Metrics: Wasserstein Distance

Computes the Wasserstein distance matrix from a list of persistence diagrams.

Author

Mathieu Carrière

Super classes

rgudhi::PythonClass -> rgudhi::SKLearnClass -> rgudhi::MetricStep -> WassersteinDistance

Methods

Public methods

• WassersteinDistance$new()

• WassersteinDistance$clone()

Inherited methods

• rgudhi::PythonClass$get_python_class()
• rgudhi::PythonClass$set_python_class()
• rgudhi::SKLearnClass$get_params()
• rgudhi::SKLearnClass$set_params()
• rgudhi::MetricStep$apply()
• rgudhi::MetricStep$fit()
• rgudhi::MetricStep$fit_transform()
• rgudhi::MetricStep$transform()

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Method new()

The WassersteinDistance constructor.

Usage

WassersteinDistance$new(
  order = 1,
  internal_p = Inf,
  mode = c("hera", "pot"),
  delta = 0.01,
  n_jobs = 1
)

Arguments

order

An integer value specifying the exponent of the Wasserstein distance. Defaults to 1.0.

internal_p

An integer value specifying the ground metric on the (upper-half) plane (i.e. the norm \(\ell_p\) in \(R^2\)). Defaults to Inf.

mode

A string specifying the method for computing the Wasserstein distance. Choices are either "pot" or "hera". Defaults to "hera".

delta

A numeric value specifying the relative error \(1+\delta\). Defaults to 0.01. Used only if mode == "hera".

n_jobs

An integer value specifying the number of jobs to use for the computation. Defaults to 1L.

Returns

An object of class WassersteinDistance.

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Method clone()

The objects of this class are cloneable with this method.

Usage

WassersteinDistance$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

if (FALSE) { # reticulate::py_module_available("gudhi")
X <- seq_circle(10)
ac <- AlphaComplex$new(points = X)
st <- ac$create_simplex_tree()
dgm <- st$compute_persistence()$persistence_intervals_in_dimension(0)
ds <- DiagramSelector$new(use = TRUE)
dgm <- ds$apply(dgm)
dis <- WassersteinDistance$new()
dis$apply(dgm, dgm)
dis$fit_transform(list(dgm))
}