Effect of data length and bin numbers on distribution entropy (DistEn) measurement in analyzing healthy aging

Multiscale distribution entropy analysis of short epileptic EEG signals

This paper proposes an information-theoretic measure for discriminating epileptic patterns in short-term electroencephalogram (EEG) recordings. Considering nonlinearity and nonstationarity in EEG signals, quantifying complexity has been preferred. To decipher abnormal epileptic EEGs, i.e., ictal and interictal EEGs, via short-term EEG recordings, a distribution entropy (DE) is used, motivated by its robustness on the signal length. In addition, to reflect the dynamic complexity inherent in EEGs, a multiscale entropy analysis is incorporated. Here, two multiscale distribution entropy (MDE) methods using the coarse-graining and moving-average procedures are presented. Using two popular epileptic EEG datasets, i.e., the Bonn and the Bern-Barcelona datasets, the performance of the proposed MDEs is verified. Experimental results show that the proposed MDEs are robust to the length of EEGs, thus reflecting complexity over multiple time scales. In addition, the proposed MDEs are consistent irrespective of the selection of short-term EEGs from the entire EEG recording. By evaluating the Man-Whitney U test and classification performance, the proposed MDEs can better discriminate epileptic EEGs than the existing methods. Moreover, the proposed MDE with the moving-average procedure performs marginally better than one with the coarse-graining. The experimental results suggest that the proposed MDEs are applicable to practical seizure detection applications.

Detection of Coronary Artery Disease Using Multi-Domain Feature Fusion of Multi-Channel Heart Sound Signals

Heart sound signals reflect valuable information about heart condition. Previous studies have suggested that the information contained in single-channel heart sound signals can be used to detect coronary artery disease (CAD). But accuracy based on single-channel heart sound signal is not satisfactory. This paper proposed a method based on multi-domain feature fusion of multi-channel heart sound signals, in which entropy features and cross entropy features are also included. A total of 36 subjects enrolled in the data collection, including 21 CAD patients and 15 non-CAD subjects. For each subject, five-channel heart sound signals were recorded synchronously for 5 min. After data segmentation and quality evaluation, 553 samples were left in the CAD group and 438 samples in the non-CAD group. The time-domain, frequency-domain, entropy, and cross entropy features were extracted. After feature selection, the optimal feature set was fed into the support vector machine for classification. The results showed that from single-channel to multi-channel, the classification accuracy has increased from 78.75% to 86.70%. After adding entropy features and cross entropy features, the classification accuracy continued to increase to 90.92%. The study indicated that the method based on multi-domain feature fusion of multi-channel heart sound signals could provide more information for CAD detection, and entropy features and cross entropy features played an important role in it.

Modified Distribution Entropy as a Complexity Measure of Heart Rate Variability (HRV) Signal

The complexity of a heart rate variability (HRV) signal is considered an important nonlinear feature to detect cardiac abnormalities. This work aims at explaining the physiological meaning of a recently developed complexity measurement method, namely, distribution entropy (DistEn), in the context of HRV signal analysis. We thereby propose modified distribution entropy (mDistEn) to remove the physiological discrepancy involved in the computation of DistEn. The proposed method generates a distance matrix that is devoid of over-exerted multi-lag signal changes. Restricted element selection in the distance matrix makes "mDistEn" a computationally inexpensive and physiologically more relevant complexity measure in comparison to DistEn.

Detection of epileptic seizure based on entropy analysis of short-term EEG

Entropy measures that assess signals’ complexity have drawn increasing attention recently in biomedical field, as they have shown the ability of capturing unique features that are intrinsic and physiologically meaningful. In this study, we applied entropy analysis to electroencephalogram (EEG) data to examine its performance in epilepsy detection based on short-term EEG, aiming at establishing a short-term analysis protocol with optimal seizure detection performance. Two classification problems were considered, i.e., 1) classifying interictal and ictal EEGs (epileptic group) from normal EEGs; and 2) classifying ictal from interictal EEGs. For each problem, we explored two protocols to analyze the entropy of EEG: i) using a single analytical window with different window lengths, and ii) using an average of multiple windows for each window length. Two entropy methods—fuzzy entropy (FuzzyEn) and distribution entropy (DistEn)–were used that have valid outputs for any given data lengths. We performed feature selection and trained classifiers based on a cross-validation process. The results show that performance of FuzzyEn and DistEn may complement each other and the best performance can be achieved by combining: 1) FuzzyEn of one 5-s window and the averaged DistEn of five 1-s windows for classifying normal from epileptic group (accuracy: 0.93, sensitivity: 0.91, specificity: 0.96); and 2) the averaged FuzzyEn of five 1-s windows and DistEn of one 5-s window for classifying ictal from interictal EEGs (accuracy: 0.91, sensitivity: 0.93, specificity: 0.90). Further studies are warranted to examine whether this proposed short-term analysis procedure can help track the epileptic activities in real time and provide prompt feedback for clinical practices.

