Entropy Profiling: A Reduced-Parametric Measure of Kolmogorov-Sinai Entropy from Short-Term HRV Signal.

Entropy profiling is a recently introduced approach that reduces parametric dependence in traditional Kolmogorov-Sinai (KS) entropy measurement algorithms. The choice of the threshold parameter r of vector distances in traditional entropy computations is crucial in deciding the accuracy of signal irregularity information retrieved by these methods. In addition to making parametric choices completely data-driven, entropy profiling generates a complete profile of entropy information as against a single entropy estimate (seen in traditional algorithms). The benefits of using "profiling" instead of "estimation" are: (a) precursory methods such as approximate and sample entropy that have had the limitation of handling short-term signals (less than 1000 samples) are now made capable of the same; (b) the entropy measure can capture complexity information from short and long-term signals without multi-scaling; and (c) this new approach facilitates enhanced information retrieval from short-term HRV signals. The novel concept of entropy profiling has greatly equipped traditional algorithms to overcome existing limitations and broaden applicability in the field of short-term signal analysis. In this work, we present a review of KS-entropy methods and their limitations in the context of short-term heart rate variability analysis and elucidate the benefits of using entropy profiling as an alternative for the same.

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.

Nonlinear Features from Multi-Modal Signals for Continuous Stress Monitoring.

Continuous monitoring of stress in individuals during their daily activities has become an inevitable need in present times. Unattended stress is a silent killer and may lead to fatal physical and mental disorders if left unidentified. Stress identification based on individual judgement often leads to under-diagnosis and delayed treatment possibilities. EEG-based stress monitoring is quite popular in this context, but impractical to use for continuous remote monitoring.Continuous remote monitoring of stress using signals acquired from everyday wearables like smart watches is the best alternative here. Non-EEG data such as heart rate and ectodermal activity can also act as indicators of physiological stress. In this work, we have explored the possibility of using nonlinear features from non-EEG data such as (a) heart rate, (b) ectodermal activity, (c) body temperature (d) SpO2 and (e) acceleration in detecting four different types of neurological states; namely (1) Relaxed state, (2) State of Physical stress, (3) State of Cognitive stress and (4) State of Emotional stress. Physiological data of 20 healthy adults have been used from the noneeg database of PhysioNet.Results: We used two machine learning models; a linear logistic regression and a nonlinear random forest to detect (a) stress from relaxed state and (4) the four different neurological states. We trained the models using linear and nonlinear features separately. For the 2-class and 4-class problems, using nonlinear features increased the accuracy of the models. Moreover, it is also proved in this study that by using nonlinear features, we can avoid the use of complex machine learning models.

Measurement of stress-induced sympathetic nervous activity using multi-wavelength PPG.

The onset of stress triggers sympathetic arousal (SA), which causes detectable changes to physiological parameters such as heart rate, blood pressure, dilation of the pupils and sweat release. The objective quantification of SA has tremendous potential to prevent and manage psychological disorders. Photoplethysmography (PPG), a non-invasive method to measure skin blood flow changes, has been used to estimate SA indirectly. However, the impact of various wavelengths of the PPG signal has not been investigated for estimating SA. In this study, we explore the feasibility of using various statistical and nonlinear features derived from peak-to-peak (AC) values of PPG signals of different wavelengths (green, blue, infrared and red) to estimate stress-induced changes in SA and compare their performances. The impact of two physical stressors: and Hand Grip are studied on 32 healthy individuals. Linear (Mean, s.d.) and nonlinear (Katz, Petrosian, Higuchi, SampEn, TotalSampEn) features are extracted from the PPG signal's AC amplitudes to identify the onset, continuation and recovery phases of those stressors. The results show that the nonlinear features are the most promising in detecting stress-induced sympathetic activity. TotalSampEn feature was capable of detecting stress-induced changes in SA for all wavelengths, whereas other features (Petrosian, AvgSampEn) are significant (AUC ≥ 0.8) only for IR and Red wavelengths. The outcomes of this study can be used to make device design decisions as well as develop stress detection algorithms.

