Approximate Entropy Values Research Articles

The value of linear and non-linear quantitative EEG analysis in paediatric epilepsy surgery: a machine learning approach

Epilepsy surgery is effective for patients with medication-resistant seizures, however 20–40% of them are not seizure free after surgery. Aim of this study is to evaluate the role of linear and non-linear EEG features to predict post-surgical outcome. We included 123 paediatric patients who underwent epilepsy surgery at Bambino Gesù Children Hospital (January 2009–April 2020). All patients had long term video-EEG monitoring. We analysed 1-min scalp interictal EEG (wakefulness and sleep) and extracted 13 linear and non-linear EEG features (power spectral density (PSD), Hjorth, approximate entropy, permutation entropy, Lyapunov and Hurst value). We used a logistic regression (LR) as feature selection process. To quantify the correlation between EEG features and surgical outcome we used an artificial neural network (ANN) model with 18 architectures. LR revealed a significant correlation between PSD of alpha band (sleep), Mobility index (sleep) and the Hurst value (sleep and awake) with outcome. The fifty-four ANN models gave a range of accuracy (46–65%) in predicting outcome. Within the fifty-four ANN models, we found a higher accuracy (64.8% ± 7.6%) in seizure outcome prediction, using features selected by LR. The combination of PSD of alpha band, mobility and the Hurst value positively correlate with good surgical outcome.

A Permutation Entropy analysis to determine significant daily intervals to improve risk stratification tasks from COVID patients.

SARS-CoV-2 infection has a wide range of clinical manifestations making its diagnosis difficult, which is an important problem to solve. We evaluated heart rate data extracted from the Stanford University database. The data set considers heart rate and step records of 118 patients, where 90 correspond to healthy individuals and 28 patients with COVID. Each daily record was divided into 5-minute segments, providing 288 data per patient. The date of symptom onset was considered as a reference point to extract subsets of data whose variability was considerable, such as 30 days before the date and 30 days after it. Each of the 60 segments of 288 data per patient was treated using Permutation Entropy, Approximate Entropy, Spectral Entropy and Singular Value Decomposition Entropy. The average of the data from each group was used to construct the circadian profiles which were analyzed using the Mann-Whitney-Wilcoxon test, determining the most relevant 5-minute segments, whose p-value was less than 0.05. In this way, the Spectral Entropy was discarded as it did not show any significantly different segment. The efficiency of the method was reflected in the performance of a logistic model for binary classification proposed in this work, which reflected an accuracy of 94.12% in the PE case, 88% in the ApEn case and 94% in the SVDE case. The proposed analysis turns out to be highly efficient when detecting significant segments that allow improving the classification tasks carried out by Machine Learning models, which provides a basis for the study of statistics such as entropy to delimit databases and improve the performance of classifier models.

A new aspect of the ApEn application to improve the PSO-ANFIS model to forecast Caspian Sea levels

Short-term forecasting of sea levels at the Caspian Sea plays an important issue for coastal planning. Therefore, a new aspect of the Approximate Entropy (ApEn) method application is studied to improve the Combined Particle Swarm Optimization and the Adaptive Network-based Fuzzy Inference System (PSO-ANFIS), Auto-Regressive Integrated Moving Average (ARIMA) models and Back Propagation Neural Networks (BP-NN). To evaluate the idea, seawater levels from 1961 to 2021 are categorized as training, validation (from 1961 to 2007 at Anzali station), and testing data (from 2008 to 2021 at Amirabad station). Results show the PSO-ANFIS model performance for forecasting the seawater level changes for four randomly selected time intervals and three critical periods. In addition, it is concluded that there are no considerable changes in the PSO-ANFIS model accuracy for embedding dimensions greater than 13 in forecasting of sea water level in the Caspian Sea. At the same time, the employed ApEn shows that there are no significant changes in approximate entropy values for block numbers more than 13 for the Caspian Sea levels. This shows the ApEn method performance to determine embedding dimensions for the forecaster models of time series. In addition, it resulted that the Caspian Sea water levels are on a decreasing trend on average by 5.495 cm every year until 2024 and the PSO-ANFIS model is reliable for 36 months as a short-term forecaster model. Comparing the developed PSO-ANFIS model with Long Short-Term Memory (LSTM) networks shows the PSO-ANFIS model significant superiority to the LSTM.

