Kernel Representation: Persistence Weighted Gaussian Kernel

Computes the persistence weighted Gaussian kernel matrix from a list of persistence diagrams. The persistence weighted Gaussian kernel is computed by convolving the persistence diagram points with weighted Gaussian kernels. See http://proceedings.mlr.press/v48/kusano16.html for more details.

Author

Mathieu Carrière

Super classes

rgudhi::PythonClass -> rgudhi::SKLearnClass -> rgudhi::KernelRepresentationStep -> PersistenceWeightedGaussianKernel

Methods

Public methods

• PersistenceWeightedGaussianKernel$new()

• PersistenceWeightedGaussianKernel$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()

---

Method new()

The PersistenceWeightedGaussianKernel constructor.

Usage

PersistenceWeightedGaussianKernel$new(
  bandwidth = 1,
  weight = ~1,
  kernel_approx = NULL,
  n_jobs = 1
)

Arguments

bandwidth

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

weight

A function or a formula coercible into a function via rlang::as_function() specifying the weight function for the persistence diagram points. Defaults to the constant function ~ 1. This function must be defined on 2D points, i.e. lists or arrays of the form \([p_x,p_y]\).

kernel_approx

A Python class specifying the kernel approximation class used to speed up computation. Defaults to NULL. Common kernel approximations classes can be found in the scikit-learn library (such as RBFSampler for instance).

n_jobs

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

Returns

An object of class PersistenceWeightedGaussianKernel.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

PersistenceWeightedGaussianKernel$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)
pwgk <- PersistenceWeightedGaussianKernel$new()
pwgk$apply(dgm, dgm)
pwgk$fit_transform(list(dgm))
}