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Zhou Z, Jiang Y, Liu W, Wu R, Li Z, Guan W. A Fast Algorithm for Estimating Two-Dimensional Sample Entropy Based on an Upper Confidence Bound and Monte Carlo Sampling. ENTROPY (BASEL, SWITZERLAND) 2024; 26:155. [PMID: 38392410 PMCID: PMC10887568 DOI: 10.3390/e26020155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Revised: 02/07/2024] [Accepted: 02/07/2024] [Indexed: 02/24/2024]
Abstract
The two-dimensional sample entropy marks a significant advance in evaluating the regularity and predictability of images in the information domain. Unlike the direct computation of sample entropy, which incurs a time complexity of O(N2) for the series with N length, the Monte Carlo-based algorithm for computing one-dimensional sample entropy (MCSampEn) markedly reduces computational costs by minimizing the dependence on N. This paper extends MCSampEn to two dimensions, referred to as MCSampEn2D. This new approach substantially accelerates the estimation of two-dimensional sample entropy, outperforming the direct method by more than a thousand fold. Despite these advancements, MCSampEn2D encounters challenges with significant errors and slow convergence rates. To counter these issues, we have incorporated an upper confidence bound (UCB) strategy in MCSampEn2D. This strategy involves assigning varied upper confidence bounds in each Monte Carlo experiment iteration to enhance the algorithm's speed and accuracy. Our evaluation of this enhanced approach, dubbed UCBMCSampEn2D, involved the use of medical and natural image data sets. The experiments demonstrate that UCBMCSampEn2D achieves a 40% reduction in computational time compared to MCSampEn2D. Furthermore, the errors with UCBMCSampEn2D are only 30% of those observed in MCSampEn2D, highlighting its improved accuracy and efficiency.
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Affiliation(s)
- Zeheng Zhou
- School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
| | - Ying Jiang
- School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
| | - Weifeng Liu
- School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
| | - Ruifan Wu
- School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
| | - Zerong Li
- School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
| | - Wenchao Guan
- School of Computer Science and Engineering, Guangdong Province Key Laboratory of Computational Science, Sun Yat-sen University, Guangzhou 510275, China
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2
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Kouka M, Cuesta-Frau D, Moltó-Gallego V. Slope Entropy Characterisation: An Asymmetric Approach to Threshold Parameters Role Analysis. ENTROPY (BASEL, SWITZERLAND) 2024; 26:82. [PMID: 38248207 PMCID: PMC10814979 DOI: 10.3390/e26010082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2023] [Revised: 01/15/2024] [Accepted: 01/15/2024] [Indexed: 01/23/2024]
Abstract
Slope Entropy (SlpEn) is a novel method recently proposed in the field of time series entropy estimation. In addition to the well-known embedded dimension parameter, m, used in other methods, it applies two additional thresholds, denoted as δ and γ, to derive a symbolic representation of a data subsequence. The original paper introducing SlpEn provided some guidelines for recommended specific values of these two parameters, which have been successfully followed in subsequent studies. However, a deeper understanding of the role of these thresholds is necessary to explore the potential for further SlpEn optimisations. Some works have already addressed the role of δ, but in this paper, we extend this investigation to include the role of γ and explore the impact of using an asymmetric scheme to select threshold values. We conduct a comparative analysis between the standard SlpEn method as initially proposed and an optimised version obtained through a grid search to maximise signal classification performance based on SlpEn. The results confirm that the optimised version achieves higher time series classification accuracy, albeit at the cost of significantly increased computational complexity.
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Affiliation(s)
- Mahdy Kouka
- Department of System Informatics and Computers, Universitat Politècnica de València, 03801 Alcoy, Spain; (M.K.); (V.M.-G.)
| | - David Cuesta-Frau
- Department of System Informatics and Computers, Universitat Politècnica de València, 03801 Alcoy, Spain; (M.K.); (V.M.-G.)
- Technological Institute of Informatics, Universitat Politècnica de València, 03801 Alcoy, Spain
| | - Vicent Moltó-Gallego
- Department of System Informatics and Computers, Universitat Politècnica de València, 03801 Alcoy, Spain; (M.K.); (V.M.-G.)
