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 functions.
These functions are directly available when EntropyHub is imported:
julia> using EntropyHub
-
-julia> names(EntropyHub) :ApEn
- :AttnEn
- :BubbEn
- ⋮
- :hXMSEn
- :rMSEn
- :rXMSEnEntropyHub._ApEn.ApEn — FunctionAp, Phi = ApEn(Sig)Returns the approximate entropy estimates Ap and the log-average number of matched vectors Phi for m = [0,1,2], estimated from the data sequence Sig using the default parameters: embedding dimension = 2, time delay = 1, radius distance threshold = 0.2*SD(Sig), logarithm = natural
Ap, Phi = ApEn(Sig::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, r::Real=0.2*std(Sig,corrected=false), Logx::Real=exp(1))Returns the approximate entropy estimates Ap of the data sequence Sig for dimensions = [0,1,...,m] using the specified keyword arguments:
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.EntropyHub._SampEn.SampEn — FunctionSamp, 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, r::Real=0.2*std(Sig,corrected=false), Logx::Real=exp(1))Returns the sample entropy estimates Samp for dimensions = [0,1,...,m] estimated from the data sequence Sig using the specified keyword arguments:
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).EntropyHub._FuzzEn.FuzzEn — FunctionFuzz, 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, r::Union{Real,Tuple{Real,Real}}=(.2,2), Fx::String="default", Logx::Real=exp(1))Returns the fuzzy entropy estimates Fuzz for dimensions = [1,...,m] estimated for the data sequence Sig using the specified keyword arguments:
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: {"sigmoid", "modsampen", "default", "gudermannian", "linear"}
r - Fuzzy function parameters, a 1 element scalar or a 2 element tuple 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))
- 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 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.EntropyHub._K2En.K2En — FunctionK2, 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, r = 0.2*SD(Sig), logarithm = natural
K2, Ci = K2En(Sig::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, r::Real=0.2*std(Sig,corrected=false), Logx::Real=exp(1))Returns the Kolmogorov entropy estimates K2 for dimensions = [1,...,m] estimated from the data sequence Sig using the 'keyword' arguments:
Arguments:
m - Embedding Dimension, a positive integer
tau - Time Delay, a positive integer
r - Radius, 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):03602EntropyHub._PermEn.PermEn — FunctionPerm, 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. Note: It is recommeneded that signal length > 5m! (see [8] and Amigo et al., Europhys. Lett. 83:60005, 2008)
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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, Typex::String="none", tpx::Union{Real,Nothing}=nothing, Logx::Real=2, Norm::Bool=false)Returns the permutation entropy estimates Perm for dimensions = [1,...,m] estimated from the data sequence Sig using the specified 'keyword' arguments:
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 PermEn value:
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: {`"none", "uniquant", "finegrain", "modified", "ampaware", "weighted", "edge"} See the EntropyHub guide for more info on PermEn variations.
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 variations.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
-
-[8] Zhe Chen, et al.
- "Improved permutation entropy for measuring complexity of time
- series under noisy condition."
- Complexity
- 1403829 (2019).
-
-[9] Maik Riedl, Andreas Müller, and Niels Wessel,
- "Practical considerations of permutation entropy."
- The European Physical Journal Special Topics
- 222.2 (2013): 249-262.EntropyHub._CondEn.CondEn — FunctionCond, 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, c::Int=6, Logx::Real=exp(1), Norm::Bool=false)Returns the corrected conditional entropy estimates (Cond) from the data sequence (Sig) using the specified 'keyword' arguments:
Arguments:
m - Embedding Dimension, an integer > 1
tau - Time Delay, a positive integer
c - # of symbols, an integer > 1
Logx - Logarithm base, a positive scalar
Norm - Normalisation of CondEn value:
[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.EntropyHub._DistEn.DistEn — FunctionDist, 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, Bins::Union{Int,String}="Sturges", Logx::Real=2, Norm::Bool=true)Returns the distribution entropy estimate (Dist) estimated from the data sequence (Sig) using the specified 'keyword' arguments:
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 DistEn value:
[false] no normalisation.