CEGH: A Hybrid Model Using CEEMD, Entropy, GRU, and History Attention for Intraday Stock Market Forecasting

Intraday stock time series are noisier and more complex than other financial time series with longer time horizons, which makes it challenging to predict. We propose a hybrid CEGH model for intraday stock market forecasting. The CEGH model contains four stages. First, we use complete ensemble empirical mode decomposition (CEEMD) to decompose the original intraday stock market data into different intrinsic mode functions (IMFs). Then, we calculate the approximate entropy (ApEn) values and sample entropy (SampEn) values of each IMF to eliminate noise. After that, we group the retained IMFs into four groups and predict the comprehensive signals of those groups using a feedforward neural network (FNN) or gate recurrent unit with history attention (GRU-HA). Finally, we obtain the final prediction results by integrating the prediction results of each group. The experiments were conducted on the U.S. and China stock markets to evaluate the proposed model. The results demonstrate that the CEGH model improved forecasting performance considerably. The creation of a collaboration between CEEMD, entropy-based denoising, and GRU-HA is our major contribution. This hybrid model could improve the signal-to-noise ratio of stock data and extract global dependence more comprehensively in intraday stock market forecasting.

Approximate entropy analysis across electroencephalographic rhythmic frequency bands during physiological aging of human brain.

Aging is the inevitable biological process that results in a progressive structural and functional decline associated with alterations in the resting/task-related brain activity, morphology, plasticity, and functionality. In the present study, we analyzed the effects of physiological aging on the human brain through entropy measures of electroencephalographic (EEG) signals. One hundred sixty-one participants were recruited and divided according to their age into young (n = 72) and elderly (n = 89) groups. Approximate entropy (ApEn) values were calculated in each participant for each EEG recording channel and both for the total EEG spectrum and for each of the main EEG frequency rhythms: delta (2-4Hz), theta (4-8Hz), alpha 1 (8-11Hz), alpha 2 (11-13Hz), beta 1 (13-20Hz), beta 2 (20-30Hz), and gamma (30-45Hz), to identify eventual statistical differences between young and elderly. To demonstrate that the ApEn represents the age-related brain changes, the computed ApEn values were used as features in an age-related classification of subjects (young vs elderly), through linear, quadratic, and cubic support vector machine (SVM). Topographic maps of the statistical results showed statistically significant difference between the ApEn values of the two groups found in the total spectrum and in delta, theta, beta 2, and gamma. The classifiers (linear, quadratic, and cubic SVMs) revealed high levels of accuracy (respectively 93.20 ± 0.37, 93.16 ± 0.30, 90.62 ± 0.62) and area under the curve (respectively 0.95, 0.94, 0.93). ApEn seems to be a powerful, very sensitive-specific measure for the study of cognitive decline and global cortical alteration/degeneration in the elderly EEG activity.

Modulation of Resting-State Brain Complexity After Bilateral Cerebellar Anodal Transcranial Direct Current Stimulation in Children with Autism Spectrum Disorders: a Randomized Controlled Trial Study.

Autism spectrum disorders (ASD) are heterogeneous neurodevelopmental disorders characterized by aberrant neural networks. Cerebellum is best known for its role in controlling motor behaviors; however, recently, there have been significant reports showed that dysfunction in cerebellar-cerebral networks contributes significantly to many of the clinical features of ASD. Hereby, this is a randomized controlled trial (RCT) study examining the potential modulating effects of bilateral anodal tDCS stimulation over cerebellar hemispheres on the resting-state brain complexity in children with ASD. Thirty-six children with ASD (aged 4-14) years old were divided equally and randomly into a tDCS treatment group, which underwent 10 sessions (20-min duration, five sessions/per week) of bilateral anodal tDCS stimulation applied over left and right cerebellar hemispheres, and control group underwent the same procedures, but with sham tDCS stimulation. Resting-state brain complexity was evaluated through recording and calculating the approximate entropy (ApxEnt) values of the resting-state electroencephalograph (EEG) data obtained from a 64-channel EEG system before and after the interventions. Repeated measures of ANOVA showed that tDCS had significant effects on the treatment group (Wilks' Lambda = 0.29, F (15, 16) = 2.67, p = 0.03) compared with the control group. Analyzed data showed a significant increase in the averaged ApxEnt values in the right frontal cortical region (F (1, 16) = 10.46, p = 0.005) after the bilateral cerebellar anodal tDCS stimulation. Besides, the Cohen's d effect size showed a large effect size (0.70-0.92) of bilateral cerebellar anodal tDCS on the ApxEnt values increases in the left and right frontal cortical regions, the right central cortical region, and left parietal cortical region. However, there were no any significant differences or increases in the brain complexity before and after the sham tDCS stimulation of the control group. Bilateral cerebellar anodal tDCS modulated and increased the brain complexity in children with ASD with no any reported adverse effect. Hereby, cerebellum and cerebellar-cerebral circuitry would serve as a promising target for non-invasive brain stimulation and neuro-modulation as a therapeutic intervention.

