Base Entropies

Functions for estimating the entropy of a single univariate time series.

The following functions also form the base entropy method used by multiscale entropy functions.


These functions are directly available when EntropyHub is imported:

import EntropyHub as EH

dir(EH)

ApEn(Sig, m=2, tau=1, r=None, Logx=numpy.exp)

ApEn estimates the approximate entropy of a univariate data sequence.

Ap, Phi = ApEn(Sig)

Returns the approximate entropy estimates (Ap) and the log-average number of matched vectors (Phi) for m = [0,1,2], estimated for the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, radius threshold = 0.2*SD(Sig), logarithm = natural

Ap, Phi = ApEn(Sig, keyword = value, ...)

Returns the approximate entropy estimates (Ap) of the data sequence (Sig) for dimensions = [0, 1, …, m] using the specified keyword arguments:

m
  • Embedding Dimension, a positive integer

tau
  • Time Delay, a positive integer

r
  • Radius Distance Threshold, a positive scalar

Logx
  • Logarithm base, a positive scalar

See also

XApEn, SampEn, MSEn, FuzzEn, PermEn, CondEn, DispEn

References
[1] Steven M. Pincus,

“Approximate entropy as a measure of system complexity.” Proceedings of the National Academy of Sciences 88.6 (1991): 2297-2301.

AttnEn(Sig, Logx=2)

AttnEn estimates the attention entropy of a univariate data sequence.

Attn, (Hxx, Hnn, Hxn, Hnx) = AttnEn(Sig)

Returns the attention entropy (Attn) calculated as the average of the sub-entropies (Hxx, Hxn, Hnn, Hnx) estimated from the data sequence (Sig) using a base-2 logarithm.

Attn, (Hxx, Hnn, Hxn, Hnx) = AttnEn(Sig, Logx = value)

Returns the attention entropy (Attn) and a four-element tuple of sub-entropies (Hxx, Hnn, Hxn, Hnx) from the data sequence (Sig) where,

Hxx
  • entropy of local-maxima intervals

Hnn
  • entropy of local minima intervals

Hxn
  • entropy of intervals between local maxima and subsequent minima

Hnx
  • entropy of intervals between local minima and subsequent maxima using the following keyword argument:

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

See also

EnofEn, SpecEn, XSpecEn, PermEn, MSEn

References
[1] Jiawei Yang, et al.,

“Classification of Interbeat Interval Time-series Using Attention Entropy.” IEEE Transactions on Affective Computing (2020)

BubbEn(Sig, m=2, tau=1, Logx=numpy.exp)

BubbEn estimates the bubble entropy of a univariate data sequence.

Bubb, H = BubbEn(Sig)

Returns the bubble entropy (Bubb) and the conditional Rényi entropy (H) estimate from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, logarithm = natural

Bubb, H = BubbEn(Sig, keyword = value, ...)

Returns the bubble entropy (Bubb) estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, an integer > 1

BubbEn returns estimates for each dimension [2, …, m]

tau
  • Time Delay, a positive integer

Logx
  • Logarithm base, a positive scalar

See also

PhasEn, MSEn

References
[1] George Manis, M.D. Aktaruzzaman and Roberto Sassi,

“Bubble entropy: An entropy almost free of parameters.” IEEE Transactions on Biomedical Engineering 64.11 (2017): 2711-2718.

CoSiEn(Sig, m=2, tau=1, r=0.1, Logx=2, Norm=0)

CoSiEn estimates the cosine similarity entropy of a univariate data sequence.

CoSi, Bm = CoSiEn(Sig) 

Returns the cosine similarity entropy (CoSi) and the corresponding global probabilities estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, angular threshold = .1, logarithm = base 2,

CoSi, Bm = CoSiEn(Sig, keyword = value, ...)

