ott.geometry.costs.ElasticSqKOverlap

class ott.geometry.costs.ElasticSqKOverlap(k, gamma=1.0)

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

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

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.

• gamma (float) – Strength of the squared k-overlap norm regularization, \(> 0\).

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.
pairwise(x, y)	Compute cost as evaluation of h() on \(x-y\).
prox_reg(z)	Proximal operator of reg().
reg(z)	Regularization function.

Attributes

norm