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Discretization schemes

Across the package, there are many functions that accept the ϵ argument. This is an indication that the underlying algorithm in some way involves a discretization of a set of points or a delay embedding.

Controlling the partitioning

Currently, there are four different ways of partitioning an embedding. The discretization scheme is controlled by ϵ, and the following ϵ will work:

  • ϵ::Int divides each axis into ϵ intervals of the same size.
  • ϵ::Float divides each axis into intervals of size ϵ.
  • ϵ::Vector{Int} divides the i-th axis into ϵᵢ intervals of the same size.
  • ϵ::Vector{Float64} divides the i-th axis into intervals of size ϵᵢ.

Where are partitions used?

One example of a binning based method is the transferoperator_grid estimator for approximating the transfer (Perron-Frobenius) operator. The transferentropy_transferoperator_grid and transferentropy_visitfreq transfer entropy estimators also both derive probability distributions over partitioned delay embeddings.