Fault Diagnosis of Rolling Bearing Based on an Improved Denoising Technique Using Complete Ensemble Empirical Mode Decomposition and Adaptive Thresholding Method

PurposeThe vibration signals captured for rolling bearing are generally polluted by excessive noise and can lose the fault information at the early development phase. Therefore, denoising is required to enhance the signal quality by improving kurtosis parameter sensitivity and envelope spectrum performance for early fault detection.MethodsIn this paper, an improved denoising technique is proposed for early faults diagnosis of rolling bearing based on the complete ensemble empirical mode decomposition (CEEMD) and adaptive thresholding (ATD) method. Firstly, the bearing vibration signals are decomposed into a set of various intrinsic mode functions (IMFs) using the CEEMD algorithm. The IMFs grouping and selection are formed based upon the approximate entropy and correlation coefficient value. After IMFs selection, the noise-predominant IMFs are subjected to adaptive thresholding for denoising and then added to the low-frequency IMFs for signal reconstruction.ResultsThe effectiveness of the proposed method denoised signals are tested on two experimental datasets based on kurtosis value and the envelope spectrum analysis. The results on the first dataset shows significant improvement in the kurtosis parameter values such as 92.99, 90.92, 97.39, and 78.35 for inner race fault in the bearing and 113.1, 170, 195.1, and 197.4 for outer race fault in the bearing rotating at four different speeds of 1797, 1772, 1750, and 1730 rpm, respectively, and enhances the amplitude of envelope spectrum to easily detect the bearing fault characteristics frequencies. The developed methods are further tested on the second dataset yielding similar improvement in kurtosis value and envelope spectrum analysis.ConclusionThe presented method results on experimental datasets illustrate that the proposed approach is an effective denoising technique for early fault detection in the rolling bearing compared to the original and other two conventional approaches.

Ultra-Short-Term Wind Speed Forecasting Using the Hybrid Model of Subseries Reconstruction and Broad Learning System

The traditional decomposition–combination wind speed forecasting model has high complexity and a long calculation time. As a result, an ultra-short-term wind speed hybrid forecasting model based on a broad learning system (BLS) that combines improved variational mode decomposition (EPSO-VMD, EVMD) and subseries reconstruction (SR) is proposed in this work. The values of K and α in the EVMD are determined by minimum mean envelope entropy (MMEE) and enhanced particle swarm optimization (EPSO), and EVMD is used to decompose the original wind speed data. SR is applied to recombine the subseries obtained by EVMD to improve the forecasting efficiency. The sample entropy (SE) is used to quantify the subseries’ complexity, and they are then adaptively divided into high-entropy and low-entropy subseries. Adjacent high-entropy subseries of approximate entropy values are merged to obtain a new group of reconstructed high-entropy subseries, while the low-entropy subseries merge into a new subseries as well. Then, the forecasting results of the reconstructed high- and low-entropy subseries are calculated via the BLS and ARIMA models. Numerical simulation results show that the proposed method is more effective than traditional methods.

Approximate Entropy in Canonical and Non-Canonical Fiction.

Computational textual aesthetics aims at studying observable differences between aesthetic categories of text. We use Approximate Entropy to measure the (un)predictability in two aesthetic text categories, i.e., canonical fiction (‘classics’) and non-canonical fiction (with lower prestige). Approximate Entropy is determined for series derived from sentence-length values and the distribution of part-of-speech-tags in windows of texts. For comparison, we also include a sample of non-fictional texts. Moreover, we use Shannon Entropy to estimate degrees of (un)predictability due to frequency distributions in the entire text. Our results show that the Approximate Entropy values can better differentiate canonical from non-canonical texts compared with Shannon Entropy, which is not true for the classification of fictional vs. expository prose. Canonical and non-canonical texts thus differ in sequential structure, while inter-genre differences are a matter of the overall distribution of local frequencies. We conclude that canonical fictional texts exhibit a higher degree of (sequential) unpredictability compared with non-canonical texts, corresponding to the popular assumption that they are more ‘demanding’ and ‘richer’. In using Approximate Entropy, we propose a new method for text classification in the context of computational textual aesthetics.