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3
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Rostaghi M, Khatibi MM, Ashory MR, Azami H. Refined Composite Multiscale Fuzzy Dispersion Entropy and Its Applications to Bearing Fault Diagnosis. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1494. [PMID: 37998186 PMCID: PMC10670069 DOI: 10.3390/e25111494] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2023] [Revised: 10/14/2023] [Accepted: 10/24/2023] [Indexed: 11/25/2023]
Abstract
Rotary machines often exhibit nonlinear behavior due to factors such as nonlinear stiffness, damping, friction, coupling effects, and defects. Consequently, their vibration signals display nonlinear characteristics. Entropy techniques prove to be effective in detecting these nonlinear dynamic characteristics. Recently, an approach called fuzzy dispersion entropy (DE-FDE) was introduced to quantify the uncertainty of time series. FDE, rooted in dispersion patterns and fuzzy set theory, addresses the sensitivity of DE to its parameters. However, FDE does not adequately account for the presence of multiple time scales inherent in signals. To address this limitation, the concept of multiscale fuzzy dispersion entropy (MFDE) was developed to capture the dynamical variability of time series across various scales of complexity. Compared to multiscale DE (MDE), MFDE exhibits reduced sensitivity to noise and higher stability. In order to enhance the stability of MFDE, we propose a refined composite MFDE (RCMFDE). In comparison with MFDE, MDE, and RCMDE, RCMFDE's performance is assessed using synthetic signals and three real bearing datasets. The results consistently demonstrate the superiority of RCMFDE in detecting various patterns within synthetic and real bearing fault data. Importantly, classifiers built upon RCMFDE achieve notably high accuracy values for bearing fault diagnosis applications, outperforming classifiers based on refined composite multiscale dispersion and sample entropy methods.
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Affiliation(s)
- Mostafa Rostaghi
- Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran; (M.R.); (M.R.A.)
| | - Mohammad Mahdi Khatibi
- Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran; (M.R.); (M.R.A.)
| | - Mohammad Reza Ashory
- Modal Analysis (MA) Research Laboratory, Faculty of Mechanical Engineering, Semnan University, Semnan 35131-19111, Iran; (M.R.); (M.R.A.)
| | - Hamed Azami
- Centre for Addiction and Mental Health, University of Toronto, Toronto, ON M6J 1H1, Canada;
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4
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Ding XW, Liu ZT, Li DY, He Y, Wu M. Electroencephalogram Emotion Recognition Based on Dispersion Entropy Feature Extraction Using Random Oversampling Imbalanced Data Processing. IEEE Trans Cogn Dev Syst 2022. [DOI: 10.1109/tcds.2021.3074811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Affiliation(s)
- Xue-Wen Ding
- School of Automation, Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, and Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, China University of Geosciences, Wuhan, China
| | - Zhen-Tao Liu
- School of Automation, Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, and Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, China University of Geosciences, Wuhan, China
| | - Dan-Yun Li
- School of Automation, Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, and Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, China University of Geosciences, Wuhan, China
| | - Yong He
- School of Automation, Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, and Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, China University of Geosciences, Wuhan, China
| | - Min Wu
- School of Automation, Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, and Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, China University of Geosciences, Wuhan, China
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5
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Chen C, da Silva B, Chen R, Li S, Li J, Liu C. Evaluation of Fast Sample Entropy Algorithms on FPGAs: From Performance to Energy Efficiency. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1177. [PMID: 36141063 PMCID: PMC9498029 DOI: 10.3390/e24091177] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Revised: 08/09/2022] [Accepted: 08/18/2022] [Indexed: 06/16/2023]
Abstract
Entropy is one of the most fundamental notions for understanding complexity. Among all the methods to calculate the entropy, sample entropy (SampEn) is a practical and common method to estimate time-series complexity. Unfortunately, SampEn is a time-consuming method growing in quadratic times with the number of elements, which makes this method unviable when processing large data series. In this work, we evaluate hardware SampEn architectures to offload computation weight, using improved SampEn algorithms and exploiting reconfigurable technologies, such as field-programmable gate arrays (FPGAs), a reconfigurable technology well-known for its high performance and power efficiency. In addition to the fundamental disclosed straightforward SampEn (SF) calculation method, this study evaluates optimized strategies, such as bucket-assist (BA) SampEn and lightweight SampEn based on BubbleSort (BS-LW) and MergeSort (MS-LW) on an embedded CPU, a high-performance CPU and on an FPGA using simulated data and real-world electrocardiograms (ECG) as input data. Irregular storage space and memory access of enhanced algorithms is also studied and estimated in this work. These fast SampEn algorithms are evaluated and profiled using metrics such as execution time, resource use, power and energy consumption based on input data length. Finally, although the implementation of fast SampEn is not significantly faster than versions running on a high-performance CPU, FPGA implementations consume one or two orders of magnitude less energy than a high-performance CPU.
