ott.problems.linear.barycenter_problem.FreeBarycenterProblem#

class ott.problems.linear.barycenter_problem.FreeBarycenterProblem(y, b=None, weights=None, cost_fn=None, epsilon=None, **kwargs)[source]#

Free Wasserstein barycenter problem [Cuturi and Doucet, 2014].

Parameters:

y (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 always specified.
weights (Optional[Array]) – Array of shape [num_measures,] containing the weights of the measures.
cost_fn (Optional[CostFn]) – Cost function used. If None, use the SqEuclidean cost.
epsilon (Optional[float]) – Epsilon regularization used to solve reg-OT problems.
kwargs (Any) –
Keyword arguments segment_point_cloud(). Only used when y is not already segmented. When passing segment_ids, 2 arguments must be specified for jitting to work:
- num_segments - the total number of measures.
- max_measure_size - maximum of support sizes of these measures.

Methods

Attributes

`flattened_b`	Array of shape `[num_measures * (N_1 + N_2 + ...),]`.
`flattened_y`	Array of shape `[num_measures * (N_1 + N_2 + ...), ndim]`.
`max_measure_size`	Maximum number of points across all measures.
`ndim`	Number of dimensions of `y`.
`num_measures`	Number of measures.
`segmented_y_b`	Tuple of arrays containing the segmented measures and weights.
`weights`	Barycenter weights of shape `[num_measures,]` that sum to 1.

ott.problems.linear.barycenter_problem.FreeBarycenterProblem