Example 6: Multiscale Increment Entropy

Import a signal of uniformly distributed pseudorandom integers in the range [1 8] and create a multiscale entropy object with the following parameters: EnType = IncrEn(), embedding dimension = 3, a quantifying resolution = 6, normalization = true.

X = ExampleData("randintegers");
Mobj = MSobject(IncrEn, m = 3, R = 6, Norm = true)

(Func = EntropyHub._IncrEn.IncrEn, m = 3, R = 6, Norm = true)

Calculate the multiscale increment entropy over 5 temporal scales using the modified graining procedure where:

$y_j^{(\tau)} =\frac{1}{\tau } \sum_{i=\left(j-1\right)\tau +1}^{j\tau } x{_i}, 1<= j <= \frac{N}{\tau }$

MSx, _ = MSEn(X, Mobj, Scales = 5, Methodx = "modified");

5-element Vector{Float64}:
 4.271928856964401
 4.305911441727119
 4.286637325462995
 4.2532727527665575
 4.277177920851601

Change the graining method to return generalized multiscale increment entropy.

$y_j^{(\tau)} =\frac{1}{\tau } \sum_{i=\left(j-1\right)\tau +1}^{j\tau } \left( x{_i} - \bar{x} \right)^{2}, 1<= j <= \frac{N}{\tau }$

MSx, _ = MSEn(X, Mobj, Scales = 5, Methodx = "generalized");

5-element Vector{Float64}:
 -0.0
  3.83143162219877
  4.24634531832518
  4.271178349238616
  4.192115013720915