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Affiliation(s)
- Chao Chen
- School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China
- Department of Electronics and Informatics (ETRO), Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium
| | - Bruno da Silva
- Department of Electronics and Informatics (ETRO), Vrije Universiteit Brussel (VUB), 1050 Brussels, Belgium
| | - Ruiqi Chen
- VeriMake Research, Nanjing Renmian Integrated Circuit Technology Co., Ltd., Nanjing 210096, China
| | - Shun Li
- College of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, China
| | - Jianqing Li
- School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China
| | - Chengyu Liu
- School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China
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6
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Liu W, Jiang Y, Xu Y. A Super Fast Algorithm for Estimating Sample Entropy. ENTROPY 2022; 24:e24040524. [PMID: 35455187 PMCID: PMC9027109 DOI: 10.3390/e24040524] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2022] [Revised: 03/30/2022] [Accepted: 04/02/2022] [Indexed: 02/05/2023]
Abstract
Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as −log(B/A), where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with m+1, for a predetermined positive integer m. It has been widely used to analyze physiological signals. As computing sample entropy is time consuming, the box-assisted, bucket-assisted, x-sort, assisted sliding box, and kd-tree-based algorithms were proposed to accelerate its computation. These algorithms require O(N2) or O(N2−1m+1) computational complexity, where N is the length of the time series analyzed. When N is big, the computational costs of these algorithms are large. We propose a super fast algorithm to estimate sample entropy based on Monte Carlo, with computational costs independent of N (the length of the time series) and the estimation converging to the exact sample entropy as the number of repeating experiments becomes large. The convergence rate of the algorithm is also established. Numerical experiments are performed for electrocardiogram time series, electroencephalogram time series, cardiac inter-beat time series, mechanical vibration signals (MVS), meteorological data (MD), and 1/f noise. Numerical results show that the proposed algorithm can gain 100–1000 times speedup compared to the kd-tree and assisted sliding box algorithms while providing satisfactory approximate accuracy.
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Affiliation(s)
- Weifeng Liu
- Guangdong Province Key Laboratory of Computational Science, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China;
| | - Ying Jiang
- Guangdong Province Key Laboratory of Computational Science, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China;
- Correspondence:
| | - Yuesheng Xu
- Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529, USA;
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7
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Discriminating Bacterial Infection from Other Causes of Fever Using Body Temperature Entropy Analysis. ENTROPY 2022; 24:e24040510. [PMID: 35455174 PMCID: PMC9024484 DOI: 10.3390/e24040510] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/23/2022] [Revised: 03/31/2022] [Accepted: 04/02/2022] [Indexed: 11/17/2022]
Abstract
Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have emerged. These are not only based on absolute thresholds but also on patterns and temporal dynamics of these time series, thus providing promising tools for early diagnosis. The present study applies three time series entropy calculation methods (Slope Entropy, Approximate Entropy, and Sample Entropy) to body temperature records of patients with bacterial infections and other causes of fever in search of possible differences that could be exploited for automatic classification. In the comparative analysis, Slope Entropy proved to be a stable and robust method that could bring higher sensitivity to the realm of entropy tools applied in this context of clinical thermometry. This method was able to find statistically significant differences between the two classes analyzed in all experiments, with sensitivity and specificity above 70% in most cases.
