ott.problems.quadratic.gw_barycenter.GWBarycenterProblem

class ott.problems.quadratic.gw_barycenter.GWBarycenterProblem(y=None, b=None, weights=None, costs=None, y_fused=None, fused_penalty=1.0, gw_loss='sqeucl', scale_cost=1.0, **kwargs)

(Fused) Gromov-Wasserstein barycenter problem [Peyré et al., 2016, Titouan et al., 2019].

Parameters:

• y (Optional[Array]) – Array of shape [num_total_points, ndim] merging the points of all measures. Alternatively, already segmented array of shape [num_measures, max_measure_size, ndim] can be passed. See also segment_point_cloud().

• b (Optional[Array]) – Array of shape [num_total_points,] containing the weights of all the points within the measures that define the barycenter problem. Same as y, pre-segmented array of weights of shape [num_measures, max_measure_size] can be passed. If y is already pre-segmented, this array must be passed.

• weights (Optional[Array]) – Array of shape [num_measures,] containing the weights of the barycenter problem.

• costs (Optional[Array]) – Alternative to y, an array of shape [num_measures, max_measure_size, max_measure_size] that defines padded cost matrices for each measure. Used in the quadratic term. Only one of y and cost can be specified.

• y_fused (Optional[Array]) – Array of shape [num_total_points, ndim_fused] containing the data of the points of all measures used to define the linear term in the fused case. Same as y, it can be specified as a pre-segmented array of shape [num_measures, max_measure_size, ndim_fused].

• gw_loss (Literal['sqeucl', 'kl']) – Gromov-Wasserstein loss.

• fused_penalty (float) – Multiplier of the linear term. Only used when y_fused != None.

• scale_cost (Union[float, Literal['mean', 'max_cost']]) – Scaling of cost matrices passed to geometries.

• kwargs (Any) – Keyword arguments for BarycenterProblem.

Methods

update_barycenter(transports, a)	Update the barycenter cost matrix.
update_features(transports, a)	Update the barycenter features in the fused case [Titouan et al., 2019].

Attributes

flattened_b	Array of shape [num_measures * (N_1 + N_2 + ...),].
flattened_y	Array of shape [num_measures * (N_1 + N_2 + ...), ndim].
gw_loss	Gromov-Wasserstein loss.
is_fused	Whether the problem is fused.
max_measure_size	Maximum number of points across all measures.
ndim	Number of dimensions of y.
ndim_fused	Number of dimensions of the fused term.
num_measures	Number of measures.
num_per_measure	[num_measures,] array containing number of points per measure.
segmented_y_b	Tuple of arrays containing segmented measures, weights, # of points.
segmented_y_fused	Feature array of shape used in the fused case.
weights	Barycenter weights of shape [num_measures,] that sum to 1.