Returns the cosine similarity entropy (CoSi) estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, an integer > 1

tau
  • Time Delay, a positive integer

r
  • Angular threshold, a value in range [0 < r < 1]

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

Norm
  • Normalisation of Sig, one of the following integers:

  1. no normalisation - default

  2. normalises Sig by removing median(Sig)

  3. normalises Sig by removing mean(Sig)

  4. normalises Sig w.r.t. SD(Sig)

  5. normalises Sig values to range [-1 1]

See also

PhasEn, SlopEn, GridEn, MSEn, hMSEn

References
[1] Theerasak Chanwimalueang and Danilo Mandic,

“Cosine similarity entropy: Self-correlation-based complexity analysis of dynamical systems.” Entropy 19.12 (2017): 652.

CondEn(Sig, m=2, tau=1, c=6, Logx=numpy.exp, Norm=False)

CondEn estimates the corrected conditional entropy of a univariate data sequence.

Cond, SEw, SEz = CondEn(Sig) 

Returns the corrected conditional entropy estimates (Cond) and the corresponding Shannon entropies (m: SEw, m+1: SEz) for m = [1,2] estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, symbols = 6, logarithm = natural, normalisation = False Note: CondEn(m=1) returns the Shannon entropy of Sig.

Cond, SEw, SEz = CondEn(Sig, keyword = value, ...)

Returns the corrected conditional entropy estimates (Cond) from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, an integer > 1

tau
  • Time Delay, a positive integer

c
  • Number of symbols, an integer > 1

Logx
  • Logarithm base, a positive scalar

Norm
  • Normalisation of Cond value, a boolean:

  • False no normalisation - default

  • True normalises w.r.t Shannon entropy of data sequence Sig.

See also

XCondEn, MSEn, PermEn, DistEn, XPermEn

References
[1] Alberto Porta, et al.,

“Measuring regularity by means of a corrected conditional entropy in sympathetic outflow.” Biological cybernetics 78.1 (1998): 71-78.

DispEn(Sig, m=2, tau=1, c=3, Typex='NCDF', Logx=numpy.exp, Fluct=False, Norm=False, rho=1)

DispEn estimates the dispersion entropy of a univariate data sequence.

Dispx, Ppi = DispEn(Sig)

Returns the dispersion entropy (Dispx) and the reverse dispersion entropy (RDE) estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, symbols = 3, logarithm = natural, data transform = normalised cumulative density function (ncdf)

Dispx, Ppi = DispEn(Sig, keyword = value, ...)

Returns the dispersion entropy (Dispx) and the reverse dispersion entropy (RDE) estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, a positive integer

tau
  • Time Delay, a positive integer

c
  • Number of symbols, an integer > 1

Typex
  • Typex of data-to-symbolic sequence transform, one of the following strings: {'linear', 'kmeans', 'ncdf', 'finesort', 'equal'}

See the EntropyHub guide for more info on these transforms.

Logx
  • Logarithm base, a positive scalar

Fluct
  • When Fluct == True, DispEn returns the fluctuation-based Dispersion entropy. [default: False]

Norm
  • Normalisation of Dispx and RDE values, a boolean:

  • False no normalisation - default

  • True normalises w.r.t # possible vector permutations (c^m or (2c -1)^m-1 if Fluct == True).

rho
  • *If Typex == 'finesort', rho is the tuning parameter (default: 1)

See also

PermEn, SyDyEn, MSEn.

References
[1] Mostafa Rostaghi and Hamed Azami,

“Dispersion entropy: A measure for time-series analysis.” IEEE Signal Processing Letters 23.5 (2016): 610-614.

[2] Hamed Azami and Javier Escudero,

“Amplitude-and fluctuation-based dispersion entropy.” Entropy 20.3 (2018): 210.

[3] Li Yuxing, Xiang Gao and Long Wang,

“Reverse dispersion entropy: A new complexity measure for sensor signal.” Sensors 19.23 (2019): 5203.

[4] Wenlong Fu, et al.,

“Fault diagnosis for rolling bearings based on fine-sorted dispersion entropy and SVM optimized with mutation SCA-PSO.” Entropy 21.4 (2019): 404.