Effects of Future Information and Trajectory Complexity on Kinematic Signal and Muscle Activation during Visual-Motor Tracking.

Visual-motor tracking movement is a common and essential behavior in daily life. However, the contribution of future information to visual-motor tracking performance is not well understood in current research. In this study, the visual-motor tracking performance with and without future-trajectories was compared. Meanwhile, three task demands were designed to investigate their impact. Eighteen healthy young participants were recruited and instructed to track a target on a screen by stretching/flexing their elbow joint. The kinematic signals (elbow joint angle) and surface electromyographic (EMG) signals of biceps and triceps were recorded. The normalized integrated jerk (NIJ) and fuzzy approximate entropy (fApEn) of the joint trajectories, as well as the multiscale fuzzy approximate entropy (MSfApEn) values of the EMG signals, were calculated. Accordingly, the NIJ values with the future-trajectory were significantly lower than those without future-trajectory (p-value < 0.01). The smoother movement with future-trajectories might be related to the increasing reliance of feedforward control. When the task demands increased, the fApEn values of joint trajectories increased significantly, as well as the MSfApEn of EMG signals (p-value < 0.05). These findings enrich our understanding about visual-motor control with future information.

On Abrupt Changes of the Approximate and Sample Entropy Values in Supercomputer Power Consumption

When calculating the Approximate Entropy (ApEn) and the Sample Entropy (SampEn) of a time series, representing the course of supercomputer power consumption, seemingly unexplained abrupt changes sometimes appear. These sudden changes occur when calculating the course of ApEn and SampEn values using a floating time window and can be manifested also in other discrete-valued time series, such as the development of prices on stock exchanges, time series from birth-death models, count-data time series, etc. These abrupt changes are not continuous and it is clear that they do not reflect real changes in the complexity degree of the analyzed time series. This can cause erroneous detection of a change in the degree of complexity of the time series, which can trigger a false alarm that something unusual is happening in the complex system being monitored (human brain, engine gearbox, financial market, supercomputer infrastructure, etc.). This work reveals in detail the mechanism of this phenomenon and also proposes measures to prevent its occurrence.

Variabilidad de la frecuencia cardiaca en pacientes con cardiopatía chagásica

Se estima la prevalencia por Trypanosoma cruzi de 436.000 habitantes en Colombia, con casos anuales de 5.250, en población expuesta de 4.792.000 habitantes. La variabilidad de la frecuencia cardiaca (VFC) es la variabilidad en el tiempo, de un latido cardiaco, medido en un análisis de periodo temporal determinado. Su análisis permite determinar el equilibrio simpático-vagal de manera indirecta. Este estudio analizó las variables temporales y No lineales, en 19 pacientes Chagásicos y 19 controles, utilizándose un polígrafo de alta resolución y el software Kubios. La variable Desviación Estandar del Intervalo RR (SDRR) en la población control arrojó un promedio de 56,23±29,6ms vs 40,62±30,1ms, en los seropositivos; La Raíz Cuadrada del Promedio de la Suma de las Diferencias al Cuadrado de todos los intervalos Adyacentes (RMSSD) fue de 34,31±21,01ms y 31,94±37,33ms, para controles y Chagas, respectivamente. El número de los intervalos RR consecutivos, que difieren en más de 50ms entre sí (NN50), en controles 76,47±78,3 latidos vs 13,47±36,8 para seropositivos, que correspondió con el porcentaje de NN50 (pNN50) 12,3±13,3% y 2,64±6,0%, respectivamente, para el mismo orden de los grupos. Valores de Entropía Aproximada (ApEn) fueron 1,249±0,134, para controles y 0,959±0,325, para seropositivos y para la Entropía Muestral (SampEn) fue de 1,358±0,264 y 1,102±0,385, para controles y chagásicos, respectivamente. Se encontró mayor irregularidad de HRV en controles, que es reflejo de un mejor estado de salud.

A Novel Hybrid Approach for Partial Discharge Signal Detection Based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Approximate Entropy.

