Vector Representation: Persistence Image

Computes persistence images from a list of persistence diagrams. A persistence image is a 2D function computed from a persistence diagram by convolving the diagram points with a weighted Gaussian kernel. The plane is then discretized into an image with pixels, which is flattened and returned as a vector. See http://jmlr.org/papers/v18/16-337.html for more details.

Author

Mathieu Carrière

Super classes

rgudhi::PythonClass -> rgudhi::SKLearnClass -> rgudhi::VectorRepresentationStep -> PersistenceImage

Methods

Public methods

• PersistenceImage$new()

• PersistenceImage$apply()

• PersistenceImage$clone()

Inherited methods

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

---

Method new()

The PersistenceImage constructor.

Usage

PersistenceImage$new(
  bandwidth = 1,
  weight = function(x) 1,
  resolution = c(20, 20),
  im_range = rep(NA_real_, 4)
)

Arguments

bandwidth

A numeric value specifying the bandwidth of the Gaussian kernel. 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 \([p_x,p_y]\).

resolution

An length-1 integer vector specifying the size (in pixels) of the persistence image. Defaults to rep(20L, 2).

im_range

A length-4 numeric vector specifying the two-dimensional domain for the persistence image, of the form \([x_{\min}, y_{\min}, x_{\max}, y_{\max}]\). Defaults to rep(NA, 4). If one of the values is NA, it can be computed from the persistence diagrams with the $fit() method.

Returns

An object of class PersistenceImage.

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Method apply()

Applies the PersistenceImage class on a single persistence diagram and outputs the result.

Usage

PersistenceImage$apply(diag)

Arguments

diag

A 3-column tibble::tibble specifying a persistence diagram.

Returns

A tibble::tibble storing the persistence image representation of the persistence diagram in a table suitable for visualization.

---

Method clone()

The objects of this class are cloneable with this method.

Usage

PersistenceImage$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)
pei <- PersistenceImage$new()
pei$apply(dgm)
pei$fit_transform(list(dgm))
}