DistEn(Sig, m=2, tau=1, Bins='Sturges', Logx=2, Norm=True)

DistEn estimates the distribution entropy of a univariate data sequence.

Dist, Ppi = DistEn(Sig) 

Returns the distribution entropy estimate (Dist) and the corresponding distribution probabilities (Ppi) estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, binning method = ‘Sturges’, logarithm = base 2, normalisation = w.r.t # of histogram bins

Dist, Ppi = DistEn(Sig, keyword = value, ...)

Returns the distribution entropy estimate (Dist) estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, a positive integer

tau
  • Time Delay, a positive integer

Bins
  • Histogram bin selection method for distance distribution, one of the following:

  • an integer > 1 indicating the number of bins,

  • or one of the following strings {'sturges', 'sqrt', 'rice', 'doanes'} [default: 'sturges']

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

Norm
  • Normalisation of Dist value, a boolean:

  • [False] no normalisation.

  • [True] normalises w.r.t # of histogram bins - default

See also

XDistEn, DistEn2D, MSEn, K2En

References
[1] Li, Peng, et al.,

“Assessing the complexity of short-term heartbeat interval series by distribution entropy.” Medical & biological engineering & computing 53.1 (2015): 77-87.

EnofEn(Sig, tau=10, S=(10, 5), Logx=numpy.exp)

EnofEn estimates the entropy of entropy of a univariate data sequence.

EoE, AvEn = EnofEn(Sig) 

Returns the entropy of entropy (EoE) and the average Shannon entropy across all windows (AvEn) estimated from the data sequence (Sig) using the default parameters: window length (samples) = 10, slices (s1,s2) = [10 5], logarithm = natural

EoE, AvEn = EnofEn(Sig, keyword = value, ...)

Returns the entropy of entropy (EoE) estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

tau
  • Window length, an integer > 1

S
  • Number of slices (s1,s2), a two-element tuple of integers > 2

Logx
  • Logarithm base, a positive scalar

See also:

SampEn, MSEn

References
[1] Chang Francis Hsu, et al.,

“Entropy of entropy: Measurement of dynamical complexity for biological systems.” Entropy 19.10 (2017): 550.

FuzzEn(Sig, m=2, tau=1, r=(0.2, 2), Fx='default', Logx=numpy.exp)

FuzzEn estimates the fuzzy entropy of a univariate data sequence.

Fuzz, Ps1, Ps2 = FuzzEn(Sig) 

Returns the fuzzy entropy estimates (Fuzz) and the average fuzzy distances (m: Ps1, m+1: Ps2) for m = [1,2] estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, fuzzy function (Fx) = 'default', fuzzy function parameters (r) = (0.2, 2), logarithm = natural

Fuzz, Ps1, Ps2 = FuzzEn(Sig, keyword = value, ...)

Returns the fuzzy entropy estimates (Fuzz) for dimensions = [1, …, m] estimated for the data sequence (Sig) using the specified name/value pair arguments:

m
  • Embedding Dimension, a positive integer [default: 2]

tau
  • Time Delay, a positive integer [default: 1]

Fx
  • Fuzzy function name, one of the following strings: {'sigmoid', 'modsampen', 'default', 'gudermannian', 'linear'}

r
  • Fuzzy function parameters, a 1 element scalar or a 2 element vector of positive values. The r parameters for each fuzzy

function are defined as follows: [default: (.2 2)]

  • sigmoid:
    • r(1) = divisor of the exponential argument

    • r(2) = value subtracted from argument (pre-division)

  • modsampen:
    • r(1) = divisor of the exponential argument

    • r(2) = value subtracted from argument (pre-division)

  • default:
    • r(1) = divisor of the exponential argument

    • r(2) = argument exponent (pre-division)

  • gudermannian:
    • r = a scalar whose value is the numerator of argument to gudermannian function: GD(x) = atan(tanh(r/x)). GD(x) is normalised to have a maximum value of 1.

