ott.solvers.quadratic.gromov_wasserstein.GromovWasserstein

class ott.solvers.quadratic.gromov_wasserstein.GromovWasserstein(*args, warm_start=None, quad_initializer=None, kwargs_init=None, **kwargs)

Gromov-Wasserstein solver.

Parameters

• args (Any) – Positional arguments for WassersteinSolver.

• warm_start (Optional[bool]) – Whether to initialize (low-rank) Sinkhorn calls using values from the previous iteration. If None, warm starts are not used for standard Sinkhorn, but used for low-rank Sinkhorn.

• quad_initializer (Union[Literal[‘random’, ‘rank2’, ‘k-means’, ‘generalized-k-means’], BaseQuadraticInitializer, None]) –

  Quadratic initializer. If the solver is entropic, QuadraticInitializer is always used. Otherwise, the quadratic initializer wraps the low-rank Sinkhorn initializers:

  • ’random’ - RandomInitializer.

  • ’rank2’ - Rank2Initializer.

  • ’k-means’ - KMeansInitializer.

  • ’generalized-k-means’ - GeneralizedKMeansInitializer.

  If None, the low-rank initializer will be selected in a problem-specific manner:

  • if both geom_xx and geom_yy are PointCloud or LRCGeometry, KMeansInitializer is used.

  • otherwise, use RandomInitializer.

• kwargs_init (Optional[Mapping[str, Any]]) – Keyword arguments when creating the initializer.

• kwargs (Any) – Keyword arguments for WassersteinSolver.

Methods

create_initializer(prob)	Create quadratic, possibly low-rank initializer.
init_state(prob, init, key)	Initialize the state of the Gromov-Wasserstein iterations.
output_from_state(state)	Create an output from a loop state.

Attributes

is_low_rank	Whether the solver is low-rank.
warm_start	Whether to initialize (low-rank) Sinkhorn using previous solutions.