Detection of fetal arrhythmias in non-invasive fetal ECG recordings using data-driven entropy profiling.

Objective.Fetal arrhythmias are a life-threatening disorder occurring in up to 2% of pregnancies. If identified, many fetal arrhythmias can be effectively treated using anti-arrhythmic therapies. In this paper, we present a novel method of detecting fetal arrhythmias in short length non-invasive fetal electrocardiography (NI-FECG) recordings.Approach.Our method consists of extracting a fetal heart rate time series from each NI-FECG recording and computing an entropy profile using a data-driven range of the entropy tolerance parameterr. To validate our approach, we apply our entropy profiling method to a large clinical data set of 318 NI-FECG recordings.Main Results.We demonstrate that our method (TotalSampEn) provides strong performance for classifying arrhythmic fetuses (AUC of 0.83) and outperforms entropy measures such asSampEn(AUC of 0.68) andFuzzyEn(AUC of 0.72). We also find that NI-FECG recordings incorrectly classified using the investigated entropy measures have significantly lower signal quality, and that excluding recordings of low signal quality (13.5% of recordings) increases the classification performance ofTotalSampEn(AUC of 0.90).Significance.The superior performance of our approach enables automated detection of fetal arrhythmias and warrants further investigation in a prospective clinical trial.

Performance Analysis of Entropy Methods in Detecting Epileptic Seizure from Surface Electroencephalograms.

Physiological signals like Electrocardiography (ECG) and Electroencephalography (EEG) are complex and nonlinear in nature. To retrieve diagnostic information from these, we need the help of nonlinear methods of analysis. Entropy estimation is a very popular approach in the nonlinear category, where entropy estimates are used as features for signal classification and analysis. In this study, we analyze and compare the performances of four entropy methods; namely Distribution entropy (DistEn), Shannon entropy (ShanEn), Renyi entropy (RenEn) and LempelZiv complexity (LempelZiv) as classification features to detect epileptic seizure (ES) from surface Electroencephalography (sEEG) signal. Experiments were conducted on sEEG data from 23 subjects, obtained from the CHB-MIT database of PhysioNet. ShanEn, RenEn and LempelZiv entropy are found to be potential features for accurate and consistent detection of ES from sEEG, across multiple channels and subjects.

Cross Entropy Profiling to Test Pattern Synchrony in Short-Term Signals.

Examining nonlinear bi-variate time series for pattern synchrony has been largely carried out by the cross sample entropy measure, X-SampEn, which is highly bound by parametric restrictions. Threshold parameter r is the one that limits X-SampEn estimations most adversely. An inappropriate r choice leads to erroneous synchrony detection, even for the case of X-SampEn analysis on simple synthetically generated signals like the MIX(P) process. This gives us an intimation of how difficult it would be for such synchrony measures to handle the more complex physiologic data. The recently introduced concept of entropy profiling has been proved to release such measures from the clutches of r dependence. In this study, we demonstrate how entropy profiling with respect to r can be implemented on cross entropy analysis, particularly X-SampEn. We have used different sets of simple MIX(P) processes for the purpose and validated the impact of X-SampEn profiling over X-SampEn estimation, with a special focus on short-term data. From results, we see that X-SampEn profiling alone can accurately classify MIX(P) signals based on pattern synchrony. Here, X-SampEn estimation fails undoubtedly, even at the higher data lengths where traditional SampEn estimation is known to perform with good accuracy.

Entropy Profiling to Detect ST Change in Heart Rate Variability Signals.