  • linear:

    r = an integer value. When r = 0, the argument of the exponential function is normalised between [0 1]. When r = 1, the minimuum value of the exponential argument is set to 0.

Logx
  • Logarithm base, a positive scalar [default: natural]

For further information on the keyword arguments, see the EntropyHub guide.

See also

SampEn, ApEn, PermEn, DispEn, XFuzzEn, FuzzEn2D, MSEn

References
[1] Weiting Chen, et al.

“Characterization of surface EMG signal based on fuzzy entropy.” IEEE Transactions on neural systems and rehabilitation engineering 15.2 (2007): 266-272.

[2] Hong-Bo Xie, Wei-Xing He, and Hui Liu

“Measuring time series regularity using nonlinear similarity-based sample entropy.” Physics Letters A 372.48 (2008): 7140-7146.

GridEn(Sig, m=3, tau=1, Logx=numpy.exp, Plotx=False)

GridEn estimates the gridded distribution entropy of a univariate data sequence.

GDE, GDR, _ = GridEn(Sig) 

Returns the gridded distribution entropy (GDE) and the gridded distribution rate (GDR) estimated from the data sequence (Sig) using the default parameters: grid coarse-grain = 3, time delay = 1, logarithm = base 2

GDE, GDR, PIx, GIx, SIx, AIx = GridEn(Sig, keyword = value)

Returns the gridded distribution entropy (GDE) estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Grid coarse-grain (m x m sectors), an integer > 1

tau
  • Time Delay, a positive integer

Logx
  • Logarithm base, a positive scalar

Plotx
  • When Plotx == True, returns gridded Poicaré plot and a bivariate histogram of the grid point distribution (default: False)

See also

PhasEn, CoSiEn, SlopEn, BubbEn, MSEn

References
[1] Chang Yan, et al.,

“Novel gridded descriptors of poincaré plot for analyzing heartbeat interval time-series.” Computers in biology and medicine 109 (2019): 280-289.

[2] Chang Yan, et al.

“Area asymmetry of heart rate variability signal.” Biomedical engineering online 16.1 (2017): 1-14.

[3] Alberto Porta, et al.,

“Temporal asymmetries of short-term heart period variability are linked to autonomic regulation.” American Journal of Physiology-Regulatory, Integrative and Comparative Physiology 295.2 (2008): R550-R557.

[4] C.K. Karmakar, A.H. Khandoker and M. Palaniswami,

“Phase asymmetry of heart rate variability signal.” Physiological measurement 36.2 (2015): 303.

IncrEn(Sig, m=2, tau=1, R=4, Logx=2, Norm=False)

IncrEn estimates the increment entropy of a univariate data sequence.

Incr = IncrEn(Sig) 

Returns the increment entropy (Incr) estimate of the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, quantifying resolution = 4, logarithm = base 2,

Incr = IncrEn(Sig, keyword = value, ...)

Returns the increment entropy (Incr) estimate of the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, an integer > 1

tau
  • Time Delay, a positive integer

R
  • Quantifying resolution, a positive scalar

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

Norm
  • Normalisation of IncrEn value, a boolean:

  • [False] no normalisation - default

  • [True] normalises w.r.t embedding dimension (m-1).

See also

PermEn, SyDyEn, MSEn

References
[1] Xiaofeng Liu, et al.,

“Increment entropy as a measure of complexity for time series.” Entropy 18.1 (2016): 22.1.

*** “Correction on Liu, X.; Jiang, A.; Xu, N.; Xue, J. - Increment

Entropy as a Measure of Complexity for Time Series, Entropy 2016, 18, 22.” Entropy 18.4 (2016): 133.

[2] Xiaofeng Liu, et al.,

“Appropriate use of the increment entropy for electrophysiological time series.” Computers in biology and medicine 95 (2018): 13-23.

