ott.geometry.low_rank.LRKGeometry.from_pointcloud

classmethod LRKGeometry.from_pointcloud(x, y, *, kernel, rank=100, std=1.0, n=1, rng=None)

Low-rank kernel approximation [Scetbon and Cuturi, 2020].

Parameters:

• x (Array) – Array of shape [n, d].

• y (Array) – Array of shape [m, d].

• kernel (Literal['gaussian', 'arccos']) – Type of the kernel to approximate.

• rank (int) – Rank of the approximation.

• std (float) –

  Depending on the kernel approximation:

  • 'gaussian' - scale of the Gibbs kernel.

  • 'arccos' - standard deviation of the random projections.

• n (int) – Order of the arc-cosine kernel, see [Cho and Saul, 2009] for reference.

• rng (Optional[Array]) – Random key used for seeding.

Return type:

LRKGeometry

Returns:

Low-rank kernel geometry.