SPDMetricBuresWasserstein {rgeomstats}

Class for the Bures-Wasserstein Metric on the Manifold of Symmetric Positive Definite Matrices

Description

An R6::R6Class object implementing the SPDMetricBuresWasserstein class. This is the class for the Bures-Wasserstein metric on the SPD manifold (Bhatia et al. 2019; Malagò et al. 2018).

Super classes

rgeomstats::PythonClass -> rgeomstats::Connection -> rgeomstats::RiemannianMetric -> SPDMetricBuresWasserstein

Public fields

n

An integer value specifying the shape of the matrices: n \times n.

Methods

Public methods

• SPDMetricBuresWasserstein$new()

• SPDMetricBuresWasserstein$clone()

Inherited methods

• rgeomstats::PythonClass$get_python_class()
• rgeomstats::PythonClass$set_python_class()
• rgeomstats::Connection$christoffels()
• rgeomstats::Connection$curvature()
• rgeomstats::Connection$curvature_derivative()
• rgeomstats::Connection$directional_curvature()
• rgeomstats::Connection$directional_curvature_derivative()
• rgeomstats::Connection$exp()
• rgeomstats::Connection$geodesic()
• rgeomstats::Connection$geodesic_equation()
• rgeomstats::Connection$injectivity_radius()
• rgeomstats::Connection$ladder_parallel_transport()
• rgeomstats::Connection$log()
• rgeomstats::Connection$parallel_transport()
• rgeomstats::RiemannianMetric$closest_neighbor_index()
• rgeomstats::RiemannianMetric$cometric_matrix()
• rgeomstats::RiemannianMetric$diameter()
• rgeomstats::RiemannianMetric$dist()
• rgeomstats::RiemannianMetric$dist_broadcast()
• rgeomstats::RiemannianMetric$dist_pairwise()
• rgeomstats::RiemannianMetric$hamiltonian()
• rgeomstats::RiemannianMetric$inner_coproduct()
• rgeomstats::RiemannianMetric$inner_product()
• rgeomstats::RiemannianMetric$inner_product_derivative_matrix()
• rgeomstats::RiemannianMetric$metric_matrix()
• rgeomstats::RiemannianMetric$norm()
• rgeomstats::RiemannianMetric$normal_basis()
• rgeomstats::RiemannianMetric$normalize()
• rgeomstats::RiemannianMetric$random_unit_tangent_vec()
• rgeomstats::RiemannianMetric$sectional_curvature()
• rgeomstats::RiemannianMetric$squared_dist()
• rgeomstats::RiemannianMetric$squared_norm()

Method new()

The SPDMetricBuresWasserstein class constructor.

Usage

SPDMetricBuresWasserstein$new(n, py_cls = NULL)

Arguments

n

An integer value specifying the shape of the matrices: n \times n.

py_cls

A Python object of class SPDMetricBuresWasserstein. Defaults to NULL in which case it is instantiated on the fly using the other input arguments.

Returns

An object of class SPDMetricBuresWasserstein.

Method clone()

The objects of this class are cloneable with this method.

Usage

SPDMetricBuresWasserstein$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Author(s)

Yann Thanwerdas

References

Bhatia R, Jain T, Lim Y (2019). “On the Bures–Wasserstein distance between positive definite matrices.” Expositiones Mathematicae, 37(2), 165–191.

Malagò L, Montrucchio L, Pistone G (2018). “Wasserstein Riemannian geometry of Gaussian densities.” Information Geometry, 1(2), 137–179.