ott.geometry.costs.ElasticSqKOverlap

ott.geometry.costs.ElasticSqKOverlap#

class ott.geometry.costs.ElasticSqKOverlap(k, *args, **kwargs)[source]#

Cost with squared k-overlap norm regularization [Argyriou et al., 2012].

\[\frac{1}{2} \|\cdot\|_2^2 + \frac{1}{2} \text{scaling_reg} \|\cdot\|_{ovk}^2\]

where \(\|\cdot\|_{ovk}^2\) is the squared k-overlap norm, see def. 2.1 of [Argyriou et al., 2012].

Parameters:
  • k (int) – Number of groups. Must be in [0, d) where \(d\) is the dimensionality of the data.

  • args – Positional arguments for RegTICost.

  • kwargs (Any) – Keyword arguments for RegTICost.

Methods

all_pairs(x, y)

Compute matrix of all pairwise costs, including the norms.

all_pairs_pairwise(x, y)

Compute matrix of all pairwise costs, excluding the norms.

barycenter(weights, xs)

Barycentric operator.

h(z)

TI function acting on difference of \(x-y\) to output cost.

h_legendre(z)

Legendre transform of h() when it is convex.

h_transform(f, **kwargs)

Compute the h-transform of a concave function.

pairwise(x, y)

Compute cost as evaluation of h() on \(x-y\).

prox_legendre_reg(z[, tau])

Proximal operator of the Legendre transform of reg().

prox_reg(z[, tau])

Proximal operator of reg().

reg(z)

Regularization function.

Attributes

norm