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8
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Munoz R, Olivares R, Taramasco C, Villarroel R, Soto R, Barcelos TS, Merino E, Alonso-Sánchez MF. Using Black Hole Algorithm to Improve EEG-Based Emotion Recognition. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2018; 2018:3050214. [PMID: 29991942 PMCID: PMC6016227 DOI: 10.1155/2018/3050214] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/19/2018] [Revised: 04/18/2018] [Accepted: 05/08/2018] [Indexed: 12/22/2022]
Abstract
Emotions are a critical aspect of human behavior. One widely used technique for research in emotion measurement is based on the use of EEG signals. In general terms, the first step of signal processing is the elimination of noise, which can be done in manual or automatic terms. The next step is determining the feature vector using, for example, entropy calculation and its variations to generate a classification model. It is possible to use this approach to classify theoretical models such as the Circumplex model. This model proposes that emotions are distributed in a two-dimensional circular space. However, methods to determine the feature vector are highly susceptible to noise that may exist in the signal. In this article, a new method to adjust the classifier is proposed using metaheuristics based on the black hole algorithm. The method is aimed at obtaining results similar to those obtained with manual noise elimination methods. In order to evaluate the proposed method, the MAHNOB HCI Tagging Database was used. Results show that using the black hole algorithm to optimize the feature vector of the Support Vector Machine we obtained an accuracy of 92.56% over 30 executions.
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Affiliation(s)
- Roberto Munoz
- Escuela de Ingeniería Civil Informática, Universidad de Valparaíso, Valparaíso, Chile
- Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - Rodrigo Olivares
- Escuela de Ingeniería Civil Informática, Universidad de Valparaíso, Valparaíso, Chile
- Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - Carla Taramasco
- Escuela de Ingeniería Civil Informática, Universidad de Valparaíso, Valparaíso, Chile
| | | | - Ricardo Soto
- Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - Thiago S. Barcelos
- Instituto Federal de Educação, Ciência e Tecnologia de São Paulo, Brazil
| | - Erick Merino
- Escuela de Ingeniería Civil Informática, Universidad de Valparaíso, Valparaíso, Chile
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9
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Hierarchical Cosine Similarity Entropy for Feature Extraction of Ship-Radiated Noise. ENTROPY 2018; 20:e20060425. [PMID: 33265515 PMCID: PMC7512944 DOI: 10.3390/e20060425] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/30/2018] [Revised: 05/25/2018] [Accepted: 05/31/2018] [Indexed: 11/23/2022]
Abstract
The classification performance of passive sonar can be improved by extracting the features of ship-radiated noise. Traditional feature extraction methods neglect the nonlinear features in ship-radiated noise, such as entropy. The multiscale sample entropy (MSE) algorithm has been widely used for quantifying the entropy of a signal, but there are still some limitations. To remedy this, the hierarchical cosine similarity entropy (HCSE) is proposed in this paper. Firstly, the hierarchical decomposition is utilized to decompose a time series into some subsequences. Then, the sample entropy (SE) is modified by utilizing Shannon entropy rather than conditional entropy and employing angular distance instead of Chebyshev distance. Finally, the complexity of each subsequence is quantified by the modified SE. Simulation results show that the HCSE method overcomes some limitations in MSE. For example, undefined entropy is not likely to occur in HCSE, and it is more suitable for short time series. Compared with MSE, the experimental results illustrate that the classification accuracy of real ship-radiated noise is significantly improved from 75% to 95.63% by using HCSE. Consequently, the proposed HCSE can be applied in practical applications.
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10
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Azami H, Escudero J. Amplitude- and Fluctuation-Based Dispersion Entropy. ENTROPY 2018; 20:e20030210. [PMID: 33265301 PMCID: PMC7512725 DOI: 10.3390/e20030210] [Citation(s) in RCA: 61] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/02/2017] [Revised: 02/05/2018] [Accepted: 03/13/2018] [Indexed: 11/16/2022]
Abstract
Dispersion entropy (DispEn) is a recently introduced entropy metric to quantify the uncertainty of time series. It is fast and, so far, it has demonstrated very good performance in the characterisation of time series. It includes a mapping step, but the effect of different mappings has not been studied yet. Here, we investigate the effect of linear and nonlinear mapping approaches in DispEn. We also inspect the sensitivity of different parameters of DispEn to noise. Moreover, we develop fluctuation-based DispEn (FDispEn) as a measure to deal with only the fluctuations of time series. Furthermore, the original and fluctuation-based forbidden dispersion patterns are introduced to discriminate deterministic from stochastic time series. Finally, we compare the performance of DispEn, FDispEn, permutation entropy, sample entropy, and Lempel–Ziv complexity on two physiological datasets. The results show that DispEn is the most consistent technique to distinguish various dynamics of the biomedical signals. Due to their advantages over existing entropy methods, DispEn and FDispEn are expected to be broadly used for the characterization of a wide variety of real-world time series. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/2326.
