oineus.sliced_wasserstein_distance_diag_corrected

oineus.sliced_wasserstein_distance_diag_corrected(dgm_1, dgm_2, n_directions=100, ignore_inf_points=False, seed=None, directions=None)

Diagonal-corrected sliced Wasserstein distance.

Makes the sliced distance behave like true Wasserstein at the diagonal. The 1D rank-matching can pair an off-diagonal point p with the diagonal projection of a different point p’; true Wasserstein never does this (such skew edges can always be straightened to p <-> diag(p) without raising the cost). The correction re-charges those matches:

• A point matched to a diagonal slot is charged |proj(p) - proj(diag(p))|, its distance to its own diagonal projection – not to whichever point’s diagonal stand-in the sort aligned it with.

• A match between two diagonal stand-ins costs zero.

Arguments are as in sliced_wasserstein_distance().

Parameters:

• n_directions (int)

• ignore_inf_points (bool)