K2En(Sig, m=2, tau=1, r=None, Logx=numpy.exp)

K2En estimates the Kolmogorov (K2) entropy of a univariate data sequence.

K2, Ci = K2En(Sig) 

Returns the Kolmogorov entropy estimates (K2) and the correlation integrals (Ci) for m = [1,2] estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, distance threshold (r) = 0.2*SD(Sig), logarithm = natural

K2, Ci = K2En(Sig, keyword = value, ...)

Returns the Kolmogorov entropy estimates (K2) for dimensions = [1, …, m] estimated from the data sequence (Sig) using the ‘keyword’ arguments:

m
  • Embedding Dimension, a positive integer

tau
  • Time Delay, a positive integer

r
  • Radius Distance Threshold, a positive scalar

Logx
  • Logarithm base, a positive scalar

See also

DistEn, XK2En, MSEn

References
[1] Peter Grassberger and Itamar Procaccia,

“Estimation of the Kolmogorov entropy from a chaotic signal.” Physical review A 28.4 (1983): 2591.

[2] Lin Gao, Jue Wang and Longwei Chen

“Event-related desynchronization and synchronization quantification in motor-related EEG by Kolmogorov entropy” J Neural Eng. 2013 Jun;10(3):03602

PermEn(Sig, m=2, tau=1, Logx=2, Norm=False, Typex='none', tpx=- 1)

PermEn estimates the permutation entropy of a univariate data sequence.

Perm, Pnorm, cPE = PermEn(Sig) 

Returns the permuation entropy estimates (Perm), the normalised permutation entropy (Pnorm) and the conditional permutation entropy (cPE) for m = [1,2] estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, logarithm = base 2, normalisation = w.r.t #symbols (m-1) Note: using the standard PermEn estimation, Perm = 0 when m = 1.

Perm, Pnorm, cPE = PermEn(Sig, m)

Returns the permutation entropy estimates (Perm) estimated from the data sequence (Sig) using the specified embedding dimensions = [1,…, m] with other default parameters as listed above.

Perm, Pnorm, cPE = PermEn(Sig, keyword = value, ...)

Returns the permutation entropy estimates (Perm) for dimensions = [1,…, m] estimated from the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, an integer > 1

tau
  • Time Delay, a positive integer

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

Norm
  • Normalisation of Pnorm value, a boolean:

  • False - normalises w.r.t log(# of permutation symbols [m-1]) - default

  • True - normalises w.r.t log(# of all possible permutations [m!])

  • Note: Normalised permutation entropy is undefined for m = 1.

** Note: When Typex = 'uniquant' and Norm = True, normalisation is calculated w.r.t. log(tpx^m) **

Typex
  • Permutation entropy variation, one of the following:

{'uniquant', 'finegrain', 'modified', 'ampaware', 'weighted', 'edge'}

See the EntropyHub guide for more info on PermEn variants.

tpx
  • Tuning parameter for associated permutation entropy variation.

  • [uniquant] ‘tpx’ is the L parameter, an integer > 1 (default = 4).

  • [finegrain] ‘tpx’ is the alpha parameter, a positive scalar (default = 1)

  • [ampaware] ‘tpx’ is the A parameter, a value in range [0 1] (default = 0.5)

  • [edge] ‘tpx’ is the r sensitivity parameter, a scalar > 0 (default = 1)

See the EntropyHub guide for more info on PermEn variants.

See also

XPermEn, MSEn, XMSEn, SampEn, ApEn, CondEn

References
[1] Christoph Bandt and Bernd Pompe,

“Permutation entropy: A natural complexity measure for time series.” Physical Review Letters, 88.17 (2002): 174102.

[2] Xiao-Feng Liu, and Wang Yue,
“Fine-grained permutation entropy as a measure of natural

complexity for time series.” Chinese Physics B 18.7 (2009): 2690.

