# ott.geometry.costs.ElasticSqKOverlap#

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

Cost with squared k-overlap norm regularization .

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

where $$\|\cdot\|_{ovk}^2$$ is the squared k-overlap norm, see def. 2.1 of .

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. 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. 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(). Regularization function.

Attributes