On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation

Zurek, Sebastian; Guzik, Przemysław; Pawlak, S.; Kośmider, Marcin; Piskorski, Jarosław

doi:10.1016/j.physa.2012.07.003

Cited by 40 publications

(27 citation statements)

References 24 publications

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“…The results are in accordance with reliability criteria − + 1 > (10 or 100)/ ( ) stating that or ( ) should be large. Indeed, ( ) is defined as a product of probabilities (14), so it is at its largest if = 1, while increased threshold augments the number of template matches 1 ( ) (4), again enlarging ( ). The reliability of̂( ) estimate is checked comparing the data length − + 1 with the required minimum 10/ ( ).…”

Section: Estimation Errors In Artificial Datamentioning

confidence: 99%

“…Research efforts are oriented towards modifications, including sample entropy (SampEn) [5], corrected conditional entropy (CApEn) [6], -nearest neighborhood entropy (KNNCE) [7], fuzzy entropy (FuzzyEn) [8], multiscale entropy (MultiScaleEn) [9], distance entropy (DistEn) [10], binarized entropy (BinEn) [11], ApEn based on wave mode [12], and speeding-up algorithms [13,14], and towards the consistency studies, including threshold selection [15][16][17][18][19][20], time lag [21], and consistency in general [4].…”

Section: Introductionmentioning

confidence: 99%

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On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments

et al. 2017

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Cross-approximate entropy (XApEn) quantifies the mutual orderliness of simultaneously recorded time series. Despite being derived from the firmly established solitary entropies, it has never reached their reputation and deployment. The aim of this study is to identify the problems that preclude wider XApEn implementation and to develop a set of solutions. Exact expressions for XApEn and its constitutive parts are derived and compared to values estimated from artificial data. This comparison revealed vast regions within the parameter space that do not guarantee reliable probability estimation, making XApEn estimates inconsistent. A simple correction to one of the XApEn procedural steps is proposed. Three sets of formulae for joint parameter selection are derived. The first one is intended to maximize threshold profile. The remaining ones minimize XApEn instability according to the strong and weak criteria. The derived expressions are verified using cardiovascular signals recorded from rats (long signals) and healthy volunteers (short clinical signals), proposing a change of traditional parameter guidelines.

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Section: Estimation Errors In Artificial Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments

et al. 2017

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“…Therefore, this particular technique by Equations (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) …”

Section: Individual Sample Learning Entropy (Isle)mentioning

confidence: 99%

“…The dimension of the used coupled Chua's circuit in continuous time domain is 6 and its embedding dimension shall be at least 2 × 6 + 1 = 13 according to the Taken's theorem. Let's choose the static QNU of lower dimension (embedding n = 6) as the learning model in sense of Equation (1) and in particularly according to Equations (12)(13)(14). Its proper pre-training by GD (16) for the first only 100 samples of the time series is shown in Figure 9; the sum of square errors (SSE) approaches 1E-5 after last epoch of pre-training.…”

Section: A Hyper-chaotic Time Seriesmentioning

confidence: 99%

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Learning Entropy: Multiscale Measure for Incremental Learning

Bukovský

2013

Entropy

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First, this paper recalls a recently introduced method of adaptive monitoring of dynamical systems and presents the most recent extension with a multiscale-enhanced approach. Then, it is shown that this concept of real-time data monitoring establishes a novel non-Shannon and non-probabilistic concept of novelty quantification, i.e., Entropy of Learning, or in short the Learning Entropy. This novel cognitive measure can be used for evaluation of each newly measured sample of data, or even of whole intervals. The Learning Entropy is quantified in respect to the inconsistency of data to the temporary governing law of system behavior that is incrementally learned by adaptive models such as linear or polynomial adaptive filters or neural networks. The paper presents this novel concept on the example of gradient descent learning technique with normalized learning rate.

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Applications of Heartbeat Complexity Analysis to Depression and Bipolar Disorder

Valenza

Citi

Lanatà

et al. 2017

Complexity and Nonlinearity in Cardiovascular Signals

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On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation

Cited by 40 publications

References 24 publications

On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments

On Consistency of Cross-Approximate Entropy in Cardiovascular and Artificial Environments

Learning Entropy: Multiscale Measure for Incremental Learning

Applications of Heartbeat Complexity Analysis to Depression and Bipolar Disorder

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