- [true] normalises w.r.t # of histogram bins - defaultSee 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.EntropyHub._SpecEn.SpecEn — FunctionSpec, 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::AbstractArray{T,1} where T<:Real; N::Int=1 + (2*size(Sig,1)), Freqs::Tuple{Real,Real}=(0,1), Logx::Real=exp(1), Norm::Bool=true)Returns the spectral entropy (Spec) and the within-band entropy (BandEn) estimate for the data sequence (Sig) using the specified 'keyword' arguments:
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 == SpecEnLogx - Logarithm base, a positive scalar (enter 0 for natural log)
Norm - Normalisation of Spec value:
[false] no normalisation.
- [true] normalises w.r.t # of spectrum/band frequency values - default.For more info, see the EntropyHub guide.
See also XSpecEn, fft, MSEn, XMSEn
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.EntropyHub._DispEn.DispEn — FunctionDispx, RDE = 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, RDE = DispEn(Sig::AbstractArray{T,1} where T<:Real; c::Int=3, m::Int=2, tau::Int=1, Typex::String="ncdf", Logx::Real=exp(1), Fluct::Bool=false, Norm::Bool=false, rho::Real=1)Returns the dispersion entropy (Dispx) and the reverse dispersion entropy (RDE) estimated from the data sequence (Sig) using the specified 'keyword' arguments:
Arguments:
m - Embedding Dimension, a positive integer
tau - Time Delay, a positive integer
c - Number of symbols, an integer > 1
Typex - Type of data-to-symbolic sequence transform, one of the following: {"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 value: [false] no normalisation - default [true] normalises w.r.t number of possible dispersion patterns (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.EntropyHub._SyDyEn.SyDyEn — FunctionSyDy, 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, c::Int=3, Typex::String="MEP", Logx::Real=exp(1), Norm::Bool=true)Returns the symbolic dynamic entropy (SyDy) and the symbolic sequence (Zt) of the data sequence (Sig) using the specified 'keyword' arguments:
Arguments:
m - Embedding Dimension, a positive integer
tau - Time Delay, a positive integer
c - Number of symbols, an integer > 1
Typex - Type of symbolic sequnce partitioning method, one of the following:
{"linear","uniform","MEP"(default),"kmeans"}Logx - Logarithm base, a positive scalar
Norm - Normalisation of SyDyEn value:
[false] no normalisation
- [true] normalises w.r.t # possible vector permutations (c^m+1) - defaultSee the EntropyHub guide for more info on these parameters.
See also DispEn, PermEn, CondEn, SampEn, MSEn
References:
[1] Yongbo Li, et al.,
- "A fault diagnosis scheme for planetary gearboxes using
- modified multi-scale symbolic dynamic entropy and mRMR feature
- selection."
- Mechanical Systems and Signal Processing
- 91 (2017): 295-312.
-
-[2] Jian Wang, et al.,
- "Fault feature extraction for multiple electrical faults of
- aviation electro-mechanical actuator based on symbolic dynamics
- entropy."
- IEEE International Conference on Signal Processing,
- Communications and Computing (ICSPCC), 2015.
-
-[3] Venkatesh Rajagopalan and Asok Ray,
- "Symbolic time series analysis via wavelet-based partitioning."
- Signal processing
- 86.11 (2006): 3309-3320.EntropyHub._IncrEn.IncrEn — FunctionIncr = 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, R::Int=4, Logx::Real=2, Norm::Bool=false)Returns the increment entropy (Incr) estimate of the data sequence (Sig) using the specified 'keyword' arguments:
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:
[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.EntropyHub._CoSiEn.CoSiEn — FunctionCoSi, 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::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, r::Real=.1, Logx::Real=2, Norm::Int=0)Returns the cosine similarity entropy (CoSi) estimated from the data sequence (Sig) using the specified 'keyword' arguments:
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:
[0] no normalisation - default
- [1] normalises `Sig` by removing median(`Sig`)
- [2] normalises `Sig` by removing mean(`Sig`)
- [3] normalises `Sig` w.r.t. SD(`Sig`)
- [4] normalises `Sig` values to range [-1 1]See also PhasEn, SlopEn, GridEn, MSEn, cMSEn
References:
[1] Theerasak Chanwimalueang and Danilo Mandic,
- "Cosine similarity entropy: Self-correlation-based complexity
- analysis of dynamical systems."