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11
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Manis G, Aktaruzzaman M, Sassi R. Low Computational Cost for Sample Entropy. ENTROPY 2018; 20:e20010061. [PMID: 33265148 PMCID: PMC7512258 DOI: 10.3390/e20010061] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 12/24/2017] [Accepted: 01/09/2018] [Indexed: 11/23/2022]
Abstract
Sample Entropy is the most popular definition of entropy and is widely used as a measure of the regularity/complexity of a time series. On the other hand, it is a computationally expensive method which may require a large amount of time when used in long series or with a large number of signals. The computationally intensive part is the similarity check between points in m dimensional space. In this paper, we propose new algorithms or extend already proposed ones, aiming to compute Sample Entropy quickly. All algorithms return exactly the same value for Sample Entropy, and no approximation techniques are used. We compare and evaluate them using cardiac inter-beat (RR) time series. We investigate three algorithms. The first one is an extension of the kd-trees algorithm, customized for Sample Entropy. The second one is an extension of an algorithm initially proposed for Approximate Entropy, again customized for Sample Entropy, but also improved to present even faster results. The last one is a completely new algorithm, presenting the fastest execution times for specific values of m, r, time series length, and signal characteristics. These algorithms are compared with the straightforward implementation, directly resulting from the definition of Sample Entropy, in order to give a clear image of the speedups achieved. All algorithms assume the classical approach to the metric, in which the maximum norm is used. The key idea of the two last suggested algorithms is to avoid unnecessary comparisons by detecting them early. We use the term unnecessary to refer to those comparisons for which we know a priori that they will fail at the similarity check. The number of avoided comparisons is proved to be very large, resulting in an analogous large reduction of execution time, making them the fastest algorithms available today for the computation of Sample Entropy.
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Affiliation(s)
- George Manis
- Department of Computer Science and Engineering, University of Ioannina, Ioannina 45110, Greece
- Correspondence: ; Tel.: +30-2651-008-806
| | - Md Aktaruzzaman
- Department of Computer Science and Engineering, Islamic University Kushtia, Kushtia 7003, Bangladesh
| | - Roberto Sassi
- Dipartimento di Informatica, Università degli Studi di Milano, Crema 26013, Italy
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12
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Accelerating the Computation of Entropy Measures by Exploiting Vectors with Dissimilarity. ENTROPY 2017. [DOI: 10.3390/e19110598] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/25/2022]
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13
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Cuesta-Frau D, Miró-Martínez P, Jordán Núñez J, Oltra-Crespo S, Molina Picó A. Noisy EEG signals classification based on entropy metrics. Performance assessment using first and second generation statistics. Comput Biol Med 2017; 87:141-151. [PMID: 28595129 DOI: 10.1016/j.compbiomed.2017.05.028] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2017] [Revised: 05/05/2017] [Accepted: 05/28/2017] [Indexed: 11/19/2022]
Abstract
This paper evaluates the performance of first generation entropy metrics, featured by the well known and widely used Approximate Entropy (ApEn) and Sample Entropy (SampEn) metrics, and what can be considered an evolution from these, Fuzzy Entropy (FuzzyEn), in the Electroencephalogram (EEG) signal classification context. The study uses the commonest artifacts found in real EEGs, such as white noise, and muscular, cardiac, and ocular artifacts. Using two different sets of publicly available EEG records, and a realistic range of amplitudes for interfering artifacts, this work optimises and assesses the robustness of these metrics against artifacts in class segmentation terms probability. The results show that the qualitative behaviour of the two datasets is similar, with SampEn and FuzzyEn performing the best, and the noise and muscular artifacts are the most confounding factors. On the contrary, there is a wide variability as regards initialization parameters. The poor performance achieved by ApEn suggests that this metric should not be used in these contexts.