To eliminate the influence of white noise in partial discharge (PD) detection, we propose a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and approximate entropy (ApEn). By introducing adaptive noise into the decomposition process, CEEMDAN can effectively separate the original signal into different intrinsic mode functions (IMFs) with distinctive frequency scales. Afterward, the approximate entropy value of each IMF is calculated to eliminate noisy IMFs. Then, correlation coefficient analysis is employed to select useful IMFs that represent dominant PD features. Finally, real IMFs are extracted for PD signal reconstruction. On the basis of EEMD, CEEMDAN can further improve reconstruction accuracy and reduce iteration numbers to solve mode mixing problems. The results on both simulated and on-site PD signals show that the proposed method can be effectively employed for noise suppression and successfully extract PD pulses. The fusion algorithm combines the CEEMDAN algorithm and the ApEn algorithm with their respective advantages and has a better de-noising effect than EMD and EEMD.

Schizophrenia detection using MultivariateEmpirical Mode Decomposition and entropy measures from multichannel EEG signal

Multivariate analysis of the EEG signal for the detection of Schizophrenia condition is proposed here. Multivariate Empirical Mode Decomposition (MEMD) is used to decompose the EEG signal into Intrinsic Mode Functions (IMF) signal. The randomness measure of the IMF signal is determined by computing the entropy of the signal. Five entropy measures such as Approximate entropy, Sample entropy, Permutation entropy, Spectral entropy, and Singular Value Decomposition entropy are measured from the IMF signal. These entropy measures showed a significant difference (p<0.01) between the healthy controls (HC) and Schizophrenia (SZ) subjects. Many state-of-the-art (SoA) machine learning classifiers are trained on the feature matrix obtained from entropy values of the IMF signal, amongst them Support Vector Machine based on Radial Basis Function (SVM-RBF) provided the highest accuracy and F1-score of 93% for the 95 features. The area under the curve (AUC) value of 0.9831 was obtained using this classifier. These performance metrics suggests that computation of randomness measure such as entropy in the multivariate IMF domain provided better discriminating power in detection of Schizophrenia condition from the multichannel EEG signal.

Footwear and Cadence Affect Gait Variability in Runners with Patellofemoral Pain.

To examine the effects of increased cadence and minimalist footwear on lower-limb variability in runners with patellofemoral pain (PFP). Fifteen (12 female, 3 male) runners with PFP ran on an instrumented treadmill with three-dimensional motion capture in three randomly ordered conditions: (i) standard shoe at preferred cadence, (ii) standard shoe +10% cadence, and (iii) minimalist shoe at preferred cadence. Vector coding was used to calculate coordination variability between strides for select lower-limb joint couplings. Approximate entropy was calculated to assess continuous variability for segment kinematic and kinetic data and compared between conditions using repeated-measures ANOVA. One-dimensional statistical parametric mapping repeated-measures ANOVA was performed on the coordination variability data. Cohen's d effect size was calculated for all comparisons. Larger approximate entropy values (i.e., greater variability) were observed for the standard shoe +10% cadence versus the standard shoe at preferred cadence for hip flexion/extension (P < 0.001; d = 1.12), hip adduction/abduction (P < 0.001; d = 0.99) and ankle dorsiflexion/plantarflexion (P < 0.001; d = 1.37) kinematics, and knee flexion/extension moments (P < 0.001; d = 0.93). Greater variability was also observed in the minimalist shoe versus the standard shoe at preferred cadence for hip internal/external rotation moments (P < 0.001; d = 0.76), knee adduction/abduction moments (P < 0.001; d = 0.51), and knee internal/external rotation moments (P < 0.001; d = 1.02). One-dimensional statistical parametric mapping repeated-measures ANOVA revealed no significant differences in coordination variability between running conditions. Greater hip and knee kinematic and kinetic variability observed with either increased cadence or minimalist footwear may be beneficial for those with PFP.

Apatite Thermochemistry: The Simple Salt Approximation.

Drouet has recently comprehensively reviewed the thermochemistry of phosphate apatites, M10(PO4)6X2. On the basis of the data assembled, he has established an optimized additive set of data values based upon the component ions, M2+, P2O5, or PO43-, and halide or OH- ions, which yield phosphoapatite enthalpy and Gibbs energy values generally within 1% of their experimental values. In this paper, we introduce and compare the Simple Salt Approximation (SSA) for generation of the same thermodynamic values by addition of values for the component salts of the apatite. SSA is widely applicable to ionic systems so that familiarity with this procedure is worthwhile. Drouet's additive values focused on phosphoapatites yield better results (at 1%) than does the more general SSA (at ∼3%), but the SSA provides an alternative to data prediction when the Drouet additive factors are not available. In addition, we here use the SSA to generate approximate entropy values and estimate the Debye temperature of phosphoapatites under ambient conditions, yielding insight into the extent of activation of their vibrational modes.