Secondary measures of regularity from an entropy profile in detecting Arrhythmia

The most recently introduced concept of a `complete entropy profile' is a non-parametric (with regard to tolerance r) approach of entropy estimation. Given a signal, on generating its complete entropy profile, numerous secondary measures of regularity can be derived from the same. These profile based measures are seen to outperform the traditional ApEn statistic (evaluated at a single r) in estimating signal regularity. In this paper, we compare the performance of ApEn (evaluated at an r = 0.15 * SD of signal and an m = 2) with that of profile based measures such as MaxApEn, TotalApEn, AvgApEn, SDApEn, kurtApEn and skewApEn, in detecting `Arrhythmic' RR interval signals from `Normal' RR interval signals. Results indisputably prove the superiority of AvgApEn (AUC > 0.9 at data lengths N ≥ 200) and MaxApEn (AUC > 0.75 at all data lengths) as regularity statistics in detecting Arrhythmia, above all the other measures used.

Stability, Consistency and Performance of Distribution Entropy in Analysing Short Length Heart Rate Variability (HRV) Signal

Distribution entropy (DistEn) is a recently developed measure of complexity that is used to analyse heart rate variability (HRV) data. Its calculation requires two input parameters—the embedding dimension m, and the number of bins M which replaces the tolerance parameter r that is used by the existing approximation entropy (ApEn) and sample entropy (SampEn) measures. The performance of DistEn can also be affected by the data length N. In our previous studies, we have analyzed stability and performance of DistEn with respect to one parameter (m or M) or combination of two parameters (N and M). However, impact of varying all the three input parameters on DistEn is not yet studied. Since DistEn is predominantly aimed at analysing short length heart rate variability (HRV) signal, it is important to comprehensively study the stability, consistency and performance of the measure using multiple case studies. In this study, we examined the impact of changing input parameters on DistEn for synthetic and physiological signals. We also compared the variations of DistEn and performance in distinguishing physiological (Elderly from Young) and pathological (Healthy from Arrhythmia) conditions with ApEn and SampEn. The results showed that DistEn values are minimally affected by the variations of input parameters compared to ApEn and SampEn. DistEn also showed the most consistent and the best performance in differentiating physiological and pathological conditions with various of input parameters among reported complexity measures. In conclusion, DistEn is found to be the best measure for analysing short length HRV time series.

Influence of embedding dimension on distribution entropy in analyzing heart rate variability

Distribution entropy (DistEn) is a recent measure of complexity that is used to analyze Heart Rate Variability (HRV) data. DistEn which is a function of data length N, number of bins M and embedding dimension m is known to be stable and consistent with respect to parameters N and M respectively. Also, (N, M) are known to have a combined effect in deciding performance of DistEn as a classification feature. But, all such analysis have mostly ignored the influence of the third parameter m on DistEn properties. Though a random fixed choice of m value has so far succeeded in portraying the effect of other parameters on DistEn, it is considered equally important to reveal the influence of a varying m on DistEn and its characteristics. This study examines the impact of m on the stability, consistency and performance of DistEn when the latter is used to analyze HRV data belonging to (i) healthy subjects discerned by age and (ii) subjects discerned by their heart's physiologic condition. Here, data length N of each signal is varied from 50 to 1000, while the number of bins M used varies from 100 to 2000. Information pertaining to m variations is obtained by carrying out experiments at four different values of embedding dimension; m = 2, 3,4 and 5. The study shows that the stability, consistency and classification performance of DistEn is not much influenced by changes in m.

Classification of 5-S Epileptic EEG Recordings Using Distribution Entropy and Sample Entropy

Epilepsy is an electrophysiological disorder of the brain, the hallmark of which is recurrent and unprovoked seizures. Electroencephalogram (EEG) measures electrical activity of the brain that is commonly applied as a non-invasive technique for seizure detection. Although a vast number of publications have been published on intelligent algorithms to classify interictal and ictal EEG, it remains an open question whether they can be detected using short-length EEG recordings. In this study, we proposed three protocols to select 5 s EEG segment for classifying interictal and ictal EEG from normal. We used the publicly-accessible Bonn database, which consists of normal, interical, and ictal EEG signals with a length of 4097 sampling points (23.6 s) per record. In this study, we selected three segments of 868 points (5 s) length from each recordings and evaluated results for each of them separately. The well-studied irregularity measure—sample entropy (SampEn)—and a more recently proposed complexity measure—distribution entropy (DistEn)—were used as classification features. A total of 20 combinations of input parameters m and τ for the calculation of SampEn and DistEn were selected for compatibility. Results showed that SampEn was undefined for half of the used combinations of input parameters and indicated a large intra-class variance. Moreover, DistEn performed robustly for short-length EEG data indicating relative independence from input parameters and small intra-class fluctuations. In addition, it showed acceptable performance for all three classification problems (interictal EEG from normal, ictal EEG from normal, and ictal EEG from interictal) compared to SampEn, which showed better results only for distinguishing normal EEG from interictal and ictal. Both SampEn and DistEn showed good reproducibility and consistency, as evidenced by the independence of results on analysing protocol.