Invariant Measures Based on the U-Correlation Integral: An Application to the Study of Human Voice

Algorithm 1

Automated estimation of attractors’ invariants.

(1) Calculate and using Eq. (8) for .

(2) Calculate using Eq. (9) and the UCIs obtained in step (1).

(3) Compute with Eq. (11) and obtain the function . Estimate within a range

  of centered at the value where is minimum.

(4) Use , and to calculate (Eq. (12)) and obtain the

  function . Estimate within a range of centered at the value where

  is minimum.

(5) Obtain (Eq. (13)) using , and . Calculate the function

  . Estimate within a range of centered at the value where is

  minimum.