[3] Chunhua Bian, et al.,

“Modified permutation-entropy analysis of heartbeat dynamics.” Physical Review E 85.2 (2012) : 021906

[4] Bilal Fadlallah, et al.,

“Weighted-permutation entropy: A complexity measure for time series incorporating amplitude information.” Physical Review E 87.2 (2013): 022911.

[5] Hamed Azami and Javier Escudero,

“Amplitude-aware permutation entropy: Illustration in spike detection and signal segmentation.” Computer methods and programs in biomedicine, 128 (2016): 40-51.

[6] Zhiqiang Huo, et al.,

“Edge Permutation Entropy: An Improved Entropy Measure for Time-Series Analysis,” 45th Annual Conference of the IEEE Industrial Electronics Soc, (2019), 5998-6003

[7] Zhe Chen, et al.

“Improved permutation entropy for measuring complexity of time series under noisy condition.” Complexity 1403829 (2019).

[8] Maik Riedl, Andreas Müller, and Niels Wessel,

“Practical considerations of permutation entropy.” The European Physical Journal Special Topics 222.2 (2013): 249-262.

PhasEn(Sig, K=4, tau=1, Logx=numpy.exp, Norm=True, Plotx=False)

PhasEn estimates the phase entropy of a univariate data sequence.

Phas = PhasEn(Sig) 

Returns the phase entropy (Phas) estimate of the data sequence (Sig) using the default parameters: angular partitions = 4, time delay = 1, logarithm = natural,

Phas = PhasEn(Sig, keyword = value, ...)

Returns the phase entropy (Phas) estimate of the data sequence (Sig) using the specified ‘keyword’ arguments:

K
  • Angular partitions (coarse graining), an integer > 1

tau
  • Time Delay, a positive integer

Logx
  • Logarithm base, a positive scalar

Norm
  • Normalisation of Phas value, a boolean:

  • [false] no normalisation

  • [true] normalises w.r.t. the # partitions Log(K) (Default)

Plotx
  • When Plotx == true, returns Poicaré plot (default: false)

See also

SampEn, ApEn, GridEn, MSEn, SlopEn, CoSiEn, BubbEn

References
[1] Ashish Rohila and Ambalika Sharma,

“Phase entropy: a new complexity measure for heart rate variability.” Physiological measurement 40.10 (2019): 105006.

SampEn(Sig, m=2, tau=1, r=None, Logx=numpy.exp)

SampEn estimates the sample entropy of a univariate data sequence.

Samp, A, B = SampEn(Sig) 

Returns the sample entropy estimates (Samp) and the number of matched state vectors (m: B, m+1: A) for m = [0, 1, 2] estimated from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, radius threshold = 0.2*SD(Sig), logarithm = natural

Samp, A, B = SampEn(Sig, keyword = value, ...)

Returns the sample entropy estimates (Samp) for dimensions = [0, 1, …, m] estimated for the data sequence (Sig) using the specified keyword arguments:

m
  • Embedding Dimension, a positive integer

tau
  • Time Delay, a positive integer

r
  • Radius Distance Threshold, a positive scalar

Logx
  • Logarithm base, a positive scalar

See also

ApEn, FuzzEn, PermEn, CondEn, XSampEn, SampEn2D, MSEn

References
[1] Joshua S Richman and J. Randall Moorman.

“Physiological time-series analysis using approximate entropy and sample entropy.” American Journal of Physiology-Heart and Circulatory Physiology 2000

SlopEn(Sig, m=2, tau=1, Lvls=(5, 45), Logx=2, Norm=True)

SlopEn estimates the slope entropy of a univariate data sequence.

Slop = SlopEn(Sig) 

Returns the slope entropy (Slop) of the data sequence (Sig) for embedding dimensions [2, …, m] using the default parameters: embedding dimension = 2, time delay = 1, angular thresholds = [5 45], logarithm = base 2

[Slop] = SlopEn(Sig, keyword = value, ...)

