ott.geometry.costs.ElasticSqKOverlap

class ott.geometry.costs.ElasticSqKOverlap(k, *args, **kwargs)

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)	Output barycenter of vectors.
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.
twist_operator(vec, dual_vec, variable)	Twist inverse operator of the cost function.

Attributes

norm