes of 1.80 ± 0.15 and 0.85 ± 0.29, respectively. When compared to atrial APDs, ventricular APDs were longer (ANOVA, P < 0.05), showed lower mean SD and CoV but similar RMS of successive differences in APDs and showed lower SD2 (P < 0.05). No difference in the remaining parameters was observed.Conclusion: Beat-to-beat variability in APD is observed in mouse hearts during regular pacing. Atrial MAPs showed greater degree of variability than ventricular MAPs. Non-linear techniques offer further insights on short-term and long-term variability and signal complexity.
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