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Affiliation(s)
- David Cuesta-Frau
- Technological Institute of Informatics, Polytechnic University of Valencia, Alcoi Campus, Plaza Ferrandiz y Carbonell 2, Alcoi, Spain.
| | - Pau Miró-Martínez
- Department of Statistics, Polytechnic University of Valencia, Alcoi Campus, Alcoi, Spain
| | - Jorge Jordán Núñez
- Department of Statistics, Polytechnic University of Valencia, Alcoi Campus, Alcoi, Spain
| | - Sandra Oltra-Crespo
- Technological Institute of Informatics, Polytechnic University of Valencia, Alcoi Campus, Plaza Ferrandiz y Carbonell 2, Alcoi, Spain
| | - Antonio Molina Picó
- Technological Institute of Informatics, Polytechnic University of Valencia, Alcoi Campus, Plaza Ferrandiz y Carbonell 2, Alcoi, Spain
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14
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Refined multiscale fuzzy entropy based on standard deviation for biomedical signal analysis. Med Biol Eng Comput 2017; 55:2037-2052. [PMID: 28462498 PMCID: PMC5644759 DOI: 10.1007/s11517-017-1647-5] [Citation(s) in RCA: 62] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2016] [Accepted: 04/01/2017] [Indexed: 11/30/2022]
Abstract
Multiscale entropy (MSE) has been a prevalent algorithm to quantify the complexity of biomedical time series. Recent developments in the field have tried to alleviate the problem of undefined MSE values for short signals. Moreover, there has been a recent interest in using other statistical moments than the mean, i.e., variance, in the coarse-graining step of the MSE. Building on these trends, here we introduce the so-called refined composite multiscale fuzzy entropy based on the standard deviation (RCMFEσ) and mean (RCMFEμ) to quantify the dynamical properties of spread and mean, respectively, over multiple time scales. We demonstrate the dependency of the RCMFEσ and RCMFEμ, in comparison with other multiscale approaches, on several straightforward signal processing concepts using a set of synthetic signals. The results evidenced that the RCMFEσ and RCMFEμ values are more stable and reliable than the classical multiscale entropy ones. We also inspect the ability of using the standard deviation as well as the mean in the coarse-graining process using magnetoencephalograms in Alzheimer’s disease and publicly available electroencephalograms recorded from focal and non-focal areas in epilepsy. Our results indicated that when the RCMFEμ cannot distinguish different types of dynamics of a particular time series at some scale factors, the RCMFEσ may do so, and vice versa. The results showed that RCMFEσ-based features lead to higher classification accuracies in comparison with the RCMFEμ-based ones. We also made freely available all the Matlab codes used in this study at 10.7488/ds/1477.
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15
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A Novel Multi-Objective Optimal Approach for Wind Power Interval Prediction. ENERGIES 2017. [DOI: 10.3390/en10040419] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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16
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Azami H, Rostaghi M, Abasolo D, Escudero J. Refined Composite Multiscale Dispersion Entropy and its Application to Biomedical Signals. IEEE Trans Biomed Eng 2017; 64:2872-2879. [PMID: 28287954 DOI: 10.1109/tbme.2017.2679136] [Citation(s) in RCA: 79] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
OBJECTIVE We propose a novel complexity measure to overcome the deficiencies of the widespread and powerful multiscale entropy (MSE), including, MSE values may be undefined for short signals, and MSE is slow for real-time applications. METHODS We introduce multiscale dispersion entropy (DisEn-MDE) as a very fast and powerful method to quantify the complexity of signals. MDE is based on our recently developed DisEn, which has a computation cost of O(N), compared with O(N2) for sample entropy used in MSE. We also propose the refined composite MDE (RCMDE) to improve the stability of MDE. RESULTS We evaluate MDE, RCMDE, and refined composite MSE (RCMSE) on synthetic signals and three biomedical datasets. The MDE, RCMDE, and RCMSE methods show similar results, although the MDE and RCMDE are faster, lead to more stable results, and discriminate different types of physiological signals better than MSE and RCMSE. CONCLUSION For noisy short and long time series, MDE and RCMDE are noticeably more stable than MSE and RCMSE, respectively. For short signals, MDE and RCMDE, unlike MSE and RCMSE, do not lead to undefined values. The proposed MDE and RCMDE are significantly faster than MSE and RCMSE, especially for long signals, and lead to larger differences between physiological conditions known to alter the complexity of the physiological recordings. SIGNIFICANCE MDE and RCMDE are expected to be useful for the analysis of physiological signals thanks to their ability to distinguish different types of dynamics. The MATLAB codes used in this paper are freely available at http://dx.doi.org/10.7488/ds/1982.
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