Multivariate Multiscale Entropies

Functions for estimating the Multivariate multiscale entropy of a multivariate time series dataset.

Just as one can calculate multiscale entropy using any Base or Cross- entropy, the same functionality is possible with multivariate multiscale entropy using any Multivariate function: MvSampEn, MvFuzzEn, MvDispEn, MvPermEn, MvCoSiEn.

To do so, we again use the MSobject function to pass a multiscale object (Mobj) to the multivariate multiscale entropy functions.

NOTE:

Multivariate multiscale entropy functions have two positional arguments:

the multivariate dataset, Data (an NxM matrix of N observations (>10 elements), and M time series (>1)),
the multiscale entropy object, Mobj -> see MSobject

EntropyHub._MvMSEn.MvMSEn — Function

MSx, CI = MvMSEn(Data, Mobj)

Returns a vector of multivariate multiscale entropy values (MSx) and the complexity index (CI) of the data sequences in Data using the parameters specified by the multiscale object (Mobj) over 3 temporal scales with coarse- graining (default).

Note

By default, the MvSampEn and MvFuzzEn multivariate entropy algorithms estimate entropy values using the "full" method by comparing delay vectors across all possible m+1 expansions of the embedding space as applied in [1]. These methods are not lower-bounded to 0, like most entropy algorithms, so MvMSEn may return negative entropy values if the base multivariate entropy function is MvSampEn and MvFuzzEn, even for stochastic processes...

MSx, CI = MSEn(Data::AbstractArray{T,2} where T<:Real, Mobj::NamedTuple; Scales::Int=3, Methodx::String="coarse", Plotx::Bool=false)

Arguments:

Scales - Number of temporal scales, an integer > 1 (default: 3)

Method - Graining method, one of the following:

          {`coarse`,`modified`,`generalized`} [default = `coarse`]  
          For further info on these graining procedures, see the EntropyHub guide.

Plotx - When Plotx == true, returns a plot of the entropy value at each time scale (i.e. the multiscale entropy curve) [default: false]

Tip

For further info on these graining procedures see the EntropyHub guide.

See also MSobject, cMvMSEn, MvFuzzEn, MvSampEn, MvPermEn, MvCoSiEn, MvDispEn

References:

[1] Ahmed Mosabber Uddin, Danilo P. Mandic
     "Multivariate multiscale entropy analysis."
     IEEE signal processing letters 19.2 (2011): 91-94.

[2] Madalena Costa, Ary Goldberger, and C-K. Peng,
     "Multiscale entropy analysis of complex physiologic time series."
     Physical review letters
     89.6 (2002): 068102.

[3] Vadim V. Nikulin, and Tom Brismar,
     "Comment on “Multiscale entropy analysis of complex physiologic
     time series”." 
     Physical Review Letters 
     92.8 (2004): 089803.

[4] Madalena Costa, Ary L. Goldberger, and C-K. Peng. 
     "Costa, Goldberger, and Peng reply." 
     Physical Review Letters
     92.8 (2004): 089804.

[5] Madalena Costa, Ary L. Goldberger and C-K. Peng,
     "Multiscale entropy analysis of biological signals." 
     Physical review E 
     71.2 (2005): 021906.

[6] Ranjit A. Thuraisingham and Georg A. Gottwald,
     "On multiscale entropy analysis for physiological data."
     Physica A: Statistical Mechanics and its Applications
     366 (2006): 323-332.

[7] Ahmed Mosabber Uddin, Danilo P. Mandic
     "Multivariate multiscale entropy: A tool for complexity
     analysis of multichannel data."
     Physical Review E 84.6 (2011): 061918.

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EntropyHub._cMvMSEn.cMvMSEn — Function

MSx, CI = cMvMSEn(Data, Mobj)

Returns a vector of composite multivariate multiscale entropy values (MSx) and the complexity index (CI) of the data sequences in Data using the parameters specified by the multiscale object (Mobj) over 3 temporal scales with coarse-graining (default).

Note

MSx, CI = cMvMSEn(Data, Mobj, Refined = True)

Returns a vector of refined-composite multiscale entropy values (MSx) for the data sequences in (Data) using the parameters specified by the multiscale object (Mobj) using the refined-composite multivariate multiscale entropy method (rcMSE) over 3 temporal scales. When Refined == true, the base entropy method must be MvSampEn or MvFuzzEn. If the entropy method is MvSampEn, cMvMSEn employs the method described in [1]. If the entropy method is MvFuzzEn, cMvMSEn employs the method described in [5].

MSx, CI = cMVMSEn(Data::AbstractArray{T,2} where T<:Real, Mobj::NamedTuple; Scales::Int=3, Refined::Bool="false", Plotx::Bool=false)

Arguments:

Scales - Number of temporal scales, an integer > 1 (default: 3)

Refined - Refined-composite MvMSEn method. When Refined == True and the entropy function specified by Mobj is MvSampEn or MvFuzzEn, cMvMSEn returns the refined-composite multivariate multiscale entropy (rcMSEn) [default: False]

Plotx - When Plotx == true, returns a plot of the entropy value at each time scale (i.e. the multiscale entropy curve) [default: false]

See also MvMSEn, MSobject, MvFuzzEn, MvSampEn, MvPermEn, MvCoSiEn, MvDispEn

References:

[1] Shuen-De Wu, et al.,
    "Time series analysis using composite multiscale entropy."
    Entropy
    15.3 (2013): 1069-1084.

[2] Shuen-De Wu, et al.,
    "Analysis of complex time series using refined composite
    multiscale entropy."
    Physics Letters A
    378.20 (2014): 1369-1374.

[3] Ahmed Mosabber Uddin, Danilo P. Mandic
    "Multivariate multiscale entropy: A tool for complexity
    analysis of multichannel data."
    Physical Review E 84.6 (2011): 061918.

[4] Ahmed Mosabber Uddin, Danilo P. Mandic
    "Multivariate multiscale entropy analysis."
    IEEE signal processing letters 19.2 (2011): 91-94.

[5] Azami, Alberto Fernández, Javier Escudero.
    "Refined multiscale fuzzy entropy based on standard deviation for
    biomedical signal analysis."
    Medical & biological engineering & computing 55 (2017): 2037-2052.

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