- Entropy
- 19.12 (2017): 652.EntropyHub._PhasEn.PhasEn — FunctionPhas = 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::AbstractArray{T,1} where T<:Real; K::Int=4, tau::Int=1, Logx::Real=exp(1), Norm::Bool=true, Plotx::Bool=false)Returns the phase entropy (Phas) estimate of the data sequence (Sig) using the specified 'keyword' arguments:
Arguments:
K - Angular partitions (coarse graining), an integer > 1
*Note: Division of partitions begins along the positive x-axis. As this point is somewhat arbitrary, it is
- recommended to use even-numbered (preferably multiples of 4) partitions for sake of symmetry.tau - Time Delay, a positive integer
Logx - Logarithm base, a positive scalar
Norm - Normalisation of Phas value:
[false] no normalisation
- [true] normalises w.r.t. the number of partitions Log(`K`)Plotx - When Plotx == true, returns Poincaré 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.EntropyHub._SlopEn.SlopEn — FunctionSlop = SlopEn(Sig)Returns the slope entropy (Slop) estimates for embedding dimensions [2, ..., m] of the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, angular thresholds = [5 45], logarithm = base 2
Slop = SlopEn(Sig::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, Lvls::AbstractArray{T,1} where T<:Real=[5, 45], Logx::Real=2, Norm::Bool=true)Returns the slope entropy (Slop) estimate of the data sequence (Sig) using the specified 'keyword' arguments:
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, a boolean operator:
[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.EntropyHub._BubbEn.BubbEn — FunctionBubb, H = BubbEn(Sig)Returns the bubble entropy (Bubb) and the conditional Rényi entropy (H) estimates of dimension m = 2 from the data sequence (Sig) using the default parameters: embedding dimension = 2, time delay = 1, logarithm = natural
Bubb, H = BubbEn(Sig::AbstractArray{T,1} where T<:Real; m::Int=2, tau::Int=1, Logx::Real=exp(1))Returns the bubble entropy (Bubb) estimate of the data sequence (Sig) using the specified 'keyword' arguments:
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.EntropyHub._GridEn.GridEn — FunctionGDE, 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)In addition to GDE and GDR, GridEn returns the following indices estimated for the data sequence (Sig) using the default parameters: [PIx] - Percentage of points below the line of identity (LI) [GIx] - Proportion of point distances above the LI [SIx] - Ratio of phase angles (w.r.t. LI) of the points above the LI [AIx] - Ratio of the cumulative area of sectors of points above the LI
GDE, GDR, ..., = GridEn(Sig::AbstractArray{T,1} where T<:Real; m::Int=3, tau::Int=1, Logx::Real=exp(1), Plotx::Bool=false)Returns the gridded distribution entropy (GDE) estimated from the data sequence (Sig) using the specified 'keyword' arguments:
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.EntropyHub._EnofEn.EnofEn — FunctionEoE, AvEn, S2 = EnofEn(Sig)Returns the entropy of entropy (EoE), the average Shannon entropy (AvEn), and the number of levels (S2) across all windows estimated from the data sequence (Sig) using the default parameters: window length (samples) = 10, slices = 10, logarithm = natural, heartbeat interval range (xmin, xmax) = (min(Sig), max(Sig))
EoE, AvEn, S2 = EnofEn(Sig::AbstractArray{T,1} where T<:Real; tau::Int=10, S::Int=10, Xrange::Tuple{Real,REal}, Logx::Real=exp(1))Returns the entropy of entropy (EoE) estimated from the data sequence (Sig) using the specified 'keyword' arguments:
Arguments:
tau - Window length, an integer > 1
S - Number of slices (s1,s2), a two-element tuple of integers > 2
Xrange - The min and max heartbeat interval, a two-element tuple where X[1] <= X[2]
Logx - Logarithm base, a positive scalar
See also SampEn, MSEn, ApEn
References:
[1] Chang Francis Hsu, et al.,
- "Entropy of entropy: Measurement of dynamical complexity for
- biological systems."
- Entropy
- 19.10 (2017): 550.EntropyHub._AttnEn.AttnEn — FunctionAv4, (Hxx,Hnn,Hxn,Hnx) = AttnEn(Sig)Returns the attention entropy (Av4) calculated as the average of the sub-entropies (Hxx,Hxn,Hnn,Hnx) estimated from the data sequence (Sig) using a base-2 logarithm.
Av4, (Hxx, Hnn, Hxn, Hnx) = AttnEn(Sig::AbstractArray{T,1} where T<:Real; Logx::Real=2)Returns the attention entropy (Av4) and the 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
Arguments:
Logx - Logarithm base, a positive scalar (Enter 0 for natural logarithm)
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)