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

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) .

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.

Author

Yann Thanwerdas

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()

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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.

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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.