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)[source]#

(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[int, 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.
`segmented_y_b`	Tuple of arrays containing the segmented measures and weights.
`segmented_y_fused`	Feature array of shape `[num_measures, max_measure_size, ndim_fused]` used in the fused case.
`weights`	Barycenter weights of shape `[num_measures,]` that sum to 1.