Kernel Representation: Persistence Sliced Wasserstein Kernel

Computes the sliced Wasserstein kernel matrix from a list of persistence diagrams. The sliced Wasserstein kernel is computed by exponentiating the corresponding sliced Wasserstein distance with a Gaussian kernel. See http://proceedings.mlr.press/v70/carriere17a.html for more details.

Author

Mathieu Carrière

Super classes

rgudhi::PythonClass -> rgudhi::SKLearnClass -> rgudhi::KernelRepresentationStep -> PersistenceSlicedWassersteinKernel

Methods

Public methods

• PersistenceSlicedWassersteinKernel$new()

• PersistenceSlicedWassersteinKernel$clone()

Inherited methods

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

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Method new()

The PersistenceSlicedWassersteinKernel constructor.

Usage

PersistenceSlicedWassersteinKernel$new(
  num_directions = 10,
  bandwidth = 1,
  n_jobs = 1
)

Arguments

num_directions

An integer value specifying the number of lines evenly sampled from \([-\pi/2,\pi/2]\) in order to approximate and speed up the kernel computation. Defaults to 10L.

bandwidth

A numeric value specifying the bandwidth of the Gaussian kernel with which persistence diagrams will be convolved. Defaults to 1.0.

n_jobs

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

Returns

An object of class PersistenceSlicedWassersteinKernel.

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Method clone()

The objects of this class are cloneable with this method.

Usage

PersistenceSlicedWassersteinKernel$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)
pswk <- PersistenceSlicedWassersteinKernel$new()
pswk$apply(dgm, dgm)
pswk$fit_transform(list(dgm))
}