Generalized Permutation Entropy

Optimzation for a parametrized relation R such that the generalized permutation entropy based on R becomes maximal.

The abstract class "R.m" is used as a pattern for parametrized relations. A parametrised relation is a function from the 2D-plane into [0,1], where R((x,y)) gives the probability of (x,y) belonging to a certain subset of the 2D-plane associated with R. To calculate the generalized permutation entropy, every point (x,y) with R((x,y))>0.5 will be considered to be part of that subset. A parametrized relations.depends on a vector of parameters that influence the value of the probalities R((x,y)).

The function "optimizeR" takes a set of data points, a parametrised relation R and pattern length n as input. This function optimizes the parameters of R such that the generlized permutation for patterns of a fixed length n will become maximal. The input set of data points is used to estimate the entropy in this process.

This collection of files contains two concrete implementations of the abstract class "R:m". The class "linearR.m" is a parametrizes a basic affine relation and "neuralNetR.m" a relation based on a neural network.

Run the script "optimizeR.m" as an example to see what happens.