Vector Representation: Silhouette

Computes persistence silhouettes from a list of persistence diagrams. A persistence silhouette is computed by taking a weighted average of the collection of 1D piecewise-linear functions given by the persistence landscapes, and then by evenly sampling this average on a given range. Finally, the corresponding vector of samples is returned. See https://arxiv.org/abs/1312.0308 for more details.

Author

Mathieu Carrière

Super classes

rgudhi::PythonClass -> rgudhi::SKLearnClass -> rgudhi::VectorRepresentationStep -> Silhouette

Methods

Public methods

• Silhouette$new()

• Silhouette$apply()

• Silhouette$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 Silhouette constructor.

Usage

Silhouette$new(
  weight = function(x) 1,
  resolution = 100,
  sample_range = rep(NA_real_, 2)
)

Arguments

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).

sample_range

A length-2 numeric vector specifying the domain for the entropy summary function, of the form \([x_{\min}, x_{\max}]\). Defaults to rep(NA, 2). It is the interval on which samples will be drawn evenly. If one of the values is NA, it can be computed from the persistence diagrams with the $fit() method.

Returns

An object of class Silhouette.

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Method apply()

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

Usage

Silhouette$apply(diag)

Arguments

diag

A 2-column tibble::tibble specifying a persistence diagram.

Returns

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

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Silhouette$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)
sil <- Silhouette$new()
sil$apply(dgm) # TO DO: fix gd because it does not set sample_range automatically
sil$fit_transform(list(dgm))
}