Elevation or depression in an electrocardiographic ST segment is an important indication of cardiac Ischemia. Computer-aided algorithms have been proposed in the recent past for the detection of ST change in ECG signals. Such algorithms are accompanied by difficulty in locating a functional ST segment from the ECG. Laborious signal processing tasks have to be carried out in order to precisely locate the start and end of an ST segment. In this work, we propose to detect ST change from heart rate variability (HRV) or RR-interval signals, rather than the ECG itself. Since HRV analysis does not require ST segment localization, we hypothesize an easier and more accurate automated ST change detection here. We use the recent concept of entropy profiling to detect ST change from RR interval data, where the estimation corresponds to irregularity information contained in the respective signals. We have compared results of SampEn, FuzzyEn and TotalSampEn (entropy profiling) on 18 normal and 28 ST-changed RR interval signals. SampEn and FuzzyEn give maximum AUCs of 0.64 and 0.62 respectively, at the data length N = 750. T otalSampEn shows a maximum AUC of 0.92 at N = 50, clearly proving its effectiveness on short-term signals and an AUC of 0.88 at N = 750, proving its efficiency over SampEn and F uzzyEn.

Multiscale entropy profiling to estimate complexity of heart rate dynamics.

In the analysis of signal regularity from a physiological system such as the human heart, Approximate entropy (H_{A}) and Sample entropy (H_{S}) have been the most popular statistical tools used so far. While studying heart rate dynamics, it nevertheless becomes more important to extract information about complexities associated with the heart, rather than the regularity of signal patterns produced by it. A complex physiological system does not necessarily produce irregular signals and vice versa. In order to equip a regularity statistic to see through the respective system's level of complexity, the idea of multiscaling was introduced in H_{S} estimation. Multiscaling ideally requires an input signal to be (a) long and (b) stationary. However, the longer the data is the less stationary it is. The requirement multiscaling places on its data length largely limits its accuracy. We propose a novel method of entropy profiling that makes multiscaling require very short signal segments, granting better prospects of signal stationarity and estimation accuracy. With entropy profiling, an efficient multiscale H_{S} based analysis requires only 500-beat signals of atrial fibrillated data, as opposed to the earlier case that required at least 20 000 beats.

Understanding Irregularity Characteristics of Short-Term HRV Signals Using Sample Entropy Profile.

Sample entropy (), a popularly used "regularity analysis" tool, has restrictions in handling short-term segments (largely ) of heart rate variability (HRV) data. For such short signals, the estimate either remains undefined or fails to retrieve "accurate" regularity information. These limitations arise due to the extreme dependence of on its functional parameters, in particular the tolerance . Evaluating at a single random choice of parameter is a major cause of concern in being able to extract reliable and complete regularity information from a given signal. Here, we hypothesize that, finding a complete profile of (in contrast to a single estimate) corresponding to a data specific set of values may facilitate enhanced information retrieval from short-term signals. We introduce a novel and computationally efficient concept of profiling in order to eliminate existing inaccuracies seen in the case of estimation. Using three different HRV datasets from the PhysioNet database-first, real and simulated, second, elderly and young, and third, healthy and arrhythmic; we demonstrate better definiteness and classification performance of profile based estimates ( and ) when compared to conventional and estimates. Our novelty is to identify the importance of reliability in short-term signal regularity analysis, and our proposed approach aims to enhance both quality and quantity of information from any short-term signal.

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.

Effect of embedding dimension on complexity measures in identifying Arrhythmia.

Entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn) are well established tools to analyze Heart Rate Variability (HRV) data. Critical parameters involved in these computations namely embedding dimension m and tolerance r are in most cases assumed to be 2 and 0.2*signal SD (standard devaition) respectively. Such assumptions do not work fairly across data sets and thus create misleading results in many cases. Problems with r have been addressed with the advent of newer entropy measures like Permutation entropy (PE), Fuzzy entropy (FuzzyEn) and Distribution entropy (DistEn) that simply eliminate, modify or replace r from calculations. On the other hand, the disadvantage of using a fixed assumed choice of m when such measures are used for data classification is yet to be investigated. The smallest variation in m may effect the extent of information retrieval from HRV data and hence it is extremely important to analyze different possibilities and outcomes of the same. In this study, we scrutinize the behavior of different entropy measures with regard to their classification performance at four different values of embedding dimension i.e., m = 2, 3,4 and 5. Normal and Arrhythmic RR intervals taken at data lengths ranging from 50 to 1000 have been used for the purpose. At any choice of m, DistEn and PE are the best measures to classify Arrhythmic data, whose AUC (Area under the ROC curve) values can go as high as 0.94 and 1 respectively. However PE performance becomes unstable with N for m > 3 (highest Δ being 0.3 at m = 5, Δ being the difference between minimum and maximum AUC). Irrespective of the choice of m, DistEn performance remains the most efficient and stable (highest Δ being only 0.03 at m = 4) for Arrhythmia classification. In the case of all other entropy measures, it is recommended that the value of m be chosen with discretion to ensure stability and efficiency in classification performance.

Distribution Entropy (DistEn): A complexity measure to detect arrhythmia from short length RR interval time series.

Heart rate complexity analysis is a powerful non-invasive means to diagnose several cardiac ailments. Non-linear tools of complexity measurement are indispensable in order to bring out the complete non-linear behavior of Physiological signals. The most popularly used non-linear tools to measure signal complexity are the entropy measures like Approximate entropy (ApEn) and Sample entropy (SampEn). But, these methods become unreliable and inaccurate at times, in particular, for short length data. Recently, a novel method of complexity measurement called Distribution Entropy (DistEn) was introduced, which showed reliable performance to capture complexity of both short term synthetic and short term physiologic data. This study aims to i) examine the competence of DistEn in discriminating Arrhythmia from Normal sinus rhythm (NSR) subjects, using RR interval time series data; ii) explore the level of consistency of DistEn with data length N; and iii) compare the performance of DistEn with ApEn and SampEn. Sixty six RR interval time series data belonging to two groups of cardiac conditions namely `Arrhythmia' and `NSR' have been used for the analysis. The data length N was varied from 50 to 1000 beats with embedding dimension m = 2 for all entropy measurements. Maximum ROC area obtained using ApEn, SampEn and DistEn were 0.83, 0.86 and 0.94 for data length 1000, 1000 and 500 beats respectively. The results show that DistEn undoubtedly exhibits a consistently high performance as a classification feature in comparison with ApEn and SampEn. Therefore, DistEn shows a promising behavior as bio marker for detecting Arrhythmia from short length RR interval data.

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

Complexity analysis of a given time series is executed using various measures of irregularity, the most commonly used being Approximate entropy (ApEn), Sample entropy (SampEn) and Fuzzy entropy (FuzzyEn). However, the dependence of these measures on the critical parameter of tolerance `r' leads to precarious results, owing to random selections of r. Attempts to eliminate the use of r in entropy calculations introduced a new measure of entropy namely distribution entropy (DistEn) based on the empirical probability distribution function (ePDF). DistEn completely avoids the use of a variance dependent parameter like r and replaces it by a parameter M, which corresponds to the number of bins used in the histogram to calculate it. When tested for synthetic data, M has been observed to produce a minimal effect on DistEn as compared to the effect of r on other entropy measures. Also, DistEn is said to be relatively stable with data length (N) variations, as far as synthetic data is concerned. However, these claims have not been analyzed for physiological data. Our study evaluates the effect of data length N and bin number M on the performance of DistEn using both synthetic and physiologic time series data. Synthetic logistic data of `Periodic' and `Chaotic' levels of complexity and 40 RR interval time series belonging to two groups of healthy aging population (young and elderly) have been used for the analysis. The stability and consistency of DistEn as a complexity measure as well as a classifier have been studied. Experiments prove that the parameters N and M are more influential in deciding the efficacy of DistEn performance in the case of physiologic data than synthetic data. Therefore, a generalized random selection of M for a given data length N may not always be an appropriate combination to yield good performance of DistEn for physiologic data.