Returns the slope entropy (Slop) estimates of the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, an integer > 1

SlopEn returns estimates for each dimension [2,…, m]

tau
  • Time Delay, a positive integer

Lvls
  • Angular thresolds, a vector of monotonically increasing values in the range [0 90] degrees.

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

Norm
  • Normalisation of SlopEn value, one of the following integers:

  • [False] no normalisation

  • [True] normalises w.r.t. the number of patterns found (default)

See also

PhasEn, GridEn, MSEn, CoSiEn, SampEn, ApEn

References
[1] David Cuesta-Frau,

“Slope Entropy: A New Time Series Complexity Estimator Based on Both Symbolic Patterns and Amplitude Information.” Entropy 21.12 (2019): 1167.

SpecEn(Sig, N=None, Freqs=(0, 1), Logx=numpy.exp, Norm=True)

SpecEn estimates the spectral entropy of a univariate data sequence.

Spec, BandEn = SpecEn(Sig) 

Returns the spectral entropy estimate of the full spectrum (Spec) and the within-band entropy (BandEn) estimated from the data sequence (Sig) using the default parameters: N-point FFT = 2*len(Sig) + 1, normalised band edge frequencies = [0 1], logarithm = base 2, normalisation = w.r.t # of spectrum/band frequency values.

Spec, BandEn = SpecEn(Sig, keyword = value, ...)

Returns the spectral entropy (Spec) and the within-band entropy (BandEn) estimate from the data sequence (Sig) using the specified ‘keyword’ arguments:

N
  • Resolution of spectrum (N-point FFT), an integer > 1

Freqs
  • Normalised band edge frequencies, a 2 element tuple with values in range [0 1] where 1 corresponds to the Nyquist frequency (Fs/2).

  • Note: When no band frequencies are entered, BandEn == SpecEn

Logx
  • Logarithm base, a positive scalar (enter 0 for natural log)

Norm
  • Normalisation of Spec value, a boolean:

  • [False] no normalisation.

  • [True] normalises w.r.t # of spectrum/band frequency values - default.

For more info, see the EntropyHub guide.

See also

XSpecEn, MSEn, numpy.fftpack

References
[1] G.E. Powell and I.C. Percival,

“A spectral entropy method for distinguishing regular and irregular motion of Hamiltonian systems.” Journal of Physics A: Mathematical and General 12.11 (1979): 2053.

[2] Tsuyoshi Inouye, et al.,

“Quantification of EEG irregularity by use of the entropy of the power spectrum.” Electroencephalography and clinical neurophysiology 79.3 (1991): 204-210.

SyDyEn(Sig, m=2, tau=1, c=3, Typex='MEP', Logx=numpy.exp, Norm=True)

SyDyEn estimates the symbolic dynamic entropy of a univariate data sequence.

SyDy, Zt = SyDyEn(Sig) 

Returns the symbolic dynamic entropy (SyDy) and the symbolic sequence (Zt) of the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, symbols = 3, logarithm = natural, symbolic partition type = maximum entropy partitioning ('MEP'), normalisation = normalises w.r.t # possible vector permutations (c^m)

SyDy, Zt = SyDyEn(Sig, keyword = value, ...)

Returns the symbolic dynamic entropy (SyDy) and the symbolic sequence (Zt) of the data sequence (Sig) using the specified ‘keyword’ arguments:

m
  • Embedding Dimension, a positive integer

tau
  • Time Delay, a positive integer

c
  • Number of symbols, an integer > 1

Typex
  • Type of symbolic sequence partitioning, one of the following:

{'linear', 'uniform', 'MEP' (default), 'kmeans'}

‘Logx
  • Logarithm base, a positive scalar

Norm
  • Normalisation of SyDyEn value, a boolean:

[False] no normalisation [True] normalises w.r.t # possible dispersion patterns (c^m+1) - default

See the EntropyHub guide for more info on these parameters.

See also

DispEn, PermEn, CondEn, SampEn, MSEn

References
[1] Yongbo Li, et al.,

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