A Rail Fault Diagnosis Method Based on Quartic C2 Hermite Improved Empirical Mode Decomposition Algorithm.

For compound fault detection of high-speed rail vibration signals, which presents a difficult problem, an early fault diagnosis method of an improved empirical mode decomposition (EMD) algorithm based on quartic C2 Hermite interpolation is presented. First, the quartic C2 Hermite interpolation improved EMD algorithm is used to decompose the original signal, and the intrinsic mode function (IMF) components are obtained. Second, singular value decomposition for the IMF components is performed to determine the principal components of the signal. Then, the signal is reconstructed and the kurtosis and approximate entropy values are calculated as the eigenvalues of fault diagnosis. Finally, fault diagnosis is executed based on the support vector machine (SVM). This method is applied for the fault diagnosis of high-speed rails, and experimental results show that the method presented in this paper is superior to the traditional EMD algorithm and greatly improves the accuracy of fault diagnosis.

Human pulses reveal health conditions by a piezoelectret sensor via the approximate entropy analysis

A piezoelectret pulse sensor combined with the approximate entropy (ApEn) analysis is utilized to detect human pulses to reveal health conditions. Inspired by the traditional Chinese medicine (TCM) with a foundation of more than 2500 years, human pulses are helpful in the diagnostics of illness as the body's vital energy circulates through blood vessels with branches connected to organs. A flexible cellular polypropylene (PP) piezoelectret film with a wooden cylinder substrate is used to emulate the pulse taking process in TCM to record the pulse characteristics. A group of 26 volunteers have been successfully diagnosed by the wearable sensing system and the approximate entropy analysis has been implemented to analyze the data. Results show a threshold approximate entropy value of 0.1 as the separation point between the volunteers of normal and abnormal health conditions.

Effects of manipulating the number of targets in U9, U11, U15 and U17 futsal players’ tactical behaviour

This study identified how the manipulation in the number of goal targets affects the tactical behaviour of players from different age groups (U9, U11, U15 and U17). Forty youth futsal players performed two small-sided games based on Gk + 4vs4 + Gk situation with one regular and two small targets. TACTO software was used to capture players and ball displacements. The following variables were computed and presented as absolute values, coefficient of variation and regularity (approximate entropy): (i) distance from each player to the team centre (DtC); (ii) distance from each player to the ball (DtB); (iii) distance between team centres (DbTC); and (iv) distance from team centre to the ball (DCtB). The team dispersion increased with two goal targets (mainly the DbTC, U9 and U17, large effects; U11 and U15, very large effects). Also, the use of two goal targets condition increased the variability in the DbTC (U9, small effects; U11 and U15 moderate effects; U17, very large effects) and DCtB (U9 and U17 moderate effects and U11 and U15 small effects). Overall, the approximate entropy values showed higher regularity in the condition with two targets. All age groups were sensitive to the manipulation of goal targets, however, the U9 were the most sensitive to the changes, as seen by the dispersion of players in the field. Thus, coaches can use one target to promote movement irregularity of players and two targets to increase the team dispersion, mainly in younger age groups that tend to be agglomerated around the ball.

Nonlinear analysis of heart rate variability of healthy subjects and patients with chronic obstructive pulmonary disease

Chronic obstructive pulmonary disease (COPD) is one of the causes of mortality worldwide with an increasing prevalence. Heart rate variability (HRV) reflects the regulation mechanism of the cardiac activity by the autonomic nervous system. The assessment of HRV by using nonlinear methods is more sensitive for the detection of complexity when compared to linear methods. This study aims to get information about the autonomic dysfunction occurred in patients with COPD by analysing the complexity of HRV. Electrocardiogram signals recorded from healthy subjects, patients with moderate COPD and severe COPD (eight subjects per group) were analysed. The HRV signals were acquired from ECG signals. Signals were reconstructed in the phase space and largest Lyapunov exponent (LLE), correlation dimension, Hurst exponent and approximate entropy (ApEn) values were calculated. It has seen that for the patients with COPD LLE, correlation dimension, Hurst exponent and ApEn values were less than control group. According to this, HRV complexity decreases in the presence of COPD. However, there is no significant difference between COPD groups and the severity of COPD has no effect on the chaoticity of the system. The results revealed that autonomic dysfunction occurred in patients with COPD is associated with reduced HRV complexity.