Vector Representation: Atol

Computes measure vectorization (e.g. point clouds, persistence diagrams, etc.) after a quantisation step according to the Atol algorithm (Royer et al. 2021) .

References

Royer M, Chazal F, Levrard C, Umeda Y, Ike Y (2021). “ATOL: measure vectorization for automatic topologically-oriented learning.” In International Conference on Artificial Intelligence and Statistics, 1000--1008. PMLR.

Author

Mathieu Carrière

Super classes

rgudhi::PythonClass -> rgudhi::SKLearnClass -> rgudhi::VectorRepresentationStep -> Atol

Methods

Public methods

• Atol$new()

• Atol$apply()

• Atol$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 Atol constructor.

Usage

Atol$new(
  quantiser,
  weighting_method = c("cloud", "iidproba"),
  contrast = c("gaussian", "laplacian", "indicator")
)

Arguments

quantiser

An object of class BaseClustering specifying any clustering algorithm from the sklearn.cluster module. It will be fitted when the $fit() method is called.

weighting_method

A string specifying the constant generic function for weighting the measure points. Choices are either "cloud" or "iidproba". Defaults to "cloud", i.e. the measure is seen as a point cloud. This will have no impact if weights are provided along with measures all the way, i.e. at $fit() and $transform() calls, through the optional argument sample_weight.

contrast

A string specifying the constant function for evaluating proximity of a measure with respect to centers. Choices are either "gaussian" or "laplacian" or "indicator". Defaults to "gaussian" (see page 3 in Royer et al. (2021) ).

Returns

An object of class Atol.

---

Method apply()

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

Usage

Atol$apply(diag)

Arguments

diag

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

Returns

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

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Atol$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)
km <- KMeans$new(n_clusters = 2, random_state = 202006)
vr <- Atol$new(quantiser = km)
vr$apply(dgm)
vr$